Maverick Philosopher

The Aporetics of Existential Meaning

For present purposes, an aporia is a set of propositions each member of which has a strong claim on our acceptance, but whose members are collectively inconsistent.  Like many a philosophical problem, the philosophical problem of the meaning of life is usefully approached from an aporetic angle.  So consider the following aporetic tetrad:

A. If life has a meaning, then it cannot be subjective.

B. The meaning of life must be subjectively appropriable by all.

C. There is no meaning that is both nonsubjective and subjectively appropriable by all.

D. Life has a meaning.

Good  though not absolutely compelling reasons have been given for both (A) and (B).  But they are in tension with one another, a tension recorded in (C), the third limb of our aporetic tetrad. One who inclines towards compatibilism with respect to existential meaning inclines toward  the rejection of  (C).  Unfortunately, (C) is not easily rejected, as I will try to show in this post.  The main difficulty concerns the subjective appropriability of an objective purpose by all even if it is granted that there is an objective purpose applicable to all. 

First of all, one cannot appropriate an objective purpose unless one knows or at least has good reasons for believing that there is one.  More importantly, one must know what the purpose is and what one must do to live in accordance with it.  Three different questions: Is there an objective purpose? What is it?  How do I live in accordance with it?  Countless millions of people, however, have lived who lacked the abilities or the opportunities to form reasonable beliefs about these matters, let alone to come to have knowledge about them. It is not enough that the objective purpose be knowable by some; it must be knowable by all.  This was argued earlier.  But for the countless millions just mentioned there was no real possibility of appropriating the objective purpose.  By ‘real possibility’ is meant something far stronger than a mere logical possibility or even a nomological possibility.  It is logically and nomologically possible for a human being to run a four-minute mile.  But it is not possible for me and plenty of others to run that fast.  So even if it is logically and nomologically possible for all human beings to know the objective purpose of life, it does not follow that all have any serious possibility of knowing it.  It is as impossible for the countless millions just mentioned to know the objective purpose of life, supposing there is one, as it is for people like me to run a four-minute mile.  It follows that the objective purpose of life, supposing there is one, is not subjectively appropriable by all, which is to say that it is not subjectively appropriable in the way it would have to be for life to be objectively meaningful.  Again, if life has a meaning, it has a purpose, and the purpose must be the same for all and appropriable by all.  Redemption from absurdity must be possible for all if it is be possible for any.  If the world is so arranged that you are barred from redemption through no fault of your own, then my redemption is not a redemption from absurdity.

Those with the abilities and opportunities to investigate the three questions just mentioned are not in a much better position.  For they are confronted with a welter of conflicting doctrines. The fortunate have the leisure to inquire and the intellect with which to inquire, but our intellects are weak and the problems stare us down with a face of seeming intractability.  If all we have to rely on are ourselves and the resources of this world, then the conclusion to draw is that human life has no meaning that is both nonsubjective and subjectively appropriable.

Some will reply that what we cannot supply has been supplied by divine revelation.  But this is no real solution.  Even if God has revealed the purpose of human existence to us, together with the means of achieving that purpose, and in a way that respects our freedom and dignity, this will not do us any good  if  we do not know the purpose and how to achieve it.  That, however, is precisely what we do not know as is clear from the conflicting accounts of the content of revelation, not to mention conflict over whether revelation is actual or even possible.  All of these are ‘up for grabs’: the existence of God, the possibility of divine revelation, the actuality of divine revelation, not to mention its content and interpretation. If I merely believe in the content of a particular (putative) revelation, the Christian revelation for example, as interpreted in a certain way by a certain ecclesiastical authority such as the Roman Catholic magisterium, that is not good enough for it leaves me with reasonable doubts.  But as long as I doubt the meaning of life and must continue to inquire, I have not yet subjectively appropriated the objective meaning of life.  The subjective certainty of faith is not enough.  What is needed  is the objective certainty of knowledge.  And it must be available to all – which is not the case for those who lived before the time of the historical revelation.

D. Life Has a Meaning  

A case has been made for each of the first three limbs.  Should we therefore conclude that life has no meaning?  That would be hasty.  It is arguable, though not compellingly arguable, that the living of a life presupposes the objective meaningfulness of life.  E. M Adams writes,

Just as belief in the intelligibility of the world is presupposed by our quest for understanding, the meaningfulness of life is presupposed in living a life.  We have to believe that life is not absurd, that it is not a tale told by an idiot, that it makes sense, in order to keep on with the struggles of life. (“The Meaning of Life,” International Journal of the Philosophy of Religion 51, 2002, pp. 71-81.)

I take Adams’ point to be that we cannot live without presupposing that our lives have meaning, objective meaning, a meaning whose source is external to us.  One who believes, not just in his study, but throughout the activities of his life, that his life and its activities have only the meaning that he gives them must suffer a loss of motivation.  If he does not, he is simply fooling himself about what he really believes and lives in a state of self-deception, or else he conveniently forgets his theoretical conviction when it comes time to act.  He maintains at the level of theory that his life has only the meaning he confers upon it, but he ‘contradicts’ this theoretical belief by the energy and passion with which he pursues his projects and perhaps also by the passion with which he tries to convince the rest of us that nothing matters except what we make matter.  For if he fully appreciated what his subjectivism amounts to he would see that his acts of meaning-bestowal are as meaningless as everything else in his life. You could say that such a person has not subjectively appropriated his subjectivism.  This is true whether the subjectivism is extreme or moderate.

Living our lives with zest and vigor and passion and commitment, we presuppose that they are objectively meaningful.  One who denies this I would suspect of self-deception or a lack of intelligence or spiritual superficiality.  One who responds, “I live a rich and full life despite my conviction that life has no objective meaning applicable to all” simply does not appreciate the existential implications of what he believes.  This is a bold assertion, many will disagree with it, some will be offended by it, and I cannot prove it; but it is reasonable to maintain it. It must also be conceded that, even if we cannot live full lives without the presupposition of objective meaningfulness, it does not follow that there is an objective meaning.  It is not easy to exclude the possibility that what we must presuppose does not hold in fact.  We must presuppose the intelligibility of the world if we are to embark seriously upon the arduous quest for understanding, but it is logically and epistemically possible that the world is unintelligible in itself.  Likewise, we must presuppose the objective meaningfulness of life if we are to live rich and full and committed lives, but it is logically and epistemically possible that our lives are objectively meaningless nonetheless. 

But if these possibilities are actual, then all the more are our lives meaningless, for then the way things are thwarts us: there is a ‘disconnect’ between what we need and must presuppose and what is true.  Given that we cannot know that this is the case, we are entitled to believe that it is not the case.  It may be that the ultimate nature of the world is such as to frustrate our purposes.  But we cannot know this and there is no point in believing it, while there is every point in believing that the presupposition of meaning is true.  Our very lives are the ‘proof’ of it. When it comes to life and its living it is reasonable to hold that the ‘proofs’ will be vital and pragmatic rather than theoretical.  We are participants first and spectators second.  We are parts of the world-whole and we are beings of meaning; it is reasonable to extrapolate that the world-whole of which we are parts is also a world of meaning and intelligibility.  If we are wrong and the truth thwarts us, then why should we value truth?  With this I conclude my case that life has meaning, whatever that meaning might be.  It has some objective meaning or other and part of what contributes to the zest and passion and subjective meaningfulness of a life is the quest for that objective meaning.

Impasse

The limbs of the aporetic tetrad are all of them defensible, yet they cannot all be true.  I leave it to the reader to find his way forward if he can.  If nothing else, I have elucidated  the philosophical problem of the meaning of human existence and have blocked some facile (non)solutions.

Actualist and Presentist Ersatzism and Arguments Against Both

For the actualist, the actual alone exists: the unactual, whether merely possible or impossible, does not exist.  The actualist is not pushing platitudes: he is not telling us that the actual alone is actual or that the merely possible is not actual.  'Merely possible' just means 'possible but not actual.' The actualist is saying something non-platitudinous, something that may be reasonably controverted, namely, that only the actual exists: the merely possible and the impossible do not exist.

Analogously for the presentist.  For the presentist, the (temporally) present alone exists: the nonpresent, whether past or future, does not exist.  The presentist is not pushing the platitude that the past is no longer.  He is saying something stronger: the past is not at all.

For the actualist, then, the merely possible does not exist.  There just is no such item as the merely possible fat man in my doorway.  Nevertheless, it is true, actually true, that there might have been a fat man in my doorway.  (My neighbor Ted from across the street is a corpulent fellow; surely he might have come over to pay me a visit. 'Might' as lately tokened is not to be read epistemically.)    The just-mentioned  truth cannot 'hang in the air'; it must be  grounded in some reality.  To put it another way, the merely possible -- whether a merely possible individual or a merely possible state of affairs -- has a 'reality' that we need somehow to accommodate.  The merely possible is not nothing.  That is a datum, a Moorean fact.

Similarly, it is true now that I hiked yesterday, even if presentism is true and the past does not exist.  So there has to be some 'reality' to the past, and we need to find a way to accommodate it.  Yesterday's gone, as Chad and Jeremy told us back in '64.  Gone but not forgotten: veridically remembered (in part) hence not a mere nothing.  That too is a datum.

The data I have just reviewed are expressed in the following two parallel aporetic tetrads, the first modal, the second temporal.

Modal Tetrad

1. The merely possible is not actual.
2. The merely possible is not nothing.
3. To exist = to be actual.
4. To exist = not to be nothing.

Temporal Tetrad

1t. The merely past is not present.
2t. The merely past is not nothing.
3t. To exist = to be present.
4. To exist = not to be nothing. 

Each tetrad has limbs that are jointly inconsistent but individually plausible. Philosophical problems arise when plausibilities come into logical conflict.  The tetrads motivate ersatzism since the first can be solved by adopting actualist ersatzism (also known simply as actualism) and the second by adopting presentist ersatzism.  (Note that one could be a presentist without being an ersatzer.)

The ersatzer solution is to deny the first limb of each tetrad by introducing substitute items that 'go proxy' for the items which, on actualism and presentism, do not exist.  These substitute items must of course exist while satisfying the strictures of actualism and presentism, respectively.  The substitute items must actually exist and presently exist, respectively.  So how does it work?

The actualist maintains, most plausibly,  that everything is actual.  But the merely possible must be accommodated: it is not nothing.  The merely possible can be accommodated by introducing actually existent abstract states of affairs and abstract properties.  Merely possible concrete states of affairs are actual abstract states of affairs that do not obtain.  Merely possible concrete individuals are abstract properties that are not instantiated.  Suppose there are n cats.  There might have been n +1.  The possibility of there being in concrete reality n + 1 cats is an abstract state of affairs that does not obtain, but might have obtained.   Suppose you believe that before Socrates came into existence there was the de re possibility that Socrates, that very individual, come into existence.  Then, if you are an actualist, you could accommodate the reality of this possibility by identifying the de re possibility of Socrates with an actually existent haecceity property, Socrateity.  The actual existence in concrete reality of Socrates would then be the being-instantiated of this haecceity property.

Possible worlds can be accommodated by identifying them with maximal abstract states of affairs or maximal abstract propositions.  Some identify worlds with maximally consistent abstract sets, but this proposal faces, I believe, Cantorian difficulties.  The main idea, however, is that possible worlds for the actualist ersatzer are maximal abstract objects.  Now one of the possible worlds is of course the actual world.  It follows immediately that the actual world must not be confused with the concrete universe.  It may sound strange, but for the actualist ersatzer, the actual world is an abstract object, a maximal proposition.

The actualist, then, rejects (1) and replaces it with

1*.  A merely possible concrete item is an actual abstract object that possibly obtains or possibly is instantiated or possibly is true.

The presentist ersatzer does something similar with (1t).  He replaces it with

1t*.  A merely past concrete item is a temporally present abstract object that did obtain or was instantiated or was true or had a member.

An Argument Against Actualist Ersatzism 

Let's examine the view that possible worlds are maximal abstract propositions.  If so, the actual world is the true maximal proposition, and actuality is truth.  Given that there is a plurality of worlds, whichever world is actual is contingently actual.  So our world, call it 'Charley,' being the one and only (absolutely) actual world, is contingently actual, i.e., contingently true.  Contingent affirmative truths, however, need truth-makers.  So Charley needs a truth-maker.  The truth-maker of Charley  is the concrete universe as we know it and love it.  Since actuality is truth, the concrete universe is not and cannot be actual.

So the concrete universe exists but is not actual!  But this contradicts (3) above, according to which existence is actuality.  The actualist ersatzer is committed to all of the following, but they cannot  all be true:

5. Actuality is truth.
6. Truth is a property of propositions, not of concreta or merelogical sums of concreta.
7. The concrete universe is a concretum or a sum of concreta.
8. Everything that exists is actual: there are no mere possibilia or impossibilia.
9. The concrete universe exists.

This is an inconsistent pentad because any four of the limbs, taken together, entails the negation of the remaining one.  For example, the conjunction of the first four limbs entails the negation of (9).

Curiously, in attempting to solve the modal tetrad, the actualist embraces an inconsistent pentad.   Not good!

An Argument Against Presentist Ersatzism

A parallel inconsistent pentad is easily constructed.  The target here is the view that times are maximal propositions.

5t. Temporal presentness is truth.
6. Truth is a property of propositions, not of concreta or merelogical sums of concreta.
7. The concrete universe is a concretum or a sum of concreta.
8t. Everything that exists is present: there are no merely past or merely future items. 
9. The concrete universe exists.

One sort of presentist erstazer is committed to all five propositions, but they obviously cannot all be true. 

Related articles

Times as Maximal Propositions

Presentism and Actualism, Tenseless Existence and Amodal Existence

Presentism Between Scylla and Charybdis

Abstracta: Omnitemporal or Timeless? An Argument from McCann

Can a Thing Exist Without Existing Now?

Still Puzzling Over Presentism

Defining Presentism

Presentism and Actualism, Tenseless Existence and Amodal Existence

John of the MavPhil commentariat drew our attention to the analogy between presentism and actualism.  An exfoliation of the analogy may prove fruitful.  Rough formulations of the two doctrines are as follows:

P. Only the (temporally) present exists.

A. Only the actual exists.

Now one of the problems that has been worrying us is how to avoid triviality and tautology.  After all, (P) is a miserable tautology if 'exists' is present-tensed.  It is clear that no presentist thinks his thesis is a tautology. It is also clear that there is a difference, albeit one hard to articulate, between presentism and the the various types of anti-presentism.  There is a substantive metaphysical dispute here, and our task is to formulate the dispute in precise terms.  This will involve clarifying the exact force of 'exists' in (P).  If not present-tensed, then what?

A similar problem arises for the actualist.  One is very strongly tempted to say that to exist is to be actual.  If 'exists' in (A) means 'is actual,' however, then (A) is a tautology.  But if 'exists' in (A) does not mean 'is actual,' what does it mean? 

We seem to have agreed that Disjunctive Presentism is a nonstarter:

DP.  Only the present existed or exists now or will exist.

That is equivalent to saying that if x existed or exists or will exists, then x presently exists.  And that is plainly false. Now corresponding to the temporal modi past, present, and future, we have the modal modi necessary, actual, and merely possible.  This suggests Disjunctive Actualism:

DA.  Only the actual necessarily exists or actually exists or merely-possibly exists.

This too is false since the merely possible is not actual.  It is no more actual than the wholly future is present.

We must also bear in the mind that neither the presentist nor the actualist intends to say something either temporally or modally 'solipsistic.'  Thus the presentist is not making the crazy claim that all that every happened or will happen is happening right now.  He is not saying that all past-tensed and future-tensed propositions are either false or meaningless and that the only true propositions are present-tensed and true right now.  The presentist, in other words, is not a solipsist of the present moment. 

Similarly wth the actualist. He is not a solipsist of this world.  He is not saying that everything possible is actual and everything actual necessary.  The actualist is not a modal monist or a modal Spinozist who maintains that there is exactly one possible world, the actual world which, in virtue of being actual and the only one possible, is necessary.  The actualist is not a necessitarian.

There is no person like me, but I am not the only person.  There is no place like here, but here is not the only place.  There is no time like now, but now is not the only time.

In sum, for both presentism and actualism, tautologism, disjunctivism, and solipsism are out! What's left?

To formulate presentism it seems we need a notion of tenseless existence, and to formulate actualism we need a notion of amodal existence (my coinage).   

We can't say that only the present presently exists, and of course we cannot say that only the present pastly or futurally exists.  So the presentist has to say that only the present tenselessly exists.  I will say more about tenseless existence in a later post. 

What do I mean by amodal existence?  Consider the following 'possible worlds' definitions of modal terms:

Necessary being: one that exists in all possible worlds
Impossible being: one that exists in no possible world
Possible being: one that exists in some and perhaps all possible worlds
Contingent being: one that exists in some but not all possible worlds
Merely possible being: one that exists in some possible worlds but not in the actual world
Actual being: one that exists in the actual world
Unactual being: one that exists either in no possible world or not in the actual world.

In each of these definitions, the occurrence of 'exists' is modally neutral analogously as 'exists' is temporally neutral in the following sentences:

It was the case that Tom exists
It is now the case that Tom exists
It will be the case that Tom exists. 

My point, then, is that the proper formulation of actualism (as opposed to possibilism) requires an amodal notion of existence just as the proper formulation of presentism requires an atemporal (tenseless) notion of existence.

But are the atemporal and amodal notions of existence free of difficulty?  This is what we need to examine.  Can the requisite logical wedges be driven between existence and the temporal determinations and between existence and the modal determinations? If not then presentism and actualism cannot even be formulated and the respective problems threaten to be pseudoproblems.

Related articles

My Existence and My Possible Nonexistence

Defining Presentism

Can a Thing Exist Without Existing Now?

Presentism Between Scylla and Charybdis

Time and Tense: Remarks on the B-Theory

Scollay Square No Longer Exists

Caesar, the Rubicon, Tenseless Truth, Determinism, and Fatalism

Caesar Is No More: The Aporetics of Reference to the Past

Here is London Ed's most recent version of his argument in his own words except for one word I added in brackets:

1. There is no such thing as Caesar any more.

2. The predicate 'there is no such thing as -- any more' is satisfied by
Caesar.

3. If a relation obtains [between] x and y, then there is such a thing as y.

4. (From 2) the relation 'is satisfied by' obtains between the predicate '--
is not a thing any more' and Caesar.

5. (3, 4) There is such a thing as Caesar.

6. (1, 5) contradiction.

Premiss (1) is Moorean. There is no longer any such thing or person as Caesar. (Or if you dispute that for reason of immortality of Caesar, choose some mortal or perishable object). (2) is a theoretical. (3) is a logical truth, and the rest is also logic. You must choose between (1) and (2), i.e. choose between
a Moorean truth, and a dubious theoretical assumption.

(1) is indeed 'Moorean,' i.e., beyond the reach of reasonable controversy.  (2) is indeed theoretical inasmuch as it involves an optional albeit plausible parsing in the Fregean manner of the Moorean sentence.

Ed tells us that (3) is a logical truth.  I deny that it is.  A logical truth is a proposition true in virtue of its logical form alone.  'Every cat is a cat' is an example of a logical truth as are 'No cat is a non-cat' and 'Either Max is a cat or Max is not a cat.'  One can test for logical truth by negating the proposition to be tested.  If the result is a logical contradiction, then the proposition is a logical truth.  For example, if we negate 'Every cat is a cat' we get 'Some cat is not a cat.' The latter sentence is a logical contradiction, so the former sentence is a logical truth. The latter is a logical contradiction because its logical form -- Some F is not an F -- has only false substitution-instances.

Negating (3) yields 'A relation obtains between x and y, but there is no such thing as y.'  But this is not a logical contradiction in the strict and narrow sense defined above.  Suppose I am thinking about the Boston Common which, unbeknownst to me, ceases to exist while I am thinking about it.  I stand in the 'thinking about' relation to the Common during the whole period of my thinking despite the fact that at the end of the period there is no such thing as the Boston Common.  There are philosophers who hold that the intentional relation is a genuine relation and not merely relation-like as Brentano thought, and that in some cases it relates an existing thinker to a nonexisting object. 

Now there are good reasons to reject this view as false, but surely it is not false as a matter of formal logic.  If it is false, it is false as a matter of metaphysics.  A philosopher such as Reinhardt Grossmann who holds that the intentional relation is a genuine relation that sometimes relates an existent thinker to a nonexistent object is not contradicting himself. 

Since (3) is not a logical truth, one way to solve Ed's problem is by rejecting (3) and holding that there are genuine relations that relate the existent to the nonexistent.  One could hold that the relation of satisfaction is such a genuine relation: it relates the existing predicate to the nonexistent emperor: Caesar satisfies the predicate despite his nonexistence.

Note that I am not advocating this solution to the puzzle; I am dismissing Ed's dismissal of this putative solution.  I am rejecting Ed's claim that one is forced to choose between (1) and (2).  One can avoid the contradiction by denying (3), and one is not barred from doing so by logic alone.

Ed claims that (1) and (5) are logical contradictories.  But they are not.  Just look carefully at both propositions and you will see.  Ed thinks they are contradictories because he assumes that 'There is no such thing as y any more' is logically equivalent to 'There is no such thing as y.'  But to make that assumption is to to assume the substantive metaphysical thesis known in the trade as

Presentism:  Necessarily, only temporally present concrete objects exist.

Given Presentism, (1) and (5) are indeed contradictory.  This is why I said earlier  that Ed's argument cannot get off the ground without Presentism.  For suppose we reject Presentism in favor of the plausible view that both past and present concreta exist, i.e., are within the range of our unrestricted quantifiers.  Then Ed's puzzle dissolves.  For then there is such a thing as Caesar, it is just that he is past.  The relation of satisfaction connects a present item with a past item both of which exist. Or, since Ed is allergic to 'exist': both of which are such that there such things as them.

So a second way to solves Ed's puzzle is by rejecting the Presentism that he presupposes.

So I count at least three ways of solving Ed's puzzle: reject (2), reject (3), reject the tacit assumption of Presentism which is needed for (1) and (5) to be contradictory.

My inclination is to say that the puzzle is genuine, but insoluble. And this because the putative solutions sire puzzles as bad as the one we started with.  Of course, I haven't proven this.  But this is what my metaphilosophy tells me must be the case.

The Aporetics of Existence and Self-Identity

Andrew B. made some powerful objections to a recent existence post.  His remarks suggest the following argument:

Argument A

1. Existence is self-identity
2. My existence is contingent:  (∃x)(x = I) & Poss ~(∃x) (x = I)
Therefore
3. My self-identity is contingent:  I = I & Poss ~ (I = I)

Argument A may be supplemented by the following consideration.  Since I am contingent, there are possible worlds in which I do not exist.  Not being in those worlds, I cannot have properties in them, including the property of self-identity. So it is not the case that I am necessarily self-identical; I am self-identical only in those worlds in which I exist, which is to say: I am contingently self-identical.  I am self-identical in some but not all worlds.

The argument can be rationally resisted. 

Consider a possible world w in which I do not exist.  In w, the proposition expressed by an utterance by me of 'I am not self-identical' is true.  But if it is true in w, then the proposition exists in w.  Now if the proposition exists in w, then so do its constituents.  On a Russellian view of propositions, I am one of the proposition's  constituents.  So for the proposition  *I am not self-identical* to be true in w, I must exist in w.  But if I exist in w, then of course I am self-identical in w, and the proposition is false in w.  But the same goes for every world in which I do not exist.  It follows that I am self-identical in every world and I exist in every world.

Of course, one needn't take a Russellian line on propositions.  One could take a Fregean view according to which propositions about me do not have me as a constituent but an abstract representative of me, a sense or mode of presentation.  But the first-person singular pronoun 'I' has the peculiarity that it cannot be replaced salva significatione by any description; so even if there is an abstract representative of me in the Fregean proposition expressed by my utterance of  'I am not self-identical,' there still has to be a referent of the representative external to the proposition.  So I have to exist in w for the proposition *I am not self-identical* to be true in w.  But if I exist in w then I am self-identical in w.  This in turn implies that the proposition is not true.  

The cognoscenti will appreciate that what I have been doing in a rough and dirty way is reproducing some of the thoughts in Timothy Williamson's paper Necessary Existents.  I am doing so to show that Argument A is not convincing.  Making use of materials from Williamson's paper, we can 'throw Argument A into reverse':

Argument B

1. Existence is self-identity
~3. My self-identity is necessary: Nec (I = I)
Therefore
~2. My existence is necessary.

In point of validity, there is nothing to choose between A and B: both are valid.  And both, I submit, have counterintuitive conclusions.  It seems to me that the arguments cancel each other out.  So I propose that we think very skeptically about the common premise that existence is self-identity, and the Quinean thin theory that commits us to it. 

The Modal Aporetics of Existential Generalization

Consider this trio of propositions:

1. '~(∃x)(x = Venus)' is possibly true.

2. Existential Generalization warrants the inference of '(∃y)~(∃x)(x = y)' from  '~(∃x)(x = Venus).'

3. '(∃y)~(∃x)(x = y)' is logically self-contradictory, hence necessarily false.

Solve the triad, either by showing that the limbs are (collectively) logically consistent or by rejecting one or more of the limbs.

Existence and Plural Predication: Could 'Exist(s)' be a First-Level Non-Distributive Predicate?

'Horses exist' is an example of an affirmative general existential sentence. What is the status of the predicate '___ exist' in such a sentence? One might maintain that 'exist(s)' is a second-level predicate; one might maintain that it is a first-level distributive predicate; one might maintain that it is a first-level non-distributive (collective) predicate. 

1. Frege famously maintained that 'exist(s)' is a second-level predicate, a predicate of concepts only, and never a first-level predicate, a predicate of objects.  Russell followed him in this.  A consequence of this view is that 'Horses exist' is not about what it seems to be about, and does not say what it seems to say.  It seems to be about horses, and seems to say of them that they exist.  But on Frege's analysis the sentence is about the concept horse and says of it, not that it exists, but that it has one or more instances.

Paradoxically, the sentence ''Horses exist'  on  Frege's  analysis says about a non-horse something that cannot be true of a horse or of any concrete thing!

For an interesting comparison, consider 'Horses surround my house.'  Since no horse could surround my house, it is clear that the sentence is not about each of the horses that surround my house.  What then is it about?  One will be tempted to reach for some such singularist analysis as: 'A set of horses surrounds my house.'  But this won't do since no such abstract object as a set could surround anything.  So if the sentence is really about a set of horses then it cannot say what it appears to say.  It must be taken to say something different from what it appears to say.  So what does 'Horses surround my house' say about a set if it is about a set? 

One might be tempted to offer this translation: 'A set of horses is such that its members are surrounding my house.' But this moves us in a circle, presupposing as it does that we already understand the irreducibly plural predication 'Horses surround my house.'  After all, if the members of a set of horses surround my house that is no different from horses surrounding my house.

The circularity here is structurally similar to that of the Fregean analysis.  If 'Horses exist' is about a concept, and says of that concept that it has instances, then of course those instances are horses that exist.  So the attempt to remove existence from individuals and make of it a property of concepts ends up reinstating  existence as a 'property' of individuals.

Pursuing the analogy a bit further, the refusal to grant that there are irreducibly plural predications such as 'Horses surround my house' is like the refusal to grant that there are irreducibly first-level existence sentences.

2.  Pursuing the analogy still further, is it possible to construe the predicate in 'Horses exist' as a non-distributive first-level predicate like the predicate in 'Horses surround my house'?  First some definitions.

A predicate F is distributive just in case it is analytic that whenever some things are F, then each is F.  Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them.  'Blue' is an example.  If some things are blue, then each of them is blue.

If a predicate is not distributive, then it is non-distributive (collective).  If some Occupy-X nimrods have the building surrounded, it does not follow that each such nimrod has the building surrounded.  If some students moved a grand piano into my living room, it does not follow that each student did.  If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct.  Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries.  If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.

I will assume for the purposes of this post that 'Horses surround my house' and 'Horses have an interesting evolutionary history' are irreducibly plural predications.  (That they are plural is obvious; that they are irreducibly plural is not.  For arguments see Thomas McKay, Plural Predication.)   And of course they are first-level as well: they are about horses, not about concepts or properties or propositional functions.  Now is 'Horses exist' assimilable to 'Horses surround my house' or is it assimilable to 'Horses are four-legged'? The predicate in the later is a distributive first-level predicate, whereas the predicate in 'Horses surround my house' is a non-distributive first-level predicate.

I am assuming that the 'Fressellian' second-level analysis is out, but I won't repeat the arguments I have given ad nauseam elsewhere.

I do not understand how 'exist(s)' could be construed as a non-distributive  predicate.  For if it is non-distributive, then it is possible that some things exist without it being the case that each of them exists.  And that I do not understand.  If horses exist, then each horse exsts.

Peter van Inwagen seems (though it not clear to me) to be saying that 'exists(s)' is a non-distributive first-level predicate. He compares 'Horses exist' to 'Horses have an interesting evolutionary history.'   'Horses exist,' he tells us, is equivalent to 'The number of horses is not zero.'  ("Being, Existence, and Ontological Commitment," p. 483)  But he denies that 'exists(s)' is second-level.  To say that the number of horses is not zero is to predicate of horses that they number more than zero. (483)  It is not to predicate of the concept horse that the cardinality of its extension is more than zero.

Now we cannot say of a horse that it surrounds a house or has an interesting evolutionary history.  We can say that of horses, but not of a horse.  Can we say of a horse that it numbers more than zero?  We can of course say of horses that they number more than zero. But I don't see how we can sensibly say of an individual horse that it numbers more than zero.  Perhaps Frege was wrong to think that number words can only be predicates of concepts which are ones-over-many.  Perhaps all one needs is the many, the plurality.  But it seems one needs at least that to swerve as logical subject.  If this is right, and to exist is to number more than zero, then we cannot sensibly say of an individual that it exists.  We can say this of individuals but not of an individual.  But surely we can say of an individual horse that it exists.  So I conclude that 'exist(s)' cannot be a first-level non-distributive predicate.

3.  And so one is driven  to the conclusion that 'exist(s)' is a first-level distributive predicate.  'Horses exist' says of each individual horse that it exists.  But isn't this equally objectionable?   The vast majority of horses are such that I have no acquaintance with them at all.  So how can my use of 'Horses exist' be about each horse? 

It is at this juncture that Frege gets his revenge:

We must not think that I mean to assert something of an African chieftain from darkest Africa who is wholly unknown to me, when I say 'All men are mortal.'  I am not saying anything about either this man or that man, but I am subordinating the concept man to the concept of what is mortal.  In the sentence 'Plato is mortal' we have an instance of subsumption, in the sentence 'All men are mortal' one of subordination.  What is being spoken about here is a concept, not an individual thing. (Posthumous Writings, p. 213)

Plato falls under the concept man; he does not fall within it.  The concept mortal does not fall under the concept man -- no concept is a man -- but falls within it.  When I say that all men are mortal I am not talking about individual men, but about the concept man, and I am saying that this concept has as part of its content the subconcept mortal. 

Similarly, my utterance of 'Horses exist' cannot be about each horse; it is about the concept horse, and says that it has instances -- which is the view I began by rejecting and for god reason.

We seem to have painted ourselves into an aporetic corner.  No exit. Kein Ausgang. A-poria. 

Moksha: Soteriological Riddles

Over lunch Friday the topic of moksha (release or liberation from samsara; enlightenment) came up in the context of Advaita Vedanta.  Moksha is attained when the identity of Atman and Brahman is realized.  My interlocutor wanted to know how such realization is possible.  If I realize my identity with the Absolute, then I cease to exist as something separate from the Absolute.  In that case, however, there is nothing left to realize anything.  How could the state of enlightenment be anything for me if there is no 'me' left after enlightenment?  How is moksha different from deep dreamless sleep or from utter nonexistence?  A form of salvation that amounts to personal annihilation seems not to be a salvation worth wanting. 

Any soteriology worth its salt must answer three questions:  Salvation of what? To what?  From what?  Brahman does not need salvation.  It is this indigent samsaric entity that I take myself to be that needs salvation.  But if what is saved is destroyed in being saved, by being merged into Brahman, then it is at best paradoxical to call this salvation.

Ramanuja is supposed to have said to Shankara, "I don't want to be sugar; I want to taste sugar."

If I were taking Shankara's side of the argument, I might say something like the following to Ramanuja and my friend:

If I am right and you really are sugar/Brahman in your innermost essence, and you merely taste it, then you are removed from it and haven't yet attained the goal.  It is just one more object over against you as subject. Your inquiry into the self, into who or what you really are, has not yet come to an end. The goal is to realize or become aware of your true self.  To do that you must ruthlessly disengage from everything  that is not-self.  If Brahman is your true self, and you realize your identity with it, then you haven't lost your self, but found your self.  You cannot be said to dissolve into the ocean of Brahman if Brahman is the true you.  To think that you you lose your self when you merge with Brahman presupposes a false identification of the self with something finite.  The self you lose is merely an object that you have wrongly identified as your true self; the self you gain is your true self.

This response is not quite satisfactory.  Consider the following aporetic triad:

1. Brahman does not need salvation.
2. I am Brahman.
3. My need for salvation is a real (not merely a samsaric, illusory) need.

The first two limbs are parts of the doctrine (Advaita Vedanta) that is the context of our soteriological discussion.  So they are nonnegotiable unless we shift out of this context.  But (3) also seems true.  The three propositions cannot, however, all be true: the conjunction of the first two limbs entails the negation of the third.

So it looks as if the advaitin has to bite the bullet and reject (3).  He has to say something like:  the very need for release from this hell of an existence itself belongs to maya, the realm of illusion.  So both the need for moksha and the one who seeks it  are illusory.   But this seems to conflict with the starting point of this whole soteriological scheme, namely, that the suffering and unsatisfactoriness of this life are  real. 

Here is another puzzle.

Using the method of Neti, Neti (not this, not this),  we end up with the result that the subject who is seeking is no object, no thing, nothing. Pursuing the question: Who or what am I? I come to the insight that I cannot be identical to any object, whether my car, my house, my clothes, my curriculum vitae, my body, any part of my body, my memories, thoughts, feelings, etc.  Any and all objects -- inner, outer, concrete, abstract --  are to be disengaged from the subject for whom they are objects. The upshot seems to be that any self or subject so disengaged from every object is nothing at all.

On the other hand, I cannot be nothing at all since I am pursuing this investigation. Coming to realize that I am not this, that, or the other thing, I must be something, not nothing. So we bang into a logical contradiction: I am nothing and I am not nothing.

As long as we remain on the discursive/dualistic plane we will get tangled up like this. So one could take these insolubilia as pointing us beyond the discursive intellect.  This is what I suggested to my friend.  I want him to take up meditation so as to explore the non-dual source of duality.  But meditation is insanely hard, and the fruits are few and far between.  It can seem like an utter waste of time.  Pointless navel-gazing!  (But see my plea for omphaloscopy .)

Besides, one can take the insolubilia -- if insolubilia they are -- as referring us, not into the transdiscursive, but back into Plato's Cave, in particular, into that especially dark corner wherein the Wittgensteinian therapists ply their trade. 

Time, Truth, and Truth-Making: An Antilogism Revisited and Transmogrified

Earlier, I presented the following, which looks to be an antilogism.  An antilogism, by definition, is an inconsistent triad.  This post considers whether the triad really is logically inconsistent, and so really is an antilogism.

1. Temporally Unrestricted Excluded Middle: The principle that every declarative sentence is either true, or if not true, then false applies unrestrictedly to all declarative sentences, whatever their tense.
2. Presentism: Only what exists at present exists.
3. Temporally Unrestricted Truth-Maker Principle: Every contingent truth has a truth-maker.

Edward objects:  "First, I don't see why the three statements are logically inconsistent. Why can't the truthmaker for a future tense statement exist now, in the present?"

Objection sustained.  The triad as it stands is not logically inconsistent.

'Miss Creant will die by lethal injection in five minutes.'  Let this be our example.  It is a future-tensed contingent declarative.  By (1) it is either true or, if not true, then false.  By (3), our sample sentence has a truth-maker, an existing truth-maker obviously, if it is true.   By (2), the truth-maker exists only at present.  Edward is right: there is no inconsistency unless we add something like:

4.  If a sentence predicts a contingent event which lies wholly in the future, and the sentence is true, then the truth-maker of the sentence, if it has one,  cannot exist at any time prior to the time of the event.

(4) is extremely plausible.  Suppose it is true now that Miss Creant will die in five minutes.  The only item that could make this true is the event of her dying.  But this event does not now exist  and cannot exist at any time prior to her dying. 

So our antilogism, under Edwardian pummeling, transmogrifies into an aporetic tetrad which, he will agree, is logically inconsistent.

The solution, for Edward, is obvious: Deny the Temporally Unrestricted Truth-Maker Principle as stated in (3).  Of course, that is a solution.  But can Edward show that it must be preferred to the other three solutions?  After all, one could deny Presentism, and many distinguished philosophers do.  I would hazard the observation that the majority of the heavy-hitters in the 20th century Anglosphere were B-theorists, and thus deniers of Presentism.  Or one could deny Unrestricted LEM, or even (4).

Although I said that (4) is extremely plausible, one could conceivably deny it by maintaining that the truth-makers of future-tensed sentences are tendencies in the present.  For example, I say to wifey, "Watch it! The pot is going to boil over!"  Assuming that that's a true prediction, one might claim that it is the present tendencies of the agitated pasta-rich water that is the truth-maker. 

Please note also that I too could solve the tetrad by denying Unrestricted T-maker.  Not by rejecting T-makers tout court in the Edwardian manner, but by restricting T-makers to contingent past- and present-tensed declaratives.  I hope Edward appreciates that the above problem does not give aid and comfort to his wholesale rejection of T-makers.

One can always solve an aporetic polyad by denying one of its limbs.  Sure.  But then you face other daunting tasks.  One is to show in a compelling way that your preferred solution should be preferred by all competent practitioners.  You have to show that your solution is THE solution and not merely a solution relative to your background assumptions and cognitive values.  A school-immanent solution is no final and absolute solution.  Another task is to show that your solution can be embedded in a theory that does not itself give rise to insoluble problems.

Excluded Middle and Future-Tensed Sentences: An Aporetic Triad

Do you remember the prediction, made in 1999, that the DOW would reach 36,000 in a few years?  Since that didn't happen, I am inclined to say that Glassman and Hasset's prediction was wrong and was wrong at the time the prediction was made.  I take that to mean that the content of their prediction was false at the time the prediction was made.  Subsequent events merely made it evident that the content of the prediction was false; said events did not first bring it about that the content of the prediction have a truth-value.

And so I am not inclined to say that the content of their irrationally exuberant prediction was neither true nor false at the time of the prediction. It had a truth-value at the time of the prediction; it was simply not evident at that time what that truth-value was.  By 'the content of the prediction' I mean the proposition expressed by 'The DOW will reach 36,000 in a few years.' 

I am also inclined to say that the contents of some predictions are true at the time the predictions are made, and thus true in advance of the events predicted.  I am not inclined to say that these predictions were neither true nor false at the time they were made.  Suppose I predict some event E and E comes to pass.  You might say to me, "You were right to predict the occurrence of E."  You would not say to me, "Although the content of your prediction was neither true nor false at the time of your prediction, said content has now acquired the truth-value, true."

It is worth noting that the expression 'come true' is ambiguous.  It could mean 'come to be known to be true' or it could mean 'come to have the truth-value, true.'  I am inclined to read it the first way.  Accordingly, when a prediction 'comes true,' what that means is that the prediction which all along was true, and thus true in advance of the contingent event predicted, is now known to be true.

So far, then, I am inclined to say that the Law of Excluded Middle applies to future-tensed sentences. If we assume Bivalence (that there are exactly two truth-values), then the Law of Excluded Middle (LEM)can be formulated as follows. For any proposition p, either p is true or p is false. Now consider a future-tensed sentence that refers to some event that is neither impossible nor necessary. An example is the DOW sentence above or  'Tom will get tenure in 2014.'  Someone who assertively utters a sentence such as this makes a prediction.  What I am currently puzzling over is whether any predictions, at the time that they are made, have a truth-value, i.e., (assuming Bivalence), are either true or false.

Why should I be puzzling over this?  Well, despite the strong linguistic inclinations recorded above, there is something strange in regarding a contingent proposition about a future event as either true or false in advance of the event's occurrence or nonoccurrence.  How could a contingent proposition be true before the event occurs that alone could make it true? 

Our problem can be set forth as an antilogism or aporetic triad:

1. U-LEM:  LEM applies unrestrictedly to all declarative sentences, whatever their tense.
2. Presentism:  Only what exists at present exists.
3. Truth-Maker Principle: Every contingent truth has a truth-maker.

Each limb of the triad is plausible.  But they can't all be true.  The conjunction of any two entails the negation of the third.  Corresponding to our (inconsistent) antilogism there are three (valid) syllogisms each of which is an argument to the negation of one of the limbs from the other two limbs.

If there is no compelling reason to adopt one ofthese syllogisms over the other two, then I would say that the problem is a genuine aporia, an insoluble problem.

People don't like to admit that there are insolubilia.  That may merely reflect their dogmatism and overpowering need for doxastic security.  Man is a proud critter loathe to confess the infirmity of reason.

Butchvarov on Semi-Realism about Facts

This post takes up where Butchvarov Against Facts left off.  See the latter post for bibliographical data concerning the essay "Facts" which I presently have under my logical microscope.  And if you are a fan of Butch's work, all of my Butchvarov posts are collected in the aptly entitled Butchvarov category.

(The following is also highly relevant to the discussion currently in progress with the Londonistas, David Brightly and Edward the Ockhamist in the combox to this post.)

Butch's position is a nuanced one as one would expect.  He appreciates the strengths and weaknesses of both realism and anti-realism.  For the realist, there are facts.  For the anti-realist, there are no facts.  Let us briefly review why both positions are both attractive yet problematic.  We will then turn to semi-realism as to a via media between Scylla and Charybdis.

1. Take some such contingently true affirmative singular sentence as  'Al is fat.'  Surely with respect to such sentences there is more to truth than the sentences that are true.  There must be something external to the sentence that contributes to its being true, and this external something is not plausibly taken to be another sentence or the say-so of some person, or anything like that.  'Al is fat' is true because there is something in extralinguistic and extramental reality that 'makes' it true.  There is this short slacker dude, Al, and the guy weighs 250 lbs.  There is nothing linguistic or mental about that.  Here is the sound core of correspondence theories of truth.  Our sample sentence is not just true; it is true because of the way the world outside the mind and outside the sentence is configured.  The 'because' is not a causal 'because.'  The question is not the empirical-causal one as to why Al is fat.  He is fat because he eats too much.  The question concerns the ontological ground of the truth of the sentential representation, 'Al is fat.'   Since it is obvious that the sentence cannot just be true -- given that it is not true in virtue of its logical form or ex vi terminorum -- we must posit something external to the sentence that 'makes' it true.  I don't see how this can be avoided even though I admit that 'makes true' is not perfectly clear.

2. Now what is the nature of this external truth-maker?  It can't be Al by himself, and it can't be fatness by itself.  Nor can it be the pair of the two.  For it could be that Al exists and fatness exists, but the first does not instantiate the second.  What's needed, apparently, is the fact of Al's being fat.  So it seems we must add the category of fact to our ontology, to our categorial inventory.  Veritas sequitur esse is not enough.  It is not enough that 'Al' and 'Fat' have worldly referents; the sentence as a whole needs a worldly referent. Truth-makers cannot be 'things' or collections of same, but must be entities of a different categorial sort.  (Or at least this is so for the simple predications we are now considering.)

3. The argument I have just  sketched, the truth-maker argument for facts, is very powerful, but it gives rises to puzzles and protests.  There is the Strawsonian protest that facts are merely hypostatized sentences, shadows genuine sentences cast upon the world.  Butchvarov quotes Strawson's seminal 1950 discussion: "If you prise the sentences off the world, you prise the facts off it too. . . ." ("Facts," 73-74)  Strawson again: "The only plausible candidate for what (in the world) makes a sentence true is the fact it states; but the fact it states is not something in the world."

Why aren't facts in the world? Consider the putative fact of my table's being two inches from the wall.  Obviously, this fact is not itself two inches from the wall or in any spatial position.  The table and the wall are in space; the fact is not.  One can drive a nail into the table or into the wall, but not into the fact, etc.  Considerations such as these suggest to the anti-realist that facts are not in the world and that they are but sentences reified.  After all, to distinguish a fact from a non-fact (whether a particular or a universal) we must have recourse to a sentence: a fact is introduced as the worldly correlate of a true sentence.  If there is no access to facts except via sentences, as the correlates of true sentences, then this will suggest to those of an anti-realist bent that facts are hypostatizations of true declarative sentences.

One might also cite the unperceivability of facts as a reason to deny their existence.  I see the table, and I see the wall.  It may also be granted that I see that the desk is about two inches from the wall.  But does it follow that I see a relational fact?  Not obviously.  If I see a relational fact, then presumably I see the relation two inches from.  But I don't see this relation.  And so, Butchvarov argues (84-85), one does not see the relational fact either.  Their invisibility is a strike against them.  A careful examination of this argument would make a nice separate post.  And indeed it did.

Another of the puzzles about facts concerns how a fact is related to its constituents.  Obviously a fact is not identical to its constituents.  This is because the constituents can exist without the fact existing.  Nor can a fact be an entity in addition to its constituents, something over and above them, for the simple reason that it is composed of them.  We can put this by saying that no fact is wholly distinct from its constituents.  The fact is more than its constituents, but apart from them it is nothing.  A third possibility is that a fact is the togetherness of its constituents, where this togetherness is grounded in a a special unifying constituent.  Thus the fact of a's being F consists of a, F-ness, and a nexus of exemplification.  But this leads to Bradley's regress. 

A fact is not something over and above its constituents but their contingent unity.  This unity, however, cannot be explained by positing a special unifying constituent, on pain of Bradley's regress. which is, pace Richard Gaskin, vicious.  So if a fact has a unifier, that unifier must be external to the fact.  But what could that be?  It would have to be something like Kant's transcendental unity of apperception.  I push this notion in an onto-theological direction in my book, A Paradigm Theory of Existence: Onto-Theology Vindicated.  But by taking this line, I move away from the realism that the positing of facts was supposed to secure.  Facts are supposed to be ontological grounds, extramental and extralinguistic.  If mind or Mind is brought in in any form to secure the unity of a truth-making fact, then we end up with some form of idealism, whether transcendental or onto-theological, or what have you.

4.  So we are in an aporetic pickle.  We have good reason to be realists and we have good reason to be anti-realists.  (The arguments above on both sides were mere sketches; they are stronger than they might appear. ) Since we cannot be both realists and anti-realists, we might try to mediate the positions and achieve a synthesis.   My book was one attempt at a synthesis.  Butchvarov's semi-realism is another.  I am having a hard time, though, understanding what exactly Butchvarov's semi-realism is supposed to be.

If the realist says that there are facts, and that anti-realist says that there aren't, the semi-realist maintains that 'There are facts' is an "Improper proposition" (87) so that both asserting it and denying it are improper.

Butchvarov relies crucially on Wittgenstein's distinction between formal and material concepts and his related distinction between saying and showing.  Object is an example of a formal concept, while book is  an example of a material concept.  That there are books can be said.  That there are objects cannot be said.  Instead, it is shown by the use of names.   

'This is an object,' unlike 'This is white,' is a pseudo-proposition.  This is because it attempts to say what can only be shown.  'This is an object' does not say anything. "It shows the logical category to which the item belongs." (75) 

Fact, like object, is a formal concept.  It follows that 'There are facts' and 'A sentence expresses a fact' are pseudo-propositions.  They are pseudo because they attempt to say what can only be shown.   But why , exactly, does 'A sentence expresses a fact' not say or state anything?  Presumably because ". . . it presupposes what it purports to say because 'fact' is the philosophical term for what sentences express." (76)

The following  cannot be said: 'This page is white is a fact.'  It cannot be said because it is ill-formed. (88)  We can of course say, 'That this page is white is a fact.'  But 'that this page is white' is not a sentence, but a noun phrase.  We cannot use this noun phrase to refer to the fact because what we end up referring to is an object, not a fact.  Though a fact is not a sentence or a proposition, it is proposition-like:  it has astructure that mirrors the structure of a proposition. No object, however, is proposition-like.  To express the fact we must use the sentence.  Using the sentence, we show what cannot be said.

Butchvarov's discussion from p. 88 to the end of his article is extremely murky and unsatisfactory.  His semi-realism is not a clear alternative to realism and anti-realism.  Butch sees the problem with crystal clarity, but I cannot see what exactly his solution is.

He tells us that semi-realism with respect to facts  differs from anti-realism by acknowledging that there is more to the truth of true sentences than the sentences that are true.  (88) Excellent!  This is a non-negotiable 'datanic' point.  If it is true that Jack loves Jill, then there must be something in the world that makes this true, and it cannot be Jack, or Jill, or loves, or the set or sum of all three.  If these three items are what the sentence 'Jack loves Jill' are about, then the truth-maker has to be distinct from each and from the set or sum of all. (88)

But Butch also tells us that semi-realism about facts differs from realism by refusing to countenance a special category of entity, the category of fact, the members of which are the referents of declarative sentences. What bothers Butchvarov is that "facts cannot be referred to or described independently of the sentences expressing them" (88)  a consideration which renders antirealim about facts plausible and the correspondence theory of truth implausible. (88)

So what is Butch's third way?  How does he get between realism and anti-realism.  He seems to be saying that there are facts but that they cannot be said, only shown.  But of course this cannot be what he is saying if one cannot say that there are facts!

If there is something that cannot be said but only shown, and what is shown are the referents of sentences, then he is saying that there are the referents of sentences in which case he is saying that there is what he says can only be shown.

This is highly unsatisfactory and barely coherent if coherent at all.  I am tempted to say to Butch, "Look, either there are facts or there aren't. Which is it?  Bringing in Wittgenstein's saying v. showing distinction only muddies already troubled waters."

So I don't see that semi-realism about facts is a viable position.  I suggest we admit that we are stuck with a genuine aporia.

The Problem of the Existence of Consciousness

I tend to the view that all philosophical problems can be represented as aporetic polyads.  What's more, I maintain that philosophical problems ought to be so represented.  You haven't begun to philosophize until you have a well-defined puzzle, a putative inconsistency of plausibilities.  When you have an aporetic polyad on the table you have something to think your teeth into.  (An interesting and auspicious typo, that; I shall let it stand.)

Consider the problem of the existence of consciousness.  Nicholas Maxwell  formulates it as follows: "Why does sentience or consciousness exist at all?"  The trouble with this formulation is that it invites the retort:  Why not?  The question smacks of gratuitousness.  Why raise it? To remove the felt gratuitiousness a motive has to be supplied for posing the question. Now a most excellent motive is contradiction-avoidance.  If a set of plausibilities form an inconsistent set, then we have a problem.  For we cannot abide a contradiction.  Philosophers love a paradox, but they hate a contradiction.  So I suggest we put the problem of the existence of consciousness as follows:

1. Consciousness (sentience) exists.
2. Consciousness is contingent: given that it exists it might not have.
3. If x contingently exists, then x has an explanation of its existence in terms of a y distinct from x.
4. Consciousness has no explanation in terms of anything distinct from it.

A tetrad of plausibilities.  Each limb makes a strong claim on our acceptance.  Unfortunately, this foursome is logically inconsistent: the conjunction of any three limbs entails the negation of the remaining one. Thus the conjunction of (1) and (2) and (3) entails the negation of (4).  So the limbs cannot all be true.  But they are all very plausible.  Therein lies the problem.  Which one ought we reject to remove the contradiction?

Note the superiority of my aporetic formulation to Maxwell's formulation.  On my formulation we have a very clear problem that cries out for a solution.  But if I merely ask, 'Why does consciousness exist?' there is no clear problem.  You could retort, 'Why shouldn't it exist?' 'What's the problem?'  There is a problem because the existence of conbsciousness conflicts with other things we take for granted.

(1) is absolutely datanic and so undeniable.  If some crazy eliminativist were to deny (1) I would show him the door and give him the boot.  (Life is too short for discussions with lunatics.)

(4) is exceedingly plausible. To explain consciousness in terms of itself would be circular, hence no explanation.  So it has to be explained, if it can be explained, in terms of something distinct from it.  Since abstract objects cannot be invoked to explain concrete consciousness, consciousness, if it can be explained, must be explained in physical and physiological and chemical and biological terms. But this is also impossible as Maxwell makes clear using a version of the 'knowledge argument' made popular by T. Nagel and F. Jackson:

But physics, and that part of natural science in principle re-ducible to physics, cannot conceivably predict and explain fully the mental, or experiential, aspect of brain processes. Being blind from birth—or being deprived of ever having oneself experienced visual sensations—cannot in itself prevent one from understanding any part of physics. It cannot prevent one from understanding the physics of colour, light, physiology of colour perception and discrimination, just as well as any nor-mally sighted person. In order to understand physical concepts, such as mass, force, wavelength, energy, spin, charge, it is not necessary to have had the experience of any particular kind of sensation, such as the visual sensation of colour. All predictions of physics must also have this feature. In order to understand what it is for a poppy to be red, however, it is necessary to have experienced a special kind of sensation at some time in one’s life, namely the visual sensation of redness. A person blind from birth, who has never experienced any visual sensation, cannot know what redness is, where redness is the perceptual property, what we (normally sighted) see and experience, and not some physical correlate of this, light of such and wave-lengths, or the molecular structure of the surface of an object which causes it to absorb and reflect light of such and such wavelengths. It follows that no set of physical statements, however comprehensive, can predict that a poppy is red, or that a person has the visual experience of redness. Associated with neurological processes going on in our brains, there are mental or experiential features which lie irredeemably beyond the scope of physical description and explanation.

(2) is also exceedingly plausible: how could consciousness (sentience)  exist necessarily?  But (3), whichis a versionof the principle of sufficient reason, is also very plausible despite the glib asseverations of those who think quantum mechanics provides counterexamples to it. 

So what will it be?  Which of the four limbs will you reject? 

I am tempted to say that the problem is genuine but insoluble, that the problem is an aporia in the strongest sense of the term: a conceptual impasse, an intellectual knot that our paltry minds cannot untie.

But this invites the metaphilosophical response that all genuine problems are soluble.  Thus arises a metaphilosophical puzzle that can be set forth as an aporetic triad:

5. Only soluble problems are genuine.
6. The problem of the existence of consciousness is not soluble.
7.  The problem of the existence of consciousness is genuine.

This too is an inconsistent set.  But each limb is plausible.  Which will you reject? 

Sentences as Names of Facts: An Aporetic Triad

There are good reasons to introduce facts as truth-makers for contingently true atomic sentences.  (Some supporting reasoning here.)  But if there are facts, and they make-true contingent atomic sentences, then what is the semantic relation between these declarative sentences and their truth-makers?  It seems we should say that such sentences name facts.  But some remarks of Leo Mollica suggest that this will lead to trouble.  Consider this aporetic triad:

1. 'Al is fat' is the name of the fact of Al's being fat.
2. 'Al is fat' has a referent only if it is true.
3. Names are essentially names: a name names whether or not it has a referent.

Each limb of the triad is very plausible, but they can't all be true.  The conjunction of (1) and (3) entails the negation of (2).  Which limb should we abandon?  It cannot be (1) given the cogency of the Truth Maker Argument and the plausible assumption that the only semantic relation between a sentence and the corresponding fact is one of naming.

(2) also seems 'ungiveupable.'  There are false sentences, and there may be false (Fregean) propositions: but a fact is not a truth-bearer but a truth-maker.  It is very hard to swallow the notion that there are 'false' or nonobtaining facts.  If 'Al is fat' is false it is because Al and fatness do not form a fact.  The existence of a fact is the unity of its constituents.  Where there is the unity of the right sort of constituents you have a fact; where there is not, you don't.

As for (3), suppose that names are only accidentally names, than a name names only on condition that it have a referent.  We would then have to conclude that if the bearer of a name ceases to exist, that the name ceases to be a name.  And that seems wrong.  When Le Verrier put forth the hypothesis of an intra-Mercurial planent  that came to be called 'Vulcan,' he did not know whether there was indeed such a planet, but he thought he had good evidence of its existence. When it was later decided that there was no good evidence of the planet in question, 'Vulcan' did not cease to be a name.  If we now say, truly, that Vlucan does not exist we employ a name whose naming is not exhausted by its having a referent.

So it seems that names name essentially.  This is the linguistic analog of intentionality: one cannot just think; if one thinks, then necessarily one thinks of something, something that may or may not exist. If I am thinking of something, and it ceases to exist, my thinking does not cease to be object-directed.  Thinking is essentially object-directed.  Analogously, names are essentially names.

So far, then, today's triad looks to be another addition the list of insolubilia.  The limbs of the triad are more reasonably accepted than rejected, but they cannot all be true.  A pretty pickle.

By the way, I insist on the primacy of the intentional over the linguistic.

Are Facts Perceivable? An Aporetic Pentad

'The table is against the wall.'  This is a true contingent sentence.  How do I know that it is true except by seeing (or otherwise sense perceiving) that the table is against the wall?  And what is this seeing if not the seeing of a fact, where a fact is not a true proposition but the truth-maker of a true proposition?  This seeing of a fact  is not the seeing of a table (by itself), nor of a wall (by itself), nor of the pair of these two physical objects, nor of a relation (by itself).  It is the seeing of a table's standing in the relation of being against a wall.  It is the seeing of a truth-making fact.  (So it seems we must add facts to the categorial inventory.)  The relation, however, is not visible, as are the table and the wall.  So how can the fact be visible, as it apparently must be if I am to be able to see (literally, with my  eyes) that the table is against the wall? That is our problem. 

Let 'Rab' symbolize a contingent relational truth about observables such as 'The table is against the wall.'  We can then set up the problem as an aporetic pentad:

1. If one knows that Rab, then one knows this by seeing that Rab (or by otherwise sense-perceiving it).
2. To see that Rab is to see a fact.
3. To see a fact is to see all its constituents.
4. The relation R is a constituent of the fact that Rab
5. The relation R is not visible (or otherwise sense-perceivable).

The pentad is inconsistent: the conjunction of any four limbs entails the negation of the remaining one.  To solve the problem, then, we must reject one of the propositions.  But which one?

(1) is well-nigh undeniable: I sometimes know that the cat is on the mat, and I know that the cat is on the mat by seeing that she is. How else would I know that the cat is on the mat?  I could know it on the basis of the testimony of a reliable witness, but then how would the witness know it?  Sooner or later there must be an appeal to direct seeing.  (5) is also undeniable: I see the cat; I see the mat; but I don't see the relation picked out by 'x is on y.'  And it doesn't matter whether whether you assay relations as relation-instances or as universals.  Either way, no relation appears to the senses.

Butchvarov denies (2), thereby converting our pentad into an argument against facts, or rather an argument against facts about observable things.  (See his "Facts" in Javier Cumpa ed., Studies in the Ontology of Reinhardt Grossmann, Ontos Verlag 2010, pp. 71-93, esp. pp. 84-85.)  But if there are no facts about observable things, then it is reasonable to hold that there are no facts at all.

So one solution to our problem is the 'No Fact Theory.'  One problem I have with Butchvarov's denial of facts is that (1) seems to entail (2).  Now Butch grants (1).  (That is a loose way of saying that Butch says things in his "Facts' article that can be reasonably interpreted to mean that if (1) were presented to him, then would grant it.)  So why doesn't he grant (2)?  In other words, if I can see (with my eyes) that the cat is on the mat, is not that excellent evidence that I am seeing a fact and not just a cat and a mat?  If you grant me that I sometimes see that such-and-such, must you not also grant me that I sometimes see facts? 

And if there are no facts,then how do we explain the truth of contingently true sentences such as 'The cat is on the mat'? There is more to the truth of this sentence than the sentence that is true.  The sentence is not just true; it is true because of something external to it.  And what could that be?  It can't be the cat by itself, or the mat by itself, or the pair of the two.  For the pair would exist if the sentence were false.  'The cat is not on the mat' is about the cat and the mat and requires their existence just as much as 'The cat is on the mat.'  The truth-maker, then, must have a proposition-like structure, and the natural candidate is the fact of the cat''s being on the mat.  This is a powerful argument for the admission of facts into the categorial inventory.

Another theory arises by denying (3).  But this denial is not plausible.  If I see the cat and the mat, why can't I see the relation -- assuming that I am seeing a fact and that a fact is composed of its constituents, one of them being a relation?  As Butch asks, rhetorically, "If you supposed that the relational fact is visible, but the relation is not, is the relation hidden?  Or too small to see?"  (85)

A third theory comes of denying (4).  One might think to deny that R is a constituent of the fact of a's standing in R to b.  But surely this theory is a nonstarter. If there are relational facts, then relations must be constituents of some facts. 

Our problem seems to be insoluble.  Each limb makes a very strong claim on our acceptance.  But they cannot all be true.  

Indeterminate Yet Existent? The Aporetics of Prime Matter and Pure Consciousness

Scott Roberts e-mails in reference to my post Hylomorphic Ontological Analysis and the Puzzle of Prime Matter: 

I have also been perplexed at hylomorphism's dependence on something called [prime]  'matter', for the same reason as you give. But I think there is a way out, though perhaps not one a hylomorphist will like. You say "Something bare of determinateness is unthinkable and hence nonexistent." But I can think of three words that refer to something one might consider real yet bare of determinateness, namely mass (or energy), consciousness (considered apart from all intentional objects of consciousness), and God (of classical theism). In each case you have something that can be thought of as giving form actuality. But that leads to an inversion of hylomorphism, namely, that now it is form that is potential, and what was formally [formerly?] thought of as matter is now Pure Act.  For example, a mathematical object which is not being thought of is a potential form that consciousness gives actuality as a thought. [. . .]

The reader is right to point out that there is something dubious about my claim that "Something bare of determinateness is unthinkable and hence nonexistent." Of the three counterexamples he gives, the clearest and best is "consciousness considered apart from all intentional objects of consciousness."  Consciousness so considered is not nothing, and yet it is indeterminate since all determinations fall on the side of the objects.  Consciousness is no-thing, a Sartrean theme which is also developed by Butchvarov. 

The reader has made me see that there is a certain structural analogy between prime matter and consciousness conceived of as pure of-ness bare of all determinacy.  For one thing, both, considered in themselves, are indeterminate or formless, and necessarily so.  If consciousness were determinate, it would be an object of consciousness and not the consciousness without which there are no (intentional) objects.  And if prime matter were determinate, it would be formed matter and thus not prime matter.  Second, neither can exist apart from its other.  There is no consciousness without objects, and there is no prime matter that exists on its own in the manner of a substance.  So, while consciousness is other than every object, it cannot exist except as the consciousness of objects (objective genitive).  And while prime matter is other than every form, and in itself formless, it requires formation to be something definite and substantial.

A third point of analogy is that both consciousness and prime matter give rise to a structurally similar puzzle.   Consider a mind-independent hylomorph A whose matter (H) is prime matter and whose form (F) is composed of lowest forms.  Which is ontologically prior, A, or its ontological parts H and F?  If the parts are prior in the manner of pre-existing ontological building blocks -- think (by analogy) of the way the stones in a stone wall are prior to the wall -- then H could not be a 'principle' in the scholastic sense but would have to something capable of independent existence.  And that is unacceptable: surely prime matter cannot exist on its own.  If, on the other hand, A is prior to its parts, then the parts would exist only for us, or in our consideration, as aspects which we bring to A.  But that won't do either because A ex hypothesi exists extramentally and so cannot in its ontological constitution require any contribution from us.

The consciousness puzzle is similar. Is consciousness (conceived as pure diaphanous of-ness of objects in the manner of Sartre, Butchvarov, and perhaps Moore) something really existent in itself or is it rather an abstract concept that we excogitate?  In other words, when we think of consciousness transcendentally as the sheer revelation of objects, are we thinking of a really existent condition of their revelation, or is consciousness so conceived merely a concept that we bring to the data?  If consciousness really exists, then we substantialize it (reify it, hypostatize it) in a manner analogous to the way we substantialize prime matter when we think of its as something capable of independent existence.  And that is puzzling.  How can something exist that is not an object of actual or possible awareness?  If, on the other hand, consciousness is not something that exists on its own but is a concept that we excogitate, then how do we account for the real fact that things are apparent to us, that things are intentional objects for us?  Besides, if consciousness were a mere concept, then consciousness as a reality would be presupposed: concepts are logically subsequent to consciousness.

So the two puzzles are structurally similar. 

Let us see if we can abstract the common pattern.  You have a term X and a distinct term Y.  The terms are introduced to make sense of a phenomenon Z.  Z is the analysandum whose analysis into X and Y is supposed to generate understanding.   X cannot exist without Y, hence it cannot exist on its own.  The same goes for Y.  The terms cannot exist without each other on pain of (i) hypostatization of each, and (ii) consequent sundering of the unity of Z.  (The diremption of Z into X and Y gives rise to the ancient problem of the unity of a complex which no one has ever solved.)  That the terms cannot exist without each other suggests that the unitary phenomenon Z is split into X and Y only by our thoughts such that the factoring into X and Y is our contribution.  On the other hand, however, the terms or factors must be capable of some sort of existence independent of our conceptual activities if the explanation that invokes them is an explanation of a real mind-independent phenomenon.

Here is a sharper form of the common aporia.  Both prime matter and pure consciousness are real.  But they are also both unreal.  Nothing, however,  can be both real and unreal on pain of violating Non-Contradiction.  How remove the contradiction without giving rise to a problem that is just as bad?

I don't say that the aporiai are insoluble, but I suspect that any solution proffered with give rise to problems of its own . . . .

Hylomorphic Ontological Analysis and the Puzzle of Prime Matter

Recent posts have discussed  hylomorphic dualism in the philosophy of mind. It is a serious contender in the arena of competing positions -- unlike say, eliminative materialism, which is not. (If you think I'm just gassing off about EM, read the entries in the eponymous category.) But now I want to take a step back from the special topic of the mind-body problem to the more general theme of hylomorphic ontological analysis as such.  In this post I examine some ideas in John Haldane's "A Return to Form in the Philosophy of Mind" in Form and Matter: Themes in Contemporary Metaphysics, ed. David S. Oderberg, Blackwell, 1999, pp. 40-64. But first some background.

In the 20th century Anglosphere, most philosophical analysis has been conceptual and linguistic. Moore and Russell were major practitioners. Decidedly less popular has been phenomenological analysis. Think Husserl. And least popular has been ontological analysis. The Iowa School (Gustav Bergmann and Co.) and Thomism are  the two major representatives of it. Ontological analysis takes as its object the (mind-independently) existent. It operates on the assumption that ordinary particulars have ontological constituents, and it tries to specify what these constituents are. These constituents are of course not spatial parts and they 'lie deeper' (whatever exactly this means) than the targets of chemical and physical analysis. They are items like these: universals, tropes, non-relational ties, Castaneda's ontological operators, Armstrong's thin particulars, Bergmann's bare particulars, and others besides.

2. Hylomorphic analysis is one type of ontological analysis. One analyzes meso-particulars such as a statue or a horse into form (morphe) and matter (hyle) among other constituents. These constituents are sometimes called principles, using the word in an old-fashioned way. Thus one speaks of the principium individuationis, the principle of individuation, or of the soul as life principle. The principle of individuation is not a statement or proposition but a real factor 'in' things that accounts for their numerical difference.

3. What motivates the hylomorphic approach? John Haldane has something interesting to say on this point:

. . . a condition of there being something for thought to take hold of is that the something has structure. Equivalently, a condition of there being thought is that there be relevant structuring principles (sortal and characterizing concepts plus logical constants.)

So we arrive at hylomorphic analysis. Every particular may be understood in terms of the instantiation of a formal principle. Its form makes it to be the kind of thing it is, providing its definitive structure, its characteristic powers and liabilities, and so on. However, since, ex hypothesi, things of the same specific sort have formally identical principles there arises the question of numerical difference. The analysis is completed by introducing the idea of matter as that which is structured and is the basis of numerical individuation within species. (49-50)

The motivation for hylomorphism is something like this. Thinking, in virtue of its intentionality, refers beyond itself to what it is not, namely, to 'objective' things and states of affairs. Whether thinking succeeds in referring beyond itself to things that exist independently of thought is of course a further question; but it is clear that thinking and indeed all forms of intentionality purport so to refer. For example, my perceiving of a distant mountain purports to reveal a physical object that exists whether I or anyone perceives it. This purport is part of the very sense of outer perception. Borrowing a line from the neglected German philosopher Wolfgang Cramer, outer perceiving is of objects as non-objects. The meaning, I hope, is clear: in outer perceiving the object is intended as more than a mere intentional object or accusative of awareness; it is intended as precisely something that exists as a non-object, as something that exists in itself, apart from the consciousness that posits it as existing in itself.

Now if one, setting aside skeptical worries, simply assumes that thought sometimes makes contact with reality, then one can ask: what must real things be like if thought is to be able to make contact with them? What must these things be like if it is to be possible for thought to "take hold of" them as Haldane puts it? The answer is that these mind-independent things must be conformable to our thought, and our thought to them. There must be some sort of isomorphism between thought and thing. Since we cannot grasp anything unstructured, reality must have structure. So there have to be principles of form and organization in things. But these formative principles must form something or determine something which, in itself, is at least relatively formless or indeterminate. There must be something which, in itself is (relatively) formless, is susceptible of being informed, or receptive of formation. In this way matter comes into the picture.

4. But now let's consider some puzzles. The proximate matter of a chair consists of its legs, seat, back. But this proximate matter itself has form. A leg, for example, has a shape and thus a form. (Form is not identical to shape, since there are forms that are not shapes; but shapes are forms.) Suppose the leg has the geometrical form of a cylinder. (Of course it will have other forms as well, the forms of smoothness and brownness, say.) The cylindrical form is the form of some matter. The matter of this cylindrical form is wood, say. But a piece of wood is a composite entity the parts of which have form and matter. For example, the complex carbohydrate cellulose is found in wood. It has a form and a proximate matter. But cellulose is made of beta-glucose molecules. Molecules are made of atoms, atoms of subatomic particles like electrons, and these of quarks, and so it goes.

The idea is that hylomorphic analysis is iterable. The iteration has a lower limit in prime or primordial or ultimate matter (materia prima.). Ultimate matter, precisley because it is ultimate, has no form of its own. As Haldane describes it, it is "stuff of no kind." (50)

Now one puzzle is this. Prime matter is not nothing. If it were nothing, then there would be no proximate matter either. Consider the lowest level of proximate matter. Consider a particle whose matter is prime matter. If prime matter is nothing at all, then this smallest particle could not exist, (since it is built up out of its components and one of them does not exist), and nothing having it as a component could exist. So prime matter is not nothing. But it is not something either. For if it were something it would have form or structure or organization. Obviously nothing can exist that is not definite and determinate. If you say the indeterminate, the apeiron, exists, WHAT are you saying exists? WHAT are you talking about? There has to be a whatness, a form, for it to be intelligible to say that something exists. 'X exists' says nothing. Recall the isomorphism between thought and reality that is part of the motivation for hylomorphic analysis. Something bare of determinateness is unthinkable and hence nonexistent.

We are driven to the conclusion that prime matter is not nothing and also not something. This certainly looks like a contradiction. But it is a contradiction apparently forced upon us if we embrace hylomorphic ontological analysis. For this analysis is iterable. One cannot stop shy of primate matter, for if there is no ultimate matter then there is no proximate matter either.

To avoid the contradiction one might say that prime matter, though not something actual is not nothing in that it is pure potency: the pure potentiality to receive forms is essentially the way Haldane puts it. (50) Does this help? Not much. What exactly is the difference between a pure potentiality to receive any form and nothing at all? Something that is not F or G or H, etc. but is receptive to these forms has no determinate nature. Without a determinate nature, how can it be anything at all?

5. Furthermore, a pure potency cannot be an ontological building block out of which to construct something actual. So should we say that prime matter is a mere abstraction? But then forms free of matter would also be mere abstractions. How can a substance be built up out of abstractions?

This second  problem concerns the status of the so-called 'principles' form and matter.  They don't have an independent existence, else they would be substances in their own right.  Is their status then merely mental?  That can't be right either since a hylomorph (a hylomorphic compound) cannot  be compounded of  components whose status is merely mental.  Why not?  Well, the typical hylomorph enjoys extramental existence, and it is difficult to see how such a thing could be built up out of constituents whose status was wholly intramental.

On Temptation and the Perfection of Jesus

Joshua Orsak e-mails: 

Your recent posts on temptation got me thinking (again) about a problem I've wrestled with a long time. I'm a Christian minister and I've long thought about a tension between Jesus Christ's focus on intentions and sin in the internal life of man and the Christian conviction summed up in Hebrews 4:15 that Jesus was tempted in all the ways that we are but did not sin. I accept Jesus' injunction against (for instance) lusting after a person in one's heart and being angry at a person as sinful mental states or attitudes. I know from many of your past posts that you, too, are sympathetic with such a view. I believe that attitudes and intentions can be sinful as well as actions, and no doubt I get that from my Christianity.

 

But it seems to me that to be tempted is at least in part to (for instance) 'lust after a woman in your heart'. To be angry at someone is to be tempted to act against them. To be attracted to a woman and think about (say) cheating on my wife is to be tempted to cheat. But isn't that lusting after her in my heart? This creates a problem with the view that Jesus was sinless and indeed has often made me question that particular doctrine. How could Jesus be tempted 'in all ways' that we are and yet not sin, since it seems that to be tempted is to adopt, if only for a moment, the attitudes he labels as sinful? I've never come up with a satisfactory answer to this question, so I was wondering what you might think of it.

I had actually never thought of this.  The problem seems genuine and worth discussing for anyone who takes Christian orthodoxy seriously.  To throw the problem into sharp relief, I will formulate it as an inconsistent pentad:

 

1. Being fully human, Jesus was subject to every manner of temptation and was actually tempted.
2. To be tempted to do X is to harbor the thought of doing X.
3. Thoughts are morally evaluable: there are such things as evil (sinful) thoughts.
4.  If a person habitually harbors evil (sinful) thoughts,  then the person is sinful.
5. Being fully divine, Jesus was wholly sinless.

 

This quintet of propositions is logically inconsistent as is obvious from the fact that if  the first four are true, then the fifth must be false.

 

To solve the problem we must reject one of the pentad's limbs.  (1) and (5) are clear commitments of orthodox Christian theology and so cannot be abandoned by anyone who wishes to remain orthodox.  (3) has a NT basis, and so it cannot be abandoned either.  But (2) and (4) are rejectable.

 

As for (2), I can be tempted to do something like cheating my inexperienced customers without harboring the thought of doing so: I might just have the thought but then suppress it or dismiss it.

 

As for (4), even if  a married person dwells on the sinful thought of a trip to Las Vegas (where, we are told, "what happens there, stays there") to hook up (in the contemporary sexual sense) with an old flame, that by itself does not make the person a sinful person.  To be a sinful person one must habitually sin in thought, word, or deed.  Going on a drunk or two does not make one a drunkard; lying a few times does not make one a liar, etc. 

 

Note that (2) and (4) are necessary to derive a contradiction.  The problem can thus be solved by rejecting one or both of these propositions.  Rejecting (2) suffices to solve the problem.

 

In sum, Jesus' being tempted and his being perfectly sinless are consistent because, while Jesus had tempting thoughts, he did not entertain them with hospitality but rejected them.  "Get behind me, Satan, etc."

 

See also: Can Mere Thoughts be Morally Wrong? and Thoughts as Objects of Moral Evaluation: Refining the Thesis.

The Aporetics of Singular Sentences

I should issue a partial retraction.  I wrote earlier,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL."  ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' )

The animadversions of Edward the Nominalist have made me see that my assertion is by no means obvious, and may in the end be just a dogma of analytic philosophy which has prevailed because endlessly repeated and rarely questioned.  Consider again this obviously valid argument:

1. Pittacus is a good man
2. Pittacus is a wise man
-----
3. Some wise man is a good man.

The traditional syllogistic renders the argument as follows: 

Every Pittacus is a wise man
Some Pittacus is a good man
-----
Some wise man is a good man.

This has the form:

Every P is a W
Some P is a G
-----
Some W is a G.

This form is easily shown to be valid by the application of the syllogistic rules. 

In my earlier post I then repeated a stock objection which I got from Peter Geach:

But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.

The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory) of 'Every Pittacus is wise'; it is its contrary. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different.

My objection, in nuce, was that 'Pittacus is wise' and 'Pittacus is not wise' are contradictories, not contraries, while 'Every Pittacus is wise' and 'Every Pittacus is not wise' ('No Pittacus is wise') are contraries.  Therefore, TFL does not capture or render perspicuous the logical form of 'Pittacus is wise.'

To this, Edward plausibly objected:

As I have argued here before, ‘Pittacus is wise’ and ‘Pittacus is not wise’ are in fact contraries. For the first implies that someone (Pittacus) is wise. The second implies that someone (Pittacus again) is not wise. Both imply the existence of Pittacus (or at least – to silence impudent quibblers - that someone is Pittacus). Thus they are contraries. Both are false when no one is Pittacus.

I now concede that this is a very good point.  A little later Edward writes,

The thing is, you really have a problem otherwise. If 'Socrates is wise' and 'Socrates is not wise' are contradictories, and if 'Socrates is not wise' implies 'someone (Socrates) is not wise', as standard MPC holds, you are committed to the thesis that the sentence is not meaningful when Socrates ceases to exist (or if he never existed because Plato made him up). Which (on my definition) is Direct Reference.

So you have this horrible choice:  Direct reference or Traditional Logic.

But must we choose?  Consider 'Vulcan is uninhabited.'  Why can't I, without jettisoning any of the characteristic tenets of MPL, just say that this sentence, though it appears singular is really general because 'Vulcan' is not a logically proper name but a definite description in disguise?  Accordingly, what the sentence says is that a certain concept -- the concept planet between Mercury and the Sun -- has as a Fregean mark (Merkmal) the concept uninhabited.

Now consider the pair 'Socrates is dead' - 'Socrates is not dead.'  Are these contraries or contradictories?  If contraries, then they can both be false.  Arguably, they are both false since Socrates does not exist, given that presentism is true. Since both are false, both are meaningful.  But then 'Socrates ' has meaning despite its not referring to anything.  So 'Socrates' has something like a Fregean sense.  But what on earth could this be, given that 'Socrates' unlike 'Vulcan'  names an individual that existed, and so has a nonqualitative thisnsess incommunicable to any other individual?

If, on the other hand, the meaning of 'Socrates' is its referent, then, given that presentism is  true and Socrates does not exist, there is no referent in which case both sentences are meaningless.

So once again we are in deep aporetic trouble.  The proper name of a past individual cannot have a reference-determining sense.  This is because any such sense would have to be a Plantingian haecceity-property, and I have already shown that these cannot exist.  But if we say that 'Socrates' does not have a reference-determining sense but refers directly in such a way as to require Socrates to exist if 'Socrates' is to have meaning, then, given presentism,  'Socrates' and the sentence of which it is a part is meaningless. 

Bad to Die Young but Not Bad to Die? An Aporetic Dyad

Herewith, a rumination on death with Epicurus as presiding shade. The following two propositions are both logically inconsistent and yet very plausible:

1. Being dead is not an evil for anyone at any time. 

2. Being dead at a young age is an evil for some.

Obviously, the limbs of the dyad cannot both be true.  Each entails the negation of the other.  And yet each limb lays serious claim to our acceptance. 

(1) is rendered credible by Epicurean reasoning along the following lines. It is reasonably maintained that bodily death is annihilation of the self or person.  Now in the absence of a person, there is nothing to possess properties, experiential or not, such as  being conscious, being dead, being nonexistent, etc. We are assuming that a person's corpse cannot be the subject of the putative state of being dead.  When I am dead and thus nonexistent my corpse will continue to exist for a time.  (Assuming my end doesn't come in the form of 'vaporization.') But I am not my corpse.   My being dead is not my corpse's being dead, for it is not dead: only what was once alive can properly be said to be dead, and my corpse is never alive.  I am dead, if I am, not my corpse.  So my corpse cannot be the subject of the putative state of my being dead.  And anyway my being dead will obtain at future times when my corpse will not exist.  So for this reason too my corpse cannot be the subject of the putative state of my being dead.

There is, then, no subject of being dead if death is annihilation.  Since there is no subject, there is, strictly speaking, no state of my being dead.  A state is a state of something in the state, and in this case nothing is in the state.  It follows that the 'state' of my being dead cannot be an evil state.  There is no such state, so it can't be evil -- or good, or anything.  It furthermore follows that being dead cannot rationally be feared -- or looked forward to either. 'I'll be glad when I'm dead 'makes  as little  sense given the cogency of the Epicurean reasoning as 'I'll be sad when I'm dead' or Warren Zevon's 'I'll sleep when I'm dead.' 

Support for (2) has its source in a widely-accepted intuition.  Suppose a happy, healthy, well-situated 20 year old full of life and promise dies suddenly and painlessly in a freak accident.  Almost all will agree that in cases like this being dead (which we distinguish from both the process and the event of dying) is an evil, and therefore neither good nor axiologically neutral.  It is an evil for the person who is dead whether or not it is an evil for anyone else.  It is an evil because it deprives him of all the intrinsic goods he would have enjoyed had he not met an untimely end.

It is not quite the same for the 90 year old.  One cannot be deprived of the impossible (as a matter of conceptual necessity), and the older one gets the closer the approach to the nomologically impossible.  (I assume that there is some age -- 150?  -- at which it become nomologically impossible for what could reasonably count as a human being to continue to live.) So one cannot employ the same reasoning in the two cases.  If we say that the being dead of the 20 year old is bad because it deprives him of future goods, we cannot give the same reason for the badness ( if it is badness) of the being dead of the 90 year old.  Someone who lives a life that is on balance happy and healthy and productive and then dies of natural causes at 90 or 100 is arguably not deprived of anything by his being dead. 

The problem, then, is that (1) and (2) cannot both be true, yet each is plausible.

The Ought-to-Be and the Ought-to-Do and the Aporetics of "Be Ye Perfect"

Is there any justification for talk of the ought-to-be in cases where they are not cases of the ought-to-do?

Let's begin by noting that if I ought to do X (pay my debts, feed my kids, keep my hands off my neighbor's wife, etc.) then my doing X ought to be. For example, given that I ought to pay my debts, then my paying a certain debt on a certain date is a state of affairs that ought to be, ought to exist, ought to obtain. So it is not as if the ought-to-do and the ought-to-be form disjoint classes. For every act X that an agent A ought to do, there is a state of affairs, A's doing X, that ought to be, and a state of affairs, A's failing to do X, that ought not be. The ought-to-do, therefore, is a  case of the   ought-to-be.

My question, however, is whether there are states of affairs that ought to be even in situations in which there are no moral agents with power sufficient to bring them about, and states of affairs that ought not be even in situations in which there are no moral agents with power sufficient to prevent them. In other words, are there non-agential oughts? Does it make sense, and is it true, to say things like 'There ought to be fewer diseases than there are' or 'There ought to be no natural disasters' or 'There ought to be morally perfect people'? Or consider

1. I ought to be a better man that I am, indeed, I ought to be morally perfect.

(1) expresses an axiological requirement but (arguably) not a moral obligation because it is simply not in my power to perfect myself, nor is it in any finite person's power or any group of finite person's   power to perfect me. Now consider the following aporetic triad: 

1. I ought to be morally perfect or at least better than I am in ways over which I have no control.

2. I lack the power to be what I ought to be, and this impotence is due to no specific fault of my own. (My impotence is 'original,' part  and parcel of the 'fallen' human condition, not derived from any   particular act or act-omission of mine.)

3. 'Ought' implies 'Can': one can be obliged to do X only if one has an effective choice as to whether to do X.

The triad is inconsistent in that (1) & (3) entails ~(2). Indeed, any two limbs, taken together, entail the negation of the remaining one.  How can the inconsistency be removed?

 A. One solution is simply to deny (1) by claiming that there is no sense of 'ought' in which one ought to be morally perfect or better than one is in ways over which one has no control.  This strikes me as counterintuitive. For there does seems to me to be some sense in which I ought to be perfect. I feel the force of the NT verse, "Be ye perfect as your heavenly father is perfect." I have the strong intuition that I ought to be, if not perfect, at least better in respects where I simply lack the power to bring about the improvement.

B. A second solution is to distinguish between agential and non-agential oughts. We can then maintain (1) as true by maintaining that the 'ought' in (1) is non-agential and expresses an axiological   requirement as opposed to a moral obligation. So interpreted, (1) is  consistent with (2) and (3).

We can then transform the above triad into an argument:

4. (1)-(3) are all true.
5. (1)-(3) would not all be true if there were no distinction between agential and non-agential oughts.
   Therefore
6. There is a distinction between agential and non-agential oughts.

C. A third solution is to maintain the truth of (1)-(3) while also maintaining that all oughts are agential. But then how avoid inconsistency? One might maintain that, when restricted to my own resources, I lack the power to do what I ought to do; yet I am morally  obliged to perfect myself; and since 'ought' implies 'can,' the power  that I need must be supplied in part from a Source external to myself.  "And this all men call God."  So God exists!

In short, the inconsistency is avoided by bringing God into the picture as one who supplies individuals with the supplemental power to do what they are morally obliged to do when that power is insufficient from their own resources. This gives rise to an argument for the existence of an external source of moral assistance:

7. I am morally obliged (ought)  to do things that I cannot do on my own.
8. 'Ought' implies 'can'.
Therefore

9. I can do things that I cannot do on my own.
   Therefore
10. There is an external source of moral assistance that makes up the difference between what I can do on my own and what I cannot.

Summary

I have sketched two arguments which need closer scrutiny. The one based on the (B) response to the triad gives some, though not a  conclusive, reason for accepting a distinction between agential and   non-agential oughts.

Self-Reference and Individual Concepts

The following can happen.  You see yourself but without self-recognition.  You see yourself, but not as  yourself.  Suppose you walk into a room which unbeknownst to you has a mirror covering the far wall.  You are slightly alarmed to see a wild-haired man with his fly open approaching you.  You are looking at yourself but you don't know it.  (The lighting is bad, you've had a few drinks . . . .) You think to yourself

1. That man has his fly open!
but not
2. I have my fly open!

Now these propositions -- assuming they are propositions -- are obviously different.  For one thing, they have different behavioral consequences.  I can believe the first without taking action with respect to my fly, or any fly.  (I'm certainly not going to go near the other guy's fly.)  But if I believe the second I will most assuredly button my fly, or pull up my zipper.

So it seems clear that (1) and (2) are different propositions.  I can believe one without believing the other.  But how can this be given the plain fact that 'that man' and 'I' refer to the same man?  Both propositions predicate the same property of the same subject.  So what makes them distinct propositions?

I know what your knee-jerk response will be.  You will say that, while 'I' and 'that man' have the same referent, they differ in sense just like 'Hesperus' and 'Phosphorus.'  Just as one can believe that Hesperus is F without believing that Phosphorus is F despite the identity of the two, one can believe that (1) without believing that (2) despite the fact that the subject terms are coreferential.

The trouble with this response is that it requires  special 'I'-senses, and indeed a different one for each user of the first-person singular pronoun.  These go together with special 'I'-propositions which are a species of indexical proposition.  When I believe that I am F, I refer to myself via a special Fregean sense which has the following property: it is necessarily a mode of presentation of me alone.  We can also think of this 'I'-sense as an individual concept or haecceity-concept.  It is a concept such that, if it is instantiated, it is instantiated (i) by me, (ii) by nothing distinct from me, (iii) and by the same person in every possible world in which it is instantiated.

But what on earth (or on Twin Earth) could this concept be, and how could I grasp it?  The concept has to 'pin me down' in every possible world in which I exist.  It has to capture my very thisness, or, in Latin, my haecceitas.  But a better Latin word is ipseitas, ipseity, selfhood, my being a self, this one and no other.    In plain old Anglo-Saxon it is the concept of me-ness, the concept of being me.

The theory, then, is that my awareness that

3. I am that man!

consists in my awareness that the concept expressed by 'I' and the concept expressed by 'that man' are instantiated by one and the same individual.  But this theory is no good because, even if my use of 'I' expresses an haecceity-concept, that is not a concept I can grasp or understand.  Maybe God can grasp my haecceity, but I surely can't.  Individuum ineffabile est said the Scholastics, echoing Aristotle. No finite mind can 'eff' the ineffable.  The individual in his individuality, in his very haecceity and ipseity, is ineffable.

Self-reference is not routed though sense, however things may stand with respect to other-reference.  When I refer to myself using the first-person singular pronoun, I do not refer to myself via a Fregean sense.

So here is the problem expressed as an aporetic pentad:

a. (1) and (2) express different Fregean propositions.
b. If two Fregean propositions are different, then they must differ in a constituent.
c. The difference can only reside in a difference in subject constituents.
d. The subject constituent of (2) is ineffable.
e. No sense (mode of presentation) or humanly-graspable concept can be ineffable.

This pentad is inconsistent:  (a)-(d), taken together, entail the negation of (e).  The only limb that has a chance of being false is (a).  One could say that (1) and (2), though clearly different, are not different by expressing different Fregean propositions.  But then what would our positive theory have to be?

 

Mental Acts Versus Mental Actions: Sellars and Bergmann

I have been assuming that there are mental acts and that there are mental actions and that they must not be confused.  It's high time for a bit of exfoliation.  Suppose I note that the front door of an elderly neighbor's house has been left ajar.  That noting is a mental act, but it is not an action.  I didn't do anything to bring about that mental state; I didn't decide to put myself in the state in question; I just happened to see that the door has been left ajar.  There is nothing active or spontaneous about the noting; it is by contrast passive and receptive.  But now suppose I deliberate about whether I should walk onto the man's property and either shut the door or inform him that it is ajar. Suppose he is a cranky old S.O.B.  with an equally irascible old dog.   I might decide that it's better to mind my own business and "let sleeping dogs lie."   The deliberating is a mental action.  So, assuming that there are mental acts and assuming that there are mental actions, it seems as clear as anything that they are different.

Why then are mental acts called acts if they are not actions?  It is because they are occurrent rather than dispositional.  Not everything mental is occurrent.  For example, you believe that every number has a successor even when you are dead drunk or dreamlessly asleep. This is not an occurrent believing.   Indeed, you have beliefs that have never occurred to you.  Surely you believe that no coyote has ever communicated with a bobcat by cellphone, although I will lay money on the proposition that you have never thought of this before.  You believe the proposition expressed by the italicized clause in that you are disposed to assent to it if the question comes up.  So in that sense you do believe that no coyote, etc. 

Mental acts are so-called, therefore, because they are actual or occurrent as opposed to potential or dispositional.  My noting that the old man's door has been left ajar is an occurrent perceptual taking that is not in the control of my will. As Wilfrid Sellars points out,

It is nonsense to speak of taking something to be the case 'on purpose.'  Taking is an act in the Aristotelian sense of 'actuality' rather than in the specialized practical sense which refers to conduct.  A taking may be, on occasion, an element of a scrutinizing -- which latter is indeed an action in the practical sense.  To take another example, one may decide to do a certain action, but it is logical nonsense to speak of deciding to will to do it; yet volitions, of course, are mental acts.  (Science and Metaphysics: Variations on Kantian Themes, Humanities Press, 1968, p. 74.)

Another example Sellars cites is drawing a conclusion from premises.  That is a mental action, but there are mental acts involved in this will-driven thinking process.  One is the 'seeing' that the conclusion follows from the premises.  It cannot be said that I decide to accept a conclusion that I 'see' follows from certain other propositions.  The will is not involved.  The 'seeing' is a mental act, but not a mental action.

Gustav Bergmann says essentially the same thing. "An act is not an activity and an activity is not an act." (Realism: A Critique of Brentano and Meinong, University of Wisconsin Press, 1967, p. 153.)  He says that this was crystal clear to Brentano and Meinong, but that in the Aristotelian-Thomistic tradition 'act' carries an implication of activity.  "In the Aristotlelian-Thomistic account . . . an act of perceiving is the 'abstracting' of a substantial form; and an 'abstracting' is an activity." (Ibid.) 

Very interesting.  It sounds right to me, though I wonder if all Thomists would agree. Not being a Thomist, I incline to the later view.  So as I use 'mental act' a mental act is not a mental action or activity.  This is of course consistent, as already indicated, with its being  the issue of certain mental actions.

A deeper and more important question is whether there are mental acts at all.  Their existence is not obvious -- or is it?  Wittgenstein appears to have denied the existence of mental acts.  Bergmann believes he did, while Geach believes he did not.  There is also the related but distinct question whether mental acts require a subject distinct from the act which remains numerically the same over time.  But is even a momentary subject needed?  Why couldn't awareness be totally subjectless, a "wind blowing towards objects" in the Sartrean image?  Butchvarov takes a line similar to Sartre's. 

Clearly, there has to be some distinction between conscious intentionality and its objects.  That's a rock-bottom datum upon which "our spade is turned" to borrow a phrase from old Ludwig.  But why must consciousness be articulated into discrete acts?  Why believe in acts at all?  What are the phenomenological and dialectical considerations that speak in their favor?

Future posts will tackle all these questions as we plunge deeper into the aporetics of mind and bang into one impasse after another.  It should prove to be a humbling experience.

The Aporetics of the Intentional Object, Part I

Here is a puzzle that may be thought to motivate a distinction between intentional and real objects, a distinction that turns out to be problematic indeed.

Puzzle.  One cannot think without thinking of something, but if one is thinking of something, it does not follow that  something is such that one is thinking of it.

Example.  Tom is thinking of the fountain of youth.  So he is thinking of something. But there is no fountain of youth.  So from the fact that Tom  is thinking of the fountain of youth, it does not follow that something is such that Tom is thinking of it.

The puzzle expressed as an aporetic dyad:

1. One cannot think without thinking of something.
2. If one is thinking of something, it does not follow that something is such that one is thinking of it.

Both limbs make a strong claim on our acceptance.  The first is utterly datanic.  The second, though exceedingly plausible, and indeed true as far as I can see, is not datanic.  It is reasonably denied by Meinong and the Meinongians.  For if some items have no being at all, and if the fountain of youth counts as a beingless item (as it does for Meinong & Co.), and if Tom is thinking of the fountain of youth, then it does follow that something is such that Tom is thinking of it.  This shows that our puzzle rests on a presupposition  which ought to be added to our dyad so as to sire the following aporetic triad or antilogism:

1. One cannot think without thinking of something.
2. If one is thinking of something, it does not follow that something is such that one is thinking of it.
3. There are no beingless items.

Though the limbs are individually plausible, they appear collectively inconsistent.  If they really are inconsistent, then we face a genuine aporia, an intellectual impasse: we have three propositions each of which we have excellent reason to think is true, but which cannot all be true on pain of logical contradiction.

There is at least the appearance of contradiction.  For if Tom is thinking of a mermaid, and there are no mermaids, then Tom is both thinking of something and not thinking of something.  Tom's thought has an object and it does not have an object.  It has an object because no one can think without thinking of something.  It does not have an object because there are no mermaids.  So we have at least an apparent contradiction.

To dispel the appearance of contradiction, one could make a distinction.  So let us distinguish the intentional object from the real object and see what happens.  Every intentional state is a directedness to an object, and the intentional object is simply that to which the intentional state is directed precisely as it is intended in the mental act with all and only the properties it is intended as having. So when Tom thinks of a mermaid, a mermaid is his intentional object.  For it is that to which his thought is directed. But there is no 'corresponding' real object because there are no mermaids in reality.  Accordingly, 'Tom's thought has an object and it does not have an object' is only apparently a contradiction since what it boils down to is 'Tom's thought has an intentional object but it does not have a real object' -- which is not a contradiction.

Unfortunately, this solution brings with it its own difficulties.  In this post I will mention just one.

The putative solution says that if I am thinking about Pegasus or Atlantis or the fountain of youth, my thinking has an intentional object, but that there is no corresponding real object.  But what if I am thinking of Peter, who exists?  In this case the theory will have to maintain that there is a real object corresponding to the intentional object.  It will have to maintain this because every intentional state has an intentional object.  The theory, then, says that when we intend the nonexistent, there is only an intentional object.  But when we intend the existent, there is both an intentional object and a corresponding real object.  There is a decisive objection to this theory.

Clearly, if I am thinking about Peter, I am thinking about him and not about some surrogate intentional object, immanent to the mental act,  which somehow mediates between the act and Peter himself.  The mental act terminates at Peter and not at an intentional object.  Intentionality, after all, is that feature of mental states whereby they refer beyond themselves to items that are neither parts of the mental act nor existentially dependent on the mental act.  Clearly, it is intrinsic to the intentionality of my thinking of Peter that my thinking intends something that exists whether or not I am thinking of it. 

This objection puts paid to the notion that intentionality relates a mind (or a state of a mind) to a merely intentional object which functions as an epistemic intermediary or epistemic surrogate. This scheme fails to accommodate the fact that intentionality by its very nature involves a transcending of the mind and its contents towards the transcendent.  Suppose I am thinking about a mountain.  Whether it exists or not, what I intend is (i) something whose nature is physical and not mental; and (ii) something that exists whether or not I am thinking about it.

The point I just made is that when I think of Peter, it is Peter himself that my thought reaches: my thought does not terminate at a merely intentional object, immanent to the act, which merely stands for or goes proxy for or represents Peter.  This  point is well-nigh datanic.  If you don't understand it, you don't understand intentionality.  One will be tempted to accommodate this point by saying that when one thinks of what exists, the IO = the RO.  But this can't be right either.  For the intentional object is always an incomplete object, a fact that reflects the finitude of the human mind.  But Peter in reality is a complete object.  Now identity is governed by the Indiscernibility of Identicals which states, roughly, that if x = y, then x and y share all properties.  But the IO and the RO do not share all properties:  The IO is indeterminate with respect to some properties while the RO is wholly determinate.  Therefore, the IO is never identical to the RO.

So the point I made cannot be accommodated by saying that the IO = the RO in the case when one thinks of the existent.

Where does this leave us?   I argued that our initial puzzle codified first as a dyad and then as a triad motivates a distinction between intentional and real objects.  The distinction was introduced in alleviation of inconsistency.  But then we noted a serious difficulty with the distinction.  But if the distinction cannot be upheld, how do we solve the aporetic triad?  It looks as if the distinction is one we need to make, but cannot make.

My Intentionality Aporia 'Ockhamized'

Edward of London proposes the following triad

O1. The proposition ‘Bill is looking for a nonexistent thing’ can be true even when there are no nonexistent things.
O2. The proposition ‘Bill is looking for a nonexistent thing’ expresses a relation between two things.
O3. Every relation is such that if it obtains, all of its relata exist.

as a nominalistic equivalent to my

W1. We sometimes think about the nonexistent.
W2. Intentionality is a relation between thinker and object of thought.
W3. Every relation R is such that, if R obtains,then all its relata exist.

Edward imposes the following contraint on aporetic polyads: "The essence of an aporetic polyad is that any proper subset of statements (including the singleton set) should be consistent on its own, and only the whole set being inconsistent."  I accept this constraint. It implies that nothing can count as an aporetic polyad if one of its limbs is self-contradictory. 

My definition runs as follows.  An aporetic polyad is a set S of n self-consistent propositions (n>1) such that (i) any n-1 members of S, taken in conjunction, entail the negation of the remaining member; (ii) each member of S has a strong claim on our acceptance.  Edward's constraint follows from this definition.  For if any member is self-inconsistent, then it cannot have a strong claim, or any claim, on our acceptance.

If I understand Edward, he is urging two points.  His first point is that my formulation of the triad is inept because (W1), unlike (O1), is self-contradictory.  If this charge sticks, then my formulation does not count as an aporetic polyad by my own definition.  His second point is that his version of the triad has a straightforward and obvious solution:  reject (O2). 

Reply to the First Point.  There is nothing self-contradictory about 'We sometimes think of the nonexistent.'  As I made clear earlier, this is a datanic, not a theoretical, claim.  On this score it contrasts with the other two limbs.  It is meant to record an obvious fact that everyone ought to grant instantly. Because the fact is obvious it is obviously self-consistent.  So if Edward denies (W1), then it is not profitable to to continue a discussion with him. 

All I can do at this point is speculate as to why Edward fails to get the point.  I suppose what he is doing is reading a theory into (W1), a theory he considers self-contradictory.    But (W1) simply records a pre-theoretical fact and is neutral with respect to such theories as Meinong's Theory of Objects.  Suppose I am imagining a winged horse.  If so, then it would be false to say that I am imagining nothing.  One cannot simply imagine, or just imagine.  It follows that I am imagining something. We are still at the level of data.  I have said nothing controversial.  One moves beyond data to theory if one interprets my imagining something that does not exist as my standing in a relation to a Meinongian nonexistent object.  That is a highly controversial but possible theory, and it is not self-contradictory contrary to what Edward implies.  But whether or not it is self-contradictory, the main point for now is that

1. BV is imagining a winged horse

Is neutral as between the following theory-laden interpretations

2. BV (or a mental act of his) stands in a dyadic relation to a Meinongian nonexistent object.

and

3. BV is imagining winged-horse-ly.

The crucial datum is that one cannot just imagine, or simply imagine.  We express this by saying that to imagine is to imagine something.  But 'imagine something' needn't be read relationally; it could be read adverbially.  Accordingly, to imagine Peter (who exists) is to imagine Peter-ly, and to imagine Polonious (who does not exist) is to imagine Polonious-ly.  I am not forced by the crucial datum to say that imagining involves a relation between subject and object; I can say that the 'object' reduces to an adverbial modification of my imagining. 

So even if the relational reading of (1) were self-contradictory -- which it isn't --  one is not bound to interpret (1) relationally.  Now (1) is just an example of (W1).  So the same goes for (W1).  (W1) is obviously true.  He who denies it is either perverse or confused.

Reply to the Second Point.  One can of course solve Edward's triad by denying (O2). But the real question is whether one can easily deny the distinct proposition  (W2).  I say no.  For one thing, the alternatives to saying that intentionality is a relation are not at all appetizing. All three of the limbs of my triad lay claim to our acceptance, and none can be easily rejected -- but they cannot all be true.  That is why there is a problem. 

The Twardowski-Meinong-Grossmann Solution to the Problem of Intentionality

Perhaps the central problem to which the phenomenon of intentionality gives rise can be set forth in terms of an aporetic triad:

1. We sometimes think about the nonexistent.
2. Intentionality is a relation between thinker and object of thought.
3. Every relation R is such that, if R obtains,then all its relata exist.

The datanic first limb is nonnegotiable, a 'Moorean fact.'  The other two limbs, being more theoretical, can be denied if one is willing to pay the price.  But something has to give since they cannot all be true. 

Brentano denied (2) with unpalatable consequences to be explored in a separate post. Why not accept (2), deny (3) and admit that there are abnormal relations, relations that connect existents with nonexistents?      

Consider the round square, that well-worn example that goes back at least to Bernard Bolzano.  Since there is no such thing, and cannot be, one will be tempted to say that the round square is an idea (presentation, Vorstellung) without an object.  That is what  Bolzano maintained using that very example of rundes Viereck.  (Theory of Science, pp. 88-89)  In section 5 of Zur Lehre vom Inhalt und Gegenstand der Vorstellungen (1894), Kasimir Twardowski criticizes Bolzano's position.

Twardowski distinguishes among the following:  there is the expression 'the round square.'  Then there is the mental act, the act of presentation (Vorstellungsact) that transpires in someone who uses the expression with understanding.  Corresponding to the act is a content (Inhalt)  which constitutes the meaning of the expression.  But there is  also a fourth item, that to which the expression refers, the round square itself, that which combines logically incompatible properties and whose existence one denies as soon as one advances from the presentation round square to a judgment about it. (Cf. the Brentanian theses that judgments are founded upon presentations, and that every judgment is existential, involving the acceptance or rejection of a presentation.)

This of course  sticks in the craw.  One hesitates to admit that there is something outside the mind to which 'round square' refers, something that has the property of nonexistence.  It smacks of a contradiction.  Clearly, 'There exists an x such that x does not exist' IS a contradiction, but this is not what a Meinongian will say.

Note that Twardowski has a couple of powerful reasons for not identifying the round square and its colleagues with mental contents.  The first is that contents exist while nonexistent objects don't.  So the round square cannot be identified with the content expressed by 'the round square.'  The second reason is that we ascribe to the round square attributes that not only cannot be ascribed to the corresponding content, but are logically incompatible to boot.  Thus no content is round and no content is square and of course no content is both round and square.  Since contents exist, they cannot have contradictory properties.

These arguments, spelled out a bit perhaps, show that mental contents cannot go proxy for nonexistent items, whether merely possible like the celebrated golden mountain or impossible like the round square.  One could extend the argument to cover abstract objects which are not mental contents or in any way mind-dependent.  They too are unsuited to go proxy for nonexistents.  For (1) abstracta exist while nonexistents do not, and (2)  the properties of nonexistent concreta cannot be attributed to abstracta.  Thus a flying horse is an animal, a golden mountain is a mountain, and a round square is round.  But no abstract object is an animal or a mountain or round.

When I think about the round square or the golden mountain (in whatever psychological mode)  the object of my thought is neither a mental content nor an abstract object.  What is it then?  Why, it is the round square or the golden mountain!  As bizarre as this sounds, it makes a certain amount of sense.  If I want to climb the golden mountain, I want to climb a physical prominence, not a mental content or an abstractum.

The position under examination, then, is not only that every mental act has a content, but that every mental act has an object as well.  But not all of these objects exist.  One obvious advantage of this approach is that it allows us to hold onto (2) of our opening triad in full generality: in every case, intentionality relates a thinker through a content to a transcendent object, and not to some surrogate object, either! 

Why is this a good thing?  Well, if intentionality is relational only in some cases, the veridical cases, then it cannot be essential to mental acts to be of an object:  whether or not an act actually has an object will depend on contingent facts in the world beyond the mind.  For Brentano, all mental acts are intentional by their very nature as mental.  The Twardowski-Meinong approach upholds this.

But the price is very steep: one must accept that there are items that actually instantiate properties (not merely possibly instantiate them), and that these items nevertheless do not exist, or indeed, as on Meinong's actual view, have any mode of being at all.  This is his famous doctrine of the Aussersein des reinen Gegenstandes, the 'extrabeing of the pure object.'  Thus the golden mountain is actually golden and actually a mountain despite having no being whatsoever.  It is a pure Sosein utterly devoid of Sein.

Some, like van Inwagen, think that Meinong's theory of objects is obviously self-contradictory.  I don't believe this is right, for reasons detailed here.  Even so, I find Meinong's theory incoherent.  'Some items have no being at all' is not a formal contradiction.  Still, I cannot get a mental grip on the notion of an item that actually has properties, but is wholly beingless.

In addition, one must accept that there are genuine relations that connect existents to nonexistents. 

The price is too steep to pay.  The Twardowski-Meinong-Grossmann solution is just as problematic as the original problem.

REFERENCE:  Reinhardt Grossmann, The Categorial Structure of the World, Indiana UP, 1983, p. 197 ff.

On Reference: An Aporetic Septad

We can divide the following seven propositions into two groups, a  datanic triad and a theoretical tetrad. The members of the datanic  triad are just given -- hence 'datanic' -- and so are not up for   grabs, whence it follows that to relieve ourselves of the ensuing contradiction we must reject one of the members of the theoretical tetrad. The funs starts when we ponder which one to reject. But first  you must appreciate that the septad is indeed inconsistent.

   D1. Sam believes that Cicero is a philosopher.
   D2. Cicero is Tully.
   D3. It is not the case that Sam believes that Tully is a philosopher.

   T1. 'Cicero' and 'Tully' have the same denotation (are coreferential)
   in all of their occurrences in the datanic sentences, both in the
   direct speech and indirect speech positions.
   T2. 'Is' in (D2) expresses strict, numerical identity where this has
   the usual properties of reflexivity, symmetry, transitivity, and the
   necessity of identity (if x = y, then necessarily, x = y).
   T3. Cicero has the property of being believed by Sam to be a
   philosopher.
   T4. If x = y, then whatever is true of x is true of y, and vice versa.
   (Indiscernibility of Identicals)

Now, do you see that this septad is pregnant with contradiction? By (T3), Cicero has a certain property, the property of being believed by Sam to be a philosopher. Therefore, given the truth of (T1) and (T4), Tully has that same property. But this implies the negation of (D3).

To remove the contradiction, we must reject one of the T-propositions. The D-propositions express the data of the problem. Obviously, they can't be rejected. Of course, nothing hinges on the particular   example. There are countless examples of the same form. Someone could  believe that 3 is one of the square roots of 9 without believing that one of the square roots of 9 is a prime number, even though 3 is a  prime number.

The Fregean solution is to reject (T1). In (D1), 'Cicero' refers to  its customary sense, not its customary referent, while in (D2), 'Cicero' refers to its customary referent. This implies that the antecedent of (T4) remains unsatisfied so that one cannot conclude  that Tully has the property of being believed by Sam to be a  philosopher.

A different solution, one proposed by Hector-Neri Castaneda, is achieved by rejecting (T2) while upholding the rest of the T-propositions. The rough idea is that 'Cicero' in all its occurrences refers to a 'thin' object, an ontological guise, a sort of ontological  part of ordinary infinitely-propertied particulars. This ontological  guise is not strictly identical to the ontological guise denoted by  'Tully,' but the two are "consubstantiated" in Castaneda's jargon.

This consubstantiation is a type of contingent sameness. Since Cicero and Tully are not strictly identical, but merely consubstantiated, the fact that Cicero has the property of being believed by Sam to be a  philosopher does not entail that Tully has this property. So the  contradiction does not arise. (Cf. The Phenomeno-Logic of the I, pp. 183-186)

Both solutions invoke what our friend 'Ockham' calls 'queer entities' using 'queer' in the good old-fashioned way.  The Fregean solution requires those abstract entities called senses and the Castanedan solution posits ontological guises.  Can 'Ockham' solve the problem while satisfying all his nominalistic scruples?

Can a man in a straight-jacket do the tango?

The Dead and the Nonexistent: Meinong Contra Epicurus

Are there nonexistent objects in the sense in which Meinong thought there are? One reason to think so  derives from the problem of reference to the dead. The problem can be displayed as an aporetic tetrad:

1. A dead person no longer exists.
2. What no longer exists does not exist at all. 
3. What does not exist at all cannot be referred to or enter as a constituent into a state of affairs.
4. Some dead persons can be referred to and can enter as constituents into states of affairs.  (For example, 'John Lennon' in 'John Lennon is dead' refers to John Lennon, who  is a constituent of the state of affairs, John Lennon's being dead.)

Despite the plausibility of each member, the above quartet is logically inconsistent.  The first three propositions entail the negation of the fourth.  Indeed, any three entail the negation of the remaining one.  Now (1) and (4) count as data due to their obviousness.  They are 'datanic' as opposed to 'theoretical' like the other two.  Therefore, to relieve the logical tension we must either reject (2) or reject (3).

To reject (2) is to reject Presentism according to which only temporally present items exist.  One could hold that both past and present items (tenselessly) exist, or that past, present, and future items (tenselessly) exist.  Such anti-presentist theories break the two-way link between existence and temporal presentness: what is temporally present exists, but what exists need not be temporally present.

But another option is to reject (3).   One could adopt the view of Alexius von Meinong according to which there are items that stand jenseits von Sein und Nichtsein, "beyond being and nonbeing."  These items have no being whatsoever.  Meinong's examples include the golden mountain (a possible object) and the round square (an impossible object).  His doctrine was misunderstood by Russell and generations of those influenced by him.  The doctrine is not that nonexistent objects have a mode of being weaker than existence, but that they have no being whatsoever. And yet they are not nothing! They are not nothing inasmuch as we can refer to them and predicate properties of them.  They are definite items of thought possessing Sosein but no Sein, but are not mere accusatives of thought.  A strange view, admittedly, and I do not accept it.  (See my A Paradigm Theory of Existence, Kluwer 2002, pp. 38-42.)  But distinguished philosophers have and do: Butchvarov, Castaneda, T. Parsons, Routley/Sylvan, et al.)

So Meinongianism is a theoretical option.  The Meinongian line gives us a way to answer Epicurus.  For Epicurus death is not an evil because when we are, death is not, and when death is, we are not.  The point is that at no time is there a subject possessing the property of  being dead.  When I am alive, I am not dead.  And when I am dead, I do not exist.  It is not just that when I am dead I no longer presently exist, but that I do not exist at all.  (Presentism seems part and parcel of the Epicurean position.)  And because I do not exist at all when I am dead, I cannot have properties.   (Anti-Meinongianism  is also part and parcel of the Epicurean position: existence is a necessary condition of property-possession.)  But then I cannot, when dead, have the property of being dead, in which case there is no state of affairs of my being dead. And that gives us a deep ontological reason for denying  that death is an evil:  if there is no state of affairs of my being dead, then there is nothing to possess the property of being evil.  (Note that it is not the property of being dead that is evil, or me the individual, but the putative state of affairs of my being dead.)

As I read Epicurus, his position on death, namely, that being dead  is not an evil for the one who is dead,  requires both Presentism and Anti-Meinongianism.   If that is right, then one can answer Epicurus either by rejecting Presentism or by accepting Meinongianism.

Anti-Presentism breaks the two-way link between existence and temporal presentness, while Meinongianism breaks the two-way link between existence and property-possession.  The anti-presentist faces the challenge of giving a coherent account of tenseless existence, while the Meinongian owes us an explanation of how there can be items which actually have properties while having no being whatsoever.  Epicureanism maintains both links  but flies in the face of the powerful intuition that death is an evil.

A good solution eludes us.  And so once  again we end up in good old Platonic fashion up against the wall of an aporia.

Life-Death Asymmetry: An Aporetic Triad

Let us consider a person whose life is going well, and who has a reasonable expectation that it will continue to go well in the near term at least.  For such a person

1. A longer being-alive is better than a shorter being-alive.

2. A longer being-dead is not worse than a shorter being-dead. (Equivalently: A shorter being-dead is not better than a longer being-dead.

3. If a longer being F is better than a shorter being F, then a shorter being non-F is better than  a longer being non-F.

I claim that each limb of the triad has a strong claim on our acceptance.  And yet they cannot all be true: (1) and (3) taken together entail the negation of (2).  Indeed, the conjunction of any two limbs entails the negation of the remaining one.  To solve the problem, then, one of the limbs must be rejected.  But which one?  Each is exceedingly plausible.

Consider (1).  Surely a longer life is better than a shorter one assuming that (i) one's life is on balance good, and (ii) one has a  reasonable expectation that the future will be like the past at least for the near future.  Suppose you are young, healthy, and happy.  It is obvious that five more years of youth, health, and happiness is better than dying tomorrow.  (In these discussions, unless otherwise stated, the assumption is the Epicurean one that that bodily death is annihilation of the self or person -- an assumption that is by no means obvous.)

From discussions with Peter Lupu, I gather that he would grant (1) even without the two assumptions.  He digs being alive and consciousness whether or not the contents of his life/consciousness are good or evil:  just being alive/conscious is for him a good thing.  My life affirmation doesn't go quite that far.  Whereas his life affirmation is unconditional, mine is conditional upon the contents of my experience.

Now consider (2).  John Lennon has been dead for 30 years.   Is it worse for him now than it was 10 years ago or 20 years ago?  Does it get worse year by year?  I mean for him alone, not for Yoko Ono or anyone else.  Intuitively, no.  Ceteris paribus, the longer we live the better; but it is not the case that the longer we are dead, the worse.  (Note that the second independent clause needs no ceteris paribus qualification.)

John F. Kennedy has been dead longer than Richard M. Nixon.  But Kennedy is no worse off than Nixon in precise point of being dead. (2), then, seems intuitively evident.

As for (3), it too seems intuitively evident.  If being respected (treated fairly, loved, provided with food, etc.) for a longer time is better than being respected (treated fairly, etc.)  for a shorter time -- and surely it is -- then being disrespected (treated unfairly, etc.) for a shorter time is better than being disrespected for a longer time.  And so if being-alive longer is better than being-alive shorter, then being non-alive shorter is better than being non-alive longer -- in contradiction to  (2).

One solution would be to reject (2), not by affirming its negation, but by maintaining that neither it nor its negation are either true or false.  If there is no subject of being dead, as presumably there is not assuming that death is anihilation, then one cannot answer the question whether it is worse to be dead for a longer time than for a shorter.

Again we are brought back to the 'problem of the subject.'

 

Can I Stand Unflinchingly for Convictions that I Accept as Only Relatively Valid?

Isaiah Berlin's great essay "Two Concepts of Liberty" concludes as follows:

'To realise the relative validity of one's convictions', said an admirable writer of our time, ' and yet stand for them unflinchingly, is what distinguishes a civilised man from a barbarian.'  To demand more than this is perhaps a deep and incurable metaphysical need; but to allow it to determine one's practice is a symptom of an equally deep, and more dangerous, moral and political immaturity. (Isaiah Berlin, Four Essays on Liberty, Oxford 1969, p. 172.)

A marginalium of mine from 1994 reads, "If I think my convictions merely relatively valid, how can I stand for them unflinchingly?  Even if this is psychologically possible, it seems to be something we ought not do."

To expand upon my 1994 thought.  The liberty of the individual to be free from coercion and obstruction -- "negative liberty (freedom)" in Berlin's terminology -- obviously comes into conflict with other things we deem valuable such as equality, security, and public order. 

Consider how liberty and security are related. Liberty worth having is liberty within a context of security, and security is security worth having only if it makes possible a robust exercise of liberty.  For example, my liberty to leave my house at any time of the day or night  is worth very little if the probability is high that I will be accosted by muggers and other unsavory types when I step out my door.  The security of a police state would prevent that but at a cost too high to pay.

So liberty and security, though both values, are competing values.  Does one rank higher than the other such that we ought to prefer one to the other?  In a concrete situation in which they come into conflict,   one must choose.  Consider for example a sobriety checkpoint on New Year's Eve when by custom booze intake is high.  Such checkpoints involve a clear violation of the (negative) liberty of the individual, and yet they are arguably justifiable in the interests of security and public order.

Now suppose you have a conservative and a libertarian.  In conflict situations, the conservative tends to rank security over liberty, while the libertarian does the opposite.  They both agree that the values in play are indeed values, but they differ as to their prioritization.  Suppose further something that seems obviously true, namely, that this value difference that divides them cannot be objectively resolved to the satisfaction of both parties by appeal to any empirical fact or by any reasoning or by any combination of the two. 

Now here's the question.  Given that the two maintain contradictory value-prioritization theses, how can either "stand unflinchingly" for his thesis given that each recognizes that each thesis is true only from his orientation, an orientation which rests crucially  on his value-prioritization, a value-prioritization that he has no objective reason to prefer over that of his opponent?

I am suggesting that a truly civilized man, one who fully appreciates this predicament he is in, must give up his unflinchingness.  He ought to flinch!  After all, his opponent has all the same intellectual and moral virtues as he has --let us assume -- is equally capable of reasoning cogently above whatever are the facts, and is equally well apprised of all empirical facts that bear on the issue.  Isn't there something "barbaric" about insisting on one's own position assuming that all of these conditions have been met?

I agree with Berlin that it would be "dangerous and immature" to claim absolute truth for convictions that rest on value judgments that cannot be objectvely established.  But once we get this far, then unflinchingness must also go by the board: what I recognize as true only from my point of view, I cannot hold in an unflinching manner.

And yet I must act, hold opinions, vote, take a stand, smite my enemies.  Suspension of judgment and retreat from the political sphere does not seem to be a viable option -- especially not in the face of a bunch of leftist totalitarians who want to so extend the public /political sphere so as to destroy the private.  A hell of a bind we are in: we are essentially agents, hence must act, hence must stand fast, be resolute and smite our dangblasted political opponents -- all the while realizing that we have no justification for our unflinchingness.

The admirable writer Berlin mentions is Joseph Schumpeter.

A Modal Ontological Argument and an Argument from Evil Compared

After leaving the polling place this morning, I headed out on a sunrise hike over the local hills whereupon the muse of philosophy bestowed upon me some good thoughts.  Suppose we compare a modal ontological argument with an argument from evil in respect of the question of evidential support for the key premise in each.  This post continues our ruminations on the topic of contingent support for noncontingent propositions.

A Modal Ontological Argument

'GCB' will abbreviate 'greatest conceivable being,' which is a rendering of Anselm of Canterbury's "that than which no greater can be conceived."  'World' abbreviates 'broadly logically possible world.'

1. The concept of the GCB is either instantiated in every  world or it is instantiated in no world.

2. The concept of the GCB is instantiated in some world.  Therefore:

3. The concept of the GCB is instantiated.

This is a valid argument: it is correct in point of logical form.  Nor does it commit any informal fallacy such as petitio principii, as I argue in Religious Studies 29 (1993), pp. 97-110.  Note also that this version of the OA does not require the controversial assumption that existence is a first-level property, an assumption that Frege famously rejects and that many read back (with some justification) into Kant.  (Frege held that the OA falls with that assumption; he was wrong: the above version is immune to the Kant-Frege objection.)

(1) expresses what I will call Anselm's Insight.  He appreciated, presumably for the first time in the history of thought, that a divine being, one worthy of worship, must be noncontingent, i.e., either necessary or impossible.  I consider (1) nonnegotiable.  If your god is contingent, then your god is not God. There is no god but God.  End of discussion.  It is premise (2) -- the key premise -- that ought to raise eyebrows.  What it says -- translating out of the patois of possible worlds -- is that it it possible that the GCB exists.

Whereas conceptual analysis of 'greatest conceivable being' suffices in support of (1), how do we support (2)?  Why should we accept it?  Some will say that the conceivability of the GCB entails its possibility.  But I deny that conceivability entails possibility.  I won't argue that now, though I do say something about conceivability here.  Suppose you grant me that conceivability does not entail BL-possibility.  You might retreat to this claim:  It may not entail it, but it is evidence for it:  the fact that we can conceive of a state of affairs S is defeasible evidence of S's possibility.

Please note that Possibly the GCB exists -- which is logically equivalent to (2) -- is necessarily true if true.  This is a consequence of the characteristic S5 axiom of modal propositional logic:  Poss p --> Nec Poss p. ('Characteristic' in the sense that it  is what distinguishes S5 from S4 which is included in S5.)  So if the only support for (2) is probabilistic or evidential, then we have the puzzle we encountered earlier: how can there be probabilistic support for a noncontingent proposition?  But now the same problem arises on the atheist side.

An Argument From Evil

4. If the concept of the GCB is instantiated, then there are no gratuitous evils.

5. There are some gratuitous evils. Therefore:

6. The concept of the GCB is not instantiated.

This too is a deductive argument, and it is valid.  It falls afoul of no informal fallacy.  (4), like (1), is nonnegotiable.  Deny it, and I show you the door.  The key premise, then, the one on which the soundness of the argument rides, is (5).  (5) is not obviously true.  Even if it is obviously true that there are evils, it is not obviously true that there are gratuitous evils. 

In fact, one might argue that the argument begs the question against the theist at line (5).  For if there are any gratuitous evils, then by definition of 'gratuitous' God cannot exist.  But I won't push this in light of the fact that in print I have resisted the claim that the modal OA begs the question at its key premise, (2) above.

So how do we know that (5) is true?  Not by conceptual analysis. If we assume, uncontroversially, that there are some evils, then the following logical equivalence holds:

7. Necessarily, there are some gratuitous evils iff the GCB does not exist.

Left-to-right is obvious: if there are gratuitous evils, ones for which there is no justification, then a being having the standard omni-attributes cannot exist.  Right-to-left:  if there is no GCB and there are some evils, then there are some gratuitous evils.  (On second thought, R-to-L may not hold, but I don't need it anyway.)

Now the RHS, if true, is necessarily true, which implies that the LHS -- There are some gratuitious evils -- is necessarily true if true. 

Can we argue for the LHS =(5)?  Perhaps one could argue like this (as one commenter suggested in an earlier thread):  If the evils are nongratuitous, then probably we would have conceived of justifying reasons for them.  But we cannot conceive of justifying reasons.  Therefore, probably there are gratuitous evils.

But now we face our old puzzle: How can the probability of there being gratuitous evils show that there are gratuitous evils given that There are gratuitous evils, if true, is necessarily true?

Conclusion

We face the same problem with both arguments, the modal OA for the existence of the GCB, and the argument from evil for the nonexistence of the GCB.  The key premises in both arguments -- (2) and (5) -- are necessarily true if true.  The only support for them is evidential from contingent facts.  But then we are back with our old puzzle:  How can contingent evidence support noncontingent propositions? 

Neither argument is probative and they appear to cancel each other out.  Sextus Empiricus would be proud of me.

Political Aporetics: A Problem with Enforced Equality

This is a sequel to yesterday's post on liberty and (material) equality and their conflict.  It should be read first. This post extends the analysis by pointing out a problem for socialists (redistributivists).  So consider the following aporetic triad, the first two limbs of which are similar to the first two limbs of yesterday's aporetic tetrad:

1. Justice demands redistribution of wealth from the richer to the poorer., and of other social goods from the haves tothe have-nots. A just society is a fair society, one in which there is a fair or equal distribution of the available social and economic goods such as power and wealth.

2. Redistribution, whether of wealth or of other goods such as power, requires an agency of redistribution which forces, via the coercive power of government, the better off to pay higher taxes, forego benefits, make sacrifices, or in some other way compensate the worse off so that greater material equality is brought about.

3. Any effective redistributive agency must possess and exercise power which is far in excess of the power available to other individual and collective agents in the society: it must be greatly UNEQUAL to the latter in power.

These three propositions are individually plausible, and for the redistributivist, not just plausible but mandatory.  (1) defines the redistributivist position, while (2) and (3) he must accept if he wants to implement his scheme of justice.  But the propositions are not jointly consistent: they cannot all be true.  Any two of them, taken together, entails the negation of the remaining one.  Thus (2) and (3), taken in conjunction, entails the negation of (1). 

The conservative/libertarian will have no trouble solving the problem.  He will reject (1).  Justice does NOT demand redistribution; indeed, justice rules it out.  The leftist/redistributivist, however, is in a jam.  He cannot reject (2) or (3) since these are facts that all must acknowledge.  And he must accept (1) since it is definatory of his position.

The redistributivist position thus appears to be internally incoherent.  The redistributivist  is committed to the acceptance of propositions that cannot all be true.  He wants equality, but to enforce it he must embrace inequality

For a concrete historical example, consider Cuba under Fidel Castro.  Who has all the money and the power?  The people?

Political Aporetics: Liberty Versus Equality

Political disagreement is ultimately rooted in philosophical disagreement.  So if the latter is objectively irresolvable, then so is the former.  I claim that both are irresolvable due to value differences that cannot be resolved either by appeal to empirical facts or by reasoning.  In illustration of my thesis, consider the the values of individual liberty and material (as opposed to formal) equality.  I will assume that both are indeed values to which all of us accord respect.  Even so, value conflict can arise  in the form of a conflict of prioritizations.  I value liberty over equality, while Peter, say, values equality over liberty.  That difference suffices to put us at serious odds despite the fact that we both value liberty and equality.  The conflict over prioritization -- our difference as to which trumps which -- makes the following aporetic tetrad objectively irresolvable:

1. Justice demands redistribution of wealth from the richer to the poorer.  A just society is a fair society, one in which there is a fair distribution of the available social and economic goods.

2. Wealth redistribution requires an agency of redistribution which forces, via the coercive power of government, the better off to pay higher taxes, forego benefits, or in some other way compensate the worse off so that greater material equality is brought about.

3. Coercive redistribution violates the liberty of the individual.

4. It is wrong to violate the liberty of the individual in the way that redistribution requires.

It is easy to see that the limbs of this tetrad, despite the plausibility of each, cannot all be true: the first three, entail the negation of the fourth.  Indeed, any three of them entails the negation of the remaining one.  To solve the inconsistency problem, one of the propositions must be rejected.  But which one?  (2) and (3) are uncontroversial and so not candidates for rejection.  This leaves (1) and (4).

The conservative/libertarian will reject (1) while the liberal/leftist will reject (4).  Each will thus solve the problem -- from his own point of view.  But surely neither amounts to an objective solution to the problem since the solutions are logically incompatible and both are equally rational and equally consistent with all relevant empirical facts.

Indeed, this is why there is a philosophical problem in the first place.  There is nothing illogical about the conservative or liberal positions: neither falls afoul of any logical rule or canon of reasoning.  And there is no empirical fact that allows us to decide between the two positions.  The difference between the positions is ultimately rooted in a value difference, specifically, a difference concerning the prioritization of liberty and equality.  To the conservative, it is self-evident that liberty is such a high value that no consideration of material equality or fairness of distribution could provide any reason to violate the liberty of the individual by, for example, taxing him at a higher rate because he is more economically productive. To the liberal,on the other hand, it is is just self-evident that justice demands redistribution and so a certain amount of coercive taking of what belongs to the productive and a giving of it to the less or non-productive(for example, in the form of food stamps).

Because the doctrinal differences are rooted in a value difference, the doctrinal difference can be objectively resolved only if the value conflict can be objectively resolved.  But the latter cannot be, not by any appeal to empirical facts and not by any abstract reasoning.  If so, the political dispute regarding liberty and equality is objectively irresolvable.

I conjecture that all of the fundamental political problems are like this.  All are at bottom philosophical problems representable by an aporetic polyad consisting of propositions which are individually plausible but not jointly consistent.  If so, a certain political pessimism is the upshot.  We cannot resolve our political differences by appeal to empirical facts or by abstract reasoning or by the two together.  We are stuck with irreconcilable differences rooted in ultimately divergent values.

The question then becomes one of figuring how we can nonetheless continue to live with each other in some semblance of peace despite our irreconcilable differences.  Federalism may be part of the answer.  See my post Can Federalism Save Us?

The Bundle Theory and the Identity of Indiscernibles

I have been defending the bundle-of-universals theory of concrete particulars (BT) against various weak objections over a series of posts, here,  here, here, and here. Now I consider a very powerful objection, one that many will consider decisive.  The objection can be cast in the mold of modus tollendo tollens:  If BT is true, then the Identity of Indiscernibles is a necessary truth.  But the Identity of Indiscernibles is not a necessary truth. Ergo, BT is not true.

1. The Identity of Indiscernibles (IdIn) is the converse of the Indiscernibility of Identicals (InId) and not to be confused with it.  InId is well-nigh self-evident, while IdInis not.  Roughly, the latter is the principle that if x and y share all properties, then x = y.  It is a strictly ontological principle despite the epistemological flavor of 'indiscernible.' As just stated, it is more of a principle-schema than a principle.  We will get different principles depending on what we count as a property.  To arrive at a plausible nontrivial principle we must first rule out haecceity properties.  If, for any x,there is a property of identity-with-x, then no two things could share all properties, and the principle would be trivially true due to the falsehood of the antecedent.  Haecceity properties are creatures of darkness in any case as I argue elsewhere.

A plausible, nontrivial, principle results if we allow as properties all and only relational and  nonrelational pure properties.  A pure property is one that makes no reference to any specific individual.   Being married would then be an example of a pure relational property: to be married is to be married to someone, but not to any specified individual.  Being married to Xanthippe, however, is an impure relational property.  Being obese would be an example of a nonrelational property.  Here then is a plausible version of the Identity of Indiscernibles:

Necessarily, for any x, for any y, and for any relational or nonrelational pure property P, if (x has P iff y has P) then x = y.

2.  It is obvious, I think, that BT entails IdIn in the above form.  Consider a concrete particular, an iron sphere say, at a time.  On BT it is nothing but a bundle of universals. This implies that it is not possible that there be a second iron sphere that shares with the first  all relational and nonrelational pure properties.  This is not possible on BT because on BT a concrete particular is nothing more than a bundle of universals.  Thus there is no ontological ingredient in a concrete particular that could serve to differentiate it from another particular having all the same relational and nonrelational pure properties.  And if it is not possible that there be two things that differ numerically without differing property-wise, then the Identity of Indiscernibles as above formulated is necessarily true.

I am assuming that BT, if true, is necessarily true.  This is a special case of the assumption that the propositions of metaphysics, if true, are necessarily true.  If this assumption is granted, then BT entails IdIn.

3.  But is IdIn true?  Since it is necessarily true if true, all it takes to refute it is a possible counterexample.  Imagine a world consisting of two iron spheres and nothing else.  (The thought experiment was proposed in a 1952 Mind article by Max Black.) They are the same size, shape, volume, chemical composition and so on.  They agree in every nonrelational respect.  But they also agree in every relational respect.  Thus, each has the property of being ten meters from an iron sphere.   What Black's example seems to show is that there can be numerical difference without property-difference.  But then IdIn is false, whence it follows that BT is false.

4.  This is a powerful objection, but is it fatal?  Here are three ways to resist the argument, fit topics for further posts.  He who has the will to blog will never be bereft of topics.

a. Maintain that BT is a contingent truth.  If so, then BT does not entail IdIn as formulated above.

b. Grant that BT entails IdIn, but deny that scenarios such as Black's are really possible.  Admit that they are conceivable, but deny that conceivability entails possibility.

c.  An immanent universal can be wholly present at different places at once.  So why can't a bundle of universals be wholly present in different places at once?  Argue that Black's world can be interpreted, not as two particulars sharing all universals, but as one particular existing in two places at the same time.  From that infer that Black's Gedankenexperiment does show that IdIn is false.

Any other paths of resistance?

A Closer Look at Material Composition and Modal Discernibility Arguments

(For David Brightly, whom I hope either to convince or argue to a standoff.)

Suppose God creates ex nihilo a bunch of TinkerToy pieces at time t suitable for assembly into various (toy) artifacts such as a house and a fort.  A unique classical mereological sum -- call it 'TTS' -- comes into existence 'automatically' at the instant of the creation ex nihilo of the TT pieces. (God doesn't have to do anything in addition to creating the TT pieces to bring TTS into existence.)   Suppose further that God at t  assembles the TT pieces (adding nothing and subtracting nothing) into a house.  Call this object 'TTH.'  So far we have: the pieces, their sum, and the house.  Now suppose that at t* (later than t) God annihilates all of the TT pieces.  This of course annihilates TTS and TTH.  During the interval from t to t* God maintains TTH in existence.

I set up the problem this way so as to exclude 'historical' and nonmodal considerations and thus to make the challenge tougher for my side.  Note that TTH and TTS are spatially coincident, temporally coincident, and such that every nonmodal property of the one is also a nonmodal property of the other.  Thus they have the same size, the same shape, the same weight, etc.  Surely the pressure is on to say that TTH = TTS?  Surely my opponents will come at me with their battle-cry, 'No difference without a difference-maker!'  There is no constituent of TTH that is not also a constituent of TTS.  So what could distinguish them?

Here is an argument that TTH and TTS are not identical:

1. NecId:  If x = y, then necessarily, x = y. 

2. If it is possible that ~(x = y), then ~(x = y). (From 1 by Contraposition)

3. If it is possible that TTS is not TTH, then TTS is not TTH. (From 2, by Universal Instantiation) 

4. It is possible that TTS is not TTH.  (God might have assembled the parts into a fort instead of a house or might have left them unassembled.)

5. TTS is not TTH. (From 3, 4 by Modus Ponens)

The gist of the argument is that if x = y, then they are identical in every possible world in which both of them exist.  But there are possible worlds in which TTS and TTH both exist but are not identical. (E.g., a world in which the pieces are assembled into a fort instead of a house.)  Therefore, TTS andf TTH are not identical.

If you are inclined to reject the argument, you must tell me which premise you reject.  Will it be (1)? Or will it be (4)? 

Your move, David.

 

Varzi, Sums, and Wholes

Achille C. Varzi, "The Extensionality of Parthood and Composition," The Philosophical Quarterly 58 (2008), p. 109:

Suppose we have a house made of Tinkertoy pieces.  Then the house qualifies as a sum of those pieces: each piece is part of the house and each part of the house overlaps at least one of the pieces . . . . Are there other things that qualify as the sums of those pieces?  UC says there aren't; the house is the only candidate: it is the sum of those pieces.

UC is Uniqueness of Composition: 

UC  If x and y are sums of the same things, then x = y,

where

(1) x is a sum of the zs =_df The zs are all parts of x and every part of x has a part in common with at least one ofthe zs. 

Perhaps commenter John, who knows some mereology and the relevant literature on material composition, can help me understand this.  What I don't understand is what entitles Varzi to assume that the Tinkertoy house -- 'TTH' to give it a name -- is identical to a classical mereological sum.  I do not deny that there is a sum of the parts of TTH.  And I do not doubt that this sum is unique.  Let us name this sum 'TTS.'  (I assume that names are Kripkean rigid designators.)  What I do not understand is the justification of the assumption, made near the beginning of his paper, of the identity of TTH and TTS.  TTH is of course a whole of parts.  But it doesn't straightaway follow that TTH is a sum of parts.

Please note that 'sum' is a technical term, one whose meaning is exactly the meaning it derives from the definitions and axioms of classical mereology.  'Whole' is a term of ordinary language whose meaning depends on context.  It seems to me that one cannot just assume that a given whole of parts is identical to a mereological sum of those same parts.

I am not denying that it might be useful for some purposes  to think of material objects like TTH as sums, but by the same token it might be useful to think of material objects as (mathematical)  sets of their parts.  But surely it would be a mistake to identify TTH with a set of its parts.  For one thing, sets are abstract while material objects are concrete.  For another, proper parthood is transitive while set-theoretic elementhood is not transitive. 

Of course, sums are not sets.  A sum of concreta is itself concrete whereas a set of concreta is itself abstract.  My point is that, just as we cannot assume that that TTH is identical to a set, we cannot assume that TTH is identical to a sum.

What is the 'dialectical situation' when it comes to the dispute between those who maintain that TTH = TTS and those who deny this identity?

It seems to me that the burden of proof rests on those who, like Varzi, identify material objects like TTH with sums especially given the arguments against the identity.  Here is one argument. (a) Taking TTH apart would destroy it, (b) but would not destroy TTS.  Therefore, (c) TTH is not identical to TTS.  This argument relies on the wholly unproblematic Indiscernibility of Identicals as a tacit premise:  If x = y, then whatever is true of x is true of y, and vice versa.  Because something is true of TTH -- namely, that taking it apart would destroy it -- that is not true of TTS, TTH cannot be identical to TTS.

The simplicity and clarity of modal discernibility arguments like this one cast grave doubt on the opening assumption that TTH is a sum.  I am not saying that Varzi and Co. have no response to the argument; they do.  My point is that their response comes too late dialectically speaking.  If you know what a sum is, you know that the identity is dubious from the outset: the discernibility arguments merely make the dubiousness explicit. Responding to these arguments strikes me as too little too late; what the identity theorist needs to do is justify his intitial assumption as soon as he makes it.

My main question, then, is this.  What justifies the initial assumption that material particulars such as Tinkertoy houses are mereological sums?  It cannot be that they are wholes of parts, for a whole needn't be a sum.  TTH is a whole but it is not a sum.  It is not a sum because a sum is a collection that is neutral with respect to the arrangement or interrelation of its parts, whereas it is essential to TTH that its parts be arranged house-wise.

 

Four-Dimensionalism to the Rescue?

Let us return to that impressive product of porcine ingenuity, Brick House.  Brick House, whose completion by the Wise Pig occurred on Friday, is composed entirely of the 10,000 Tuesday Bricks.  I grant that there is a sum, call it 'Brick Sum,' that is the classical mereological sum of the Tuesday Bricks.  Brick Sum is 'generated' -- if you care to put it that way -- by Unrestricted Composition, the classical axiom which states that "Whenever there are some things, then there exists a fusion [sum] of those things." (D. Lewis, Parts of Classes, p. 74)  I also grant that Brick Sum is unique by Uniqueness of Composition according to which "It never happens that the same things have two different fusions [sums]." (Ibid.)  But I deny Lewis' Composition as Identity.  Accordingly, Brick Sum cannot be identical to the Tuesday Bricks.   After all, it is one while they are many.

Now the question I am debating with commenter John is whether Brick House is identical to Brick Sum.  This ought not be confused with the question whether Brick House is identical to the Tuesday Bricks.  This second question has an easy negative answer inasmuch as the former is one while the latter are many.  Clearly, one thing cannot be many things.

The question, then, is whether Brick House is identical to Brick Sum.  Here is a reason to think that they are not identical.  Brick Sum exists regardless of the arrangement of its parts: they can be scattered throughout the land; they can be piled up in one place; they can be moving away from each other; they can be arranged to form a wall, or a corral, or a house, or whatever.  All of this without prejudice to the existence and the identity of Brick Sum.  Now suppose Hezbollah Wolf, a 'porcicide' bomber, enters Brick House and blows it and himself up at time t on Friday evening. At time t* later than t, Brick Sum still exists while Brick House does not.  This shows that they cannot be identical; for if they were identical, then the destruction of Brick House would be the destruction of Brick Sum. 

This argument, however, rests on an assumption, namely, that Brick Sum exists both at t and at t*.   This won't be true if Four Dimensionalism is true.  If bricks and houses are occurrents rather than continuants, if they are composed of temporal parts, then we cannot say, strictly and philosophically, that Brick Sum at t still exists at t*.  And if we cannot say this, then the above argument fails.

But all is not lost since there remains a modal consideration.  Brick House and Brick Sum both exist at time t in the actual world.  But there are plenty of possible worlds in which, at t, the latter exists but not the former.  Thus it might have been the case at t that the bricks were arranged corral-wise rather than house-wise.  So Brick Sum has a property that Brick House lacks, namely, the modal property of being such that its parts could have been arranged in non-house-wise fashion.  Therefore, by the Indiscernibility of Identicals, Brick House is not identical to Brick Sum.

So even if the historical discernibility argument fails on Four Dimensionalism, the modal discernibility argument seems to work even assuming Four Dimensionalism.

Please note that my thesis is not that Brick House is a sum that violates Uniqueness of Composition, but that Brick House is not a classical mereological sum.    If Brick House were a sum, then it would be Brick Sum.  But I have just argued that it cannot be Brick Sum.  So it cannot identified with any classical sum.  It is a whole of parts all right, but an unmereological whole.  What does that mean?  It means that it is a whole that cannot be adequately understood using only the resources of classical mereology.

 

Van Inwagen on Arbitrary Undetached Parts

In order to get clear about Dion-Theon and related identity puzzles we need to get clear about the Doctrine of Arbitrary Undetached Parts (DAUP) and see what bearing it has on the puzzles. Peter van Inwagen provides the following statement of DAUP:

For every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t. ("The Doctrine of Arbitrary Undetached Parts" in Ontology, Identity, and Modality, CUP, 2001, 75.) 

Suppose I am smoking a cigar. DAUP implies that the middle two-thirds of the cigar is just as much a concrete material object as the whole cigar. This middle two-thirds is an undetached part of the cigar, but also an arbitrary undetached part since I could have arbitrarily selected uncountably many other lengths such as the middle three-fourths. Applied to Tibbles the cat, DAUP implies that Tibbles-minus-one-hair is just as full-fledged a material object as Tibbles. Van Inwagen maintains that DAUP is false.

I will reconstruct van Inwagen's argument for the falsity of DAUP as clearly as I can. Consider Descartes and his left leg L. To keep it simple, we make the unCartesian assumption that Descartes is just a live body. DAUP implies that L is a material object as much as Descartes himself. DAUP also implies that there is a material object we can call D-minus. This is Descartes-minus-L. It is obvious that Descartes and D-minus are not the same. (For one thing, they are differently shaped. For another, they are 'differently abled' in PC jargon.) At time t, D-minus and L are undetached nonoverlapping proper parts of Descartes, and both are just as much full-fledged material objects as Descartes himself is.

Now suppose a little later, at t*, L becomes detached from D-minus. In plain English, Descartes at t* loses his leg. (To avoid certain complications, we also assume that the leg is not only removed but also annihilated.) Does D-minus still exist after t*?  Van Inwagen thinks it is obvious that D-minus does exist after the operation at t*. DAUP implies that the undetached parts of material objects are themselves material objects. So D-minus prior to t* is a material object. Its becoming detached from L does not affect D-minus or its parts, and if the separation of L from D-minus were to cause D-minus to cease to exist, then, van Inwagen claims, D-minus could not properly be called a material object. Descartes himself also exists after the operation at t*. Surely one can survive the loss of a leg. So after t* both D-minus and Descartes exist. But if they both exist, then they are identical. For otherwise there would be two material objects having exactly the same size, shape, position, mass, velocity, etc., and that is impossible.

In sum, at time t, D-minus and Descartes are not identical, while at the later time t* they are identical. The result is the following inconsistent tetrad:

D-minus before t* = D-minus after t*

D-minus after t* = Descartes after t*

Descartes after t* = Descartes before t*

It is not the case that  D-minus before t* = Descartes before t*

The first three propositions entail the negation of the fourth. From this contradiction van Inwagen infers that there never was any such thing as D-minus. If so, then DAUP is false. But as van Inwagen realizes, his refutation of DAUP has a counterintuitive consequence, namely, that L does not exist either: there never was any such thing as Descartes' left leg. For it seems obvious that D-minus and L stand or fall together, to repeat van Inwagen's pun.

That is, D-minus exists if and only if L exists, and D-minus does not exist if and only if L does not exist. D-minus is an arbitrary undetached proper part of Descartes if and only if L is an arbitrary undetached proper part of Descartes. At this point, I think it becomes clear that van Inwagen's solution to the Dion/Theon or Descartes/D-minus puzzle is not compelling. He solves the puzzle by denying that there was ever any such material object as D-minus. But if there was no D-minus, then there was never any such material object as Descartes' left leg. It is obvious, however, that there was such a material object as Descartes' left leg L. So how could it be maintained that there was no such object as Descartes-minus? Van Inwagen makes it clear (p. 82, n. 12) that he does not deny that there are undetached parts. What I take him to be denying is that, for any P and O, where P is an undetached part of material object O, there is a complementary proper part of O, O-minus-P. So perhaps van Inwagen can say that L is a non-arbitrary undetached part of Descartes and that this is consistent with there being no D-minus. If so, he would have to reject the following supplementation principle of mereology which seems intuitively sound:

For any x, y, z, if x is a proper part of y, then there exists a z such that z is a part of y and z does not overlap x , where x overlaps y =df there exists a z such that z is a part of x and z is a part of y.

What the above supplementation principle says is that you cannot have a whole with only one proper part. Every whole having a proper part has a second proper part that supplements or complements the first so as to constitute a whole. Now Descartes' leg is a proper part of Descartes. So the existence of D-minus falls out of the supplementation principle.

It seems, then, that van Inwagen's rejection of DAUP  issues in a dilemma.  If there is no such object as Descartes minus his left leg, then there is no such object as Descartes' left leg, which is highly counterintuitive, to put it mildly.  But if van Inwagen holds onto the left leg, then it seems his must reject the seemingly obvious supplementation principle lately mentioned.

My interim conclusion is that van Inwagen's solution to the Descartes/D-minus puzzle by rejection of DAUP is not compelling.

Van Inwagen Contra Lewis on Composition as Identity

Modifying an example employed by Donald Baxter and David Lewis, suppose I own a parcel of land A consisting of exactly two adjoining lots B and C. It would be an insane boast were I to claim to own three parcels of land, B, C, and A. That would be 'double-counting': I count A as if it is a parcel in addition to B and C, when in fact all the land in A is in B and C taken together. Lewis, rejecting 'double-counting,' will say that A = (B + C). Thus A is identical to what composes it. This is an instance of the thesis of composition as identity.

Or suppose there are some cats.  Then, by Unrestricted Composition ("Whenever there are some things, then there exists a fusion [sum] of those things"), there exists a sum that the cats compose.  But by Composition as Identity, this sum is identical to what compose it, taken collectively, not distributively.  Thus the sum is the cats, and they are it.  I agree with van Inwagen that this notion of Composition as Identity is very hard to make sense of, for reasons at the end of the above link.  But Peter van Inwagen's argument against Composition as Identity strikes me as equally puzzling.  Van Inwagen argues against it as follows:

Suppose that there exists nothing but my big parcel of land and such parts as it may have. And suppose it has no proper parts but the six small parcels. . . . Suppose that we have a bunch of sentences containing quantifiers, and that we want to determine their truth-values: 'ExEyEz(y is a part of x & z is a part of x & y is not the same size as z)'; that sort of thing. How many items in our domain of quantification? Seven, right? That is, there are seven objects, and not six objects or one object, that are possible values of our variables, and that we must take account of when we are determining the truth-value of our sentences. ("Composition as Identity," Philosophical Perspectives 8 (1994), p. 213)

In terms of my original example, Lewis is saying that A is identical to what composes it. Van Inwagen is denying this and saying that A is not identical to what composes it. His reason is that there must be at least three entities in the domain of quantification to make the relevant quantified sentences true. A is therefore a third entity in addition to B and C. It is this that I don't understand. Van Inwagen's argument strikes me as a non sequitur. Or perhaps I just don't understand it. Consider this obviously true quantified sentence:

1. For any x, there is a y such that x = y.

(1) features two distinct bound variables, 'x'and 'y.' But it does not follow that there must be two entities in the domain of quantification for (1) to be true. It might be that the domain consists of exactly one individual a. Applying Existential Instantiation to (1), we get

 2. a = a.

Relative to a domain consisting of a alone, (1) and (2) are logically equivalent. From the fact that there are two variables in (1), it does not follow that there are two entities in the domain relative to which (1) is evaluated. Now consider

3. There is an x, y and z such that x is a proper part of z & y is a proper part of z.

(3) contains three distinct variables, but it does not follow that the domain of quantification must contain three distinct entities for (3) to be true. Suppose that Lewis is right, and that A = (B + C). It will then be possible to existentially instantiate (3) using only two entities, thus:

4. B is a proper part of (B + C) & C is a proper part of (B + C).

If van Inwagen thinks that a quantified sentence in n variables can be evaluated only relative to a domain containing n entities (or values), then I refute him using (1) above. If van Inwagen holds that (3) requires three entities for its evaluation, then I say he has simply begged the question against Lewis by assuming that (B + C) is not identical to A. It is important not to confuse the level of representation with the level of reality. That there are two different names for a thing does not imply that there are really two things. ('Hesperus' and 'Phosphorus' both name the same planet, Venus, to coin an example.) Likewise, the fact that there are two distinct bound variables at the level of linguistic representation does not entail that at the level of reality there are two distinct values. There might be or there might not be.

So I cannot see that van Inwagen has given me any reason to think that A is a third entity in addition to B and C. But it doesn't follow that I think that Lewis' thesis is correct. Both are wrong.  Here is the problem. 'A = (B + C)' is the logical contradictory of '~ (A = (B + C)).' Thus one will be tempted to plump for one or the other limb of the contradiction. But there are reasons to reject both limbs.

Surely A is more than the mereological sum of B and C. This is because A involves a further ontological ingredient, namely, the connectedness or adjacency of B and C. To put it another way, A is a unity of its parts, not a pure manifold. The Lewis approach leaves out unity. Suppose B is in Arizona and C is in Ohio. Then the mereological sum (B + C) automatically exists, by Unrestricted Composition.   But this scattered object is not identical to the object which is B-adjoining-C. On the latter I can build a house whose square footage is greater than that of B or C; on the scattered object I cannot. But A is not a third entity. It is obvious that A is not wholly distinct from B and C inasmuch as A is composed of B and C as its sole nonoverlapping proper parts. Analysis of A discloses nothing other than B and C.  But neither is A identical to  B + C.

In short, both limbs of the contradiction are unacceptable. How then are we to avoid the contradiction?

Perhaps we can say that A is identical,  not to the sum B + C, but to B-adjoining-C, an unmereological whole.  But this needs explaining, doesn't  it?

Mereological Innocence and Composition as Identity

This is the third in a series.  Part I, Part II.  What follows is a 10th example of eliminativist/reductivist ambiguity.

One of the axioms of mereology is Unrestricted Composition.  Here is David Lewis' formulation (Parts of Classes, Basil Blackwell 1991, p. 74):

Unrestricted Composition: Whenever there are some things, then there exists a fusion of those things.

A fusion is a mereological sum, so I'll use 'sum.'  The axiom assures us that, for example, if there are some cats, then there exists a sum of those cats.  The cats are many but the sum is one.  So it is not unreasonable to think that if there are five cats that compose the sum, the sum is a sixth thing.  One could argue as follows:  (a) The sum is distinct from each of the cats.  (b)There are five cats, each of which exists, and by UC the sum also exists.  Therefore, (c) at least six things exist.

But consider this example, adapted from Donald Baxter.  You proceed with six bottles of beer to the supermarket 'six items or fewer' checkout line.  The attendant protests your use of the line on the ground that you have seven items: six bottles of beer plus one mereological sum.  This would be an outrage, of course.  The example suggests that the argument to (c) above has gone wrong.

Lewis avoids the mistake -- assuming it is one -- by pleading that "Mereology is ontologically innocent." (PC 81)  That means that a commitment to a cat-sum is not a further commitment over and above the commitment to the cats that compose the sum.  The cat-sum just is the cats, and they are it.  This is the thesis of Composition as Identity.  The xs compose the y by being identical to the y.  As Lewis says,

Take them together or take them separately, the cats are the same portion of Reality either way.  Commit yourself to their existence all together or one at a time, it's the same commitment either way.  If you draw up an inventory of Reality according to your scheme of things, it would be double counting to list the cats and also list their fusion.  In general, if you are already committed to some things, you incur no further commitment when you affirm the existence of their fusion. (PC 81-82)

I'm sorry, but this doesn't make much sense.  Glance back at Unrestricted Composition.  It is not a tautology.  It does not say that whenever there are some things, then there are some things.  It says that whenever there are some things, then there exists a fusion or sum of those things.  Now if the sum of the xs is just the xs, then UC is a tautology.  But  if UC is not a tautology, then Composition as Identity is false.  How can Unrestricted Composition and Composition as Identity both be true?

The problem is already present at the purely syntactic level.  'Y is identical to the xs' is unproblematic if the xs are identical to one another.  For then the open sentence collapses into 'y is identical to x.'  But if the xs are distinct from each other, then 'y is identical to the xs' is syntactically malformed.  How can one thing be identical to many things?  If one thing is identical to many things, then it is not one thing but many things.  A contradiction ensues: the one thing is one thing and not one thing because it is many things.  The gaps in the predicate '. . . is identical to ____' must either be both filled with singular terms or both filled with plural terms.

And now we come back to our main theme, eliminativist/reductivist ambiguity.  Lewis wants to say that there is the sum of the xs (by Unrestricted Composition) but that the the sum of the xs is identical to the xs.  So he seems to be making a reductionist claim: sums reduce to their members.  But I say the thesis is unstable and topples over into eliminativism:  there are no mereological sums.  For if the sum is just its members, then all that exists is the members so that the sum does not exist!

Fist and Hand, Statue and Lump: The Aporetics of Composition

1. Some maintain that a hand, and that same hand made into a fist, are identical. And there are those who would say the same about a piece of bronze and the statue made out of it, namely, that they are identical at every time at which both exist. This is not an unreasonable thing to say. After all, fist and hand, statue and bronze, are spatially coincident and neither has a physical part the other doesn't have. A fist is just a certain familiar arrangement of hand-parts. There is no part of the fist that is not part of the hand, and vice versa. So at looks as if first and hand are identical.  But we need to be clear as to what identity is.

2. Identity is standardly taken to be an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity (NecId). The first principle says that, if two items are numerically identical, then they share all properties. The second says that if two items are numerically identical, then this is necessarily the case.  Both principles strike me as beyond epistemic reproach.  'Identity' is short for 'numerical identity.'

3. Despite the considerations of #1, it looks as if fist and hand, statue and hunk of bronze, cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form. The hand can, while the fist cannot, survive adoption of a different 'posture.'  In both cases, something is true of the one that is not true of the other.  So even at the times at which the fist is the hand, and the bronze is the statue, the two are not identical: the 'is' is not the 'is' of identity.  It is the 'is' of composition and what you have are two things, not one.

What I have just given is a modal discernibility argument.  Let me spell it out.  Consider a time t at which the hand is in the shape of a fist.  At t, the hand, but not the fist, has the modal property of being possibly such as to to be unfisted.  So the hand cannot be identical to the fist given that, for any x, y, if x = y, then x, y share all properties.

But there is also this nonmodal discernibility argument.  The hunk of bronze existed long before the statue came into existence, and the hunk of bronze exists while the form of a statue.  So the hunk of bronze exists at more times that the statues does, which implies the the hunk of bronze is not identical to the statue.

There is also this consideration.  Identity is symmetrical.  So we can say either fist = hand or hand = fist.  But is it the fist or the hand that both are?  Intuitively, it is the hand.  The hand is the fundamental reality here, not the fist.  So how can fist and hand be identical?  It seems that fist and hand are numerically distinct, albeit spatially coincident, concrete individuals.

4.  The Law of Excluded Middle seems very secure indeed, especially in application to presently existing things.  So either the fist is identical to the hand, and there is just one thing, a fisted hand, or the fist is not identical to the hand and there are two spatially coincident things, a fist and a hand.  So which is it?

5. If you say that the fist = the hand, then when you make a fist nothing new comes into existence, and when the potter makes a pot out of clay, nothing new comes into existence.  And when a mason makes a wall out of stones, nothing new comes into existence.  He started with some stones and he ended with some stones.  Given that the stones exist, and that the mason's work did not cause anything new to come into existence, must we not say that the single composite entity, the wall, does not exist?  (For if it did exist, then there would be an existent in addition to the stones.)  But it sounds crazy to say that the wall the mason has just finished constructing does not exist.

6. If, on the other hand, you say that the fist is not identical to the hand, then you can say that the making of a fist causes a new thing to come into existence, the fist.  And similarly with the statue and the wall.  After the mason stacks n stones into a wall, he has as a result of his efforts n +1 objects, the original n stones and the wall. 

But this is also counterintuitive.  Consider the potter at his wheel.  As the lump of clay spins, the potter shapes the lump into a series of many (continuum-many?) intermediate shapes before he stops with one that satisfies him.  Thus we have a series of objects (proto-pots) each of which is a concrete individual numericallt distinct from the clay yet (i) spatially conicident with it, and (ii) sharing with it every momentary property.  And that is hard to swallow, is it not?

7.  We appear to be at an impasse.  We cannot comfortably say that the fist = the hand, nor can we comfortably say that the fist is not identical to the hand. Nor can we comfortably give up LEM.  If there are no fists, statues, walls, artifacts generally, then there cannot be any puzzles about their composition.  But we cannot comfortably say that there are no such things either.

Do we have here an example of a problem that is both genuine but insoluble?

The Aporetics of Artifacts: Puzzling Over Van Inwagen's Denial of Artifacts

This post is a sequel to Van Inwagen on the Ship of Theseus.  Peter van Inwagen, Material Beings (Cornell UP, 1990), p. 31, writes: 

The question 'In virtue of what do these n blocks compose this house of blocks?' is a question about n + 1 objects, one of them radically different from the others. But the question 'What could we do to get these n blocks to compose something? is a question about n rather similar objects. . . . . questions of the former sort turn our minds to various metaphysical and linguistic questions about the "special" n + 1st [read: n + 1th] object and our words for it: What are the identity conditions for houses of blocks?

Why does van Inwagen think that a house of blocks is an object radically different from the blocks that compose it? And why does he think that if there are, say, 1000 blocks, then in the place where the house is, there are 1001 objects? Not only do I find these notions repugnant to my philosophical sense, I suspect that it is their extremism that motivates van Inwagen to recoil from them and embrace something equally absurd, namely, that there are no such things as houses of blocks or inanimate concrete partite entities generally. 

In other words, if one begins by assuming that if a house of blocks, for example, is a whole of parts, then it is an object radically different from the objects that compose it, an object numerically additional to the objects that compose it; then, recoiling from these extreme positions, one will be tempted to embrace an equal but opposite extremism according to which there are no such inanimate partite entities as houses of blocks. What then should we say about a house of blocks?

First off, it is not identical to any one of its proper parts. Second, it is not identical to the mereological sum of its parts: the parts exist whether or not the house exists. From this it follows that there is a sense in which the house is 'something more' than its parts. But surely it is not an object "radically different" from, or numerically additional to, its proper parts. If there is a house of 1000 blocks in a place, there are not 1001 objects or entities in that place. After all, the house is composed of the blocks, and of nothing else.

So on the one hand the house is 'something more' than its constituent blocks, while on the other hand it is not a "radically different" object above and beyond them. Think of how absurd it would be for me to demand that you show me your house after you have shown me every part of it. "You've shown me every single part of your house, but where is the bloody house?"

The house, thought not identical to the blocks that compose it,  is not wholly diverse from the blocks that compose it .  The house is the blocks arranged housewise. The house is not the blocks, and the house is not some further entity "radically different" from the blocks. The house is just the blocks in a certain familiar arrangement. Should we conclude that the house exists or that it does not exist? I say it exists: the house is the blocks arranged housewise, and the existence of the house is the housewise unity of the blocks. Van Inwagen seems to think that there is no house, there are just the blocks. (Of course, he doesn't believe in the blocks either since they too are inanimate partite entities; but to keep the discussion simple, we may assume that the blocks are simples.)  

Now if it is allowed that the house exists, it seems clear that the house does not exist in the way the blocks do. But this does not strike me as a good reason for saying that the house does not exist at all. What is wrong with saying that the house is a dependent existent? And what is wrong with saying that about partite entities generally? They exist, but they do not exist in addition to their parts, but as the unity or connectedness of their parts. Saying this, we avoid van Inwagen's absurd thesis that inanimate partite entities do not exist. Of course, this commits me to saying that there are at least two modes of existence, a dependent mode and an independent mode. I suspect van Inwagen would find such a distinction incoherent. But that is a topic for a separate post.

The problem can be set forth as an aporetic pentad:

1. The house is not identical to the blocks that compose it.

2. The house is not wholly diverse from the blocks that compose it; it is not an object numerically additional to the blocks that compose it:  given that the house is composed of n blocks, the house itself is not an n + 1th object.

3. The house exists.

4. The constituent blocks exist.

5.  'Exists' is univocal as between wholes and parts: wholes and their parts exist in the same sense.

Each limb has a strong claim on our acceptance.  But they cannot all be true.  Any four of the propositions, taken together, entails the negation of the remaining one.  For example, if the first four are all true, then the fifth must be false.  To solve the problem, one of the limbs must be rejected.  But which one? 

To me it seems obvious that the first four are all true.  So I reject (5).  Rejecting (5), I can say that the house exists as the connectedness of the blocks.  Thus the mode of existence of the whole is different from the mode of existence of its simple parts.  But this solution requires us to believe in modes of existence, which is sure to inspire opposition among analytic philosophers.  Van Inwagen, if I understand him, denies (2) and (3) while accepting the others.

But van I's solution is just crazy, is it not?  Mine is less crazy.  But perhaps you, dear reader, have a better suggestion.

 

Van Inwagen on the Ship of Theseus

Peter van Inwagen's Material Beings (Cornell UP, 1990) is a very strange book, but he is a brilliant man, so one can expect to learn something from it. A central claim is that artifacts such as tables and chairs and ships do not exist. One can appreciate  that if there are no ships then the ancient puzzle about identity known as the Ship of Theseus has a very quick (dis)solution. 

The Ship of Theseus is a puzzle about diachronic artifact identity. Here is one version. You have a ship, or a rowboat, or any object, composed entirely of wooden planks. You remove one of the planks and replace it with an aluminum plank of the same size. The wooden plank is placed in a warehouse. After this minor replacement, you have a ship and indeed numerically the same ship as the one you started with. It is not a numerically different ship. Now replace a second wooden plank with an aluminum plank, and place the second wooden plank in the warehouse. Again, the numerical identity of the original ship has been preserved. Continue the replacement process until all of the wooden planks have been replaced with aluminum planks. You now have a wholly aluminum ship that is presumably numerically identical to the original wholly wooden ship despite the fact that none of the original matter is to be found in the aluminum ship. After all, the aluminum ship 'grew out of' the original wooden ship by minor changes each of which is identity-preserving.

Now take the wooden planks from the warehouse and assemble them in the form of a ship and in such a way that the planks bear the same relations to one another as the planks in the original wooden ship bore to one another. You now have two ships, a wooden one and an aluminum one. The question is: which of these ships is identical to the original wooden one?

Suppose the two ships collide on the high seas, and suppose the captain of the original ship had taken a solemn vow to go down with his ship. Where does his duty lie? With the wooden ship or with the aluminum one? Is the original ship identical to the resultant aluminum ship? One will be tempted to say 'yes' since the aluminum ship 'grew out' of the original wooden ship by minor transformations each of which was identity-preserving. Or is the original ship identical to the wooden ship that resulted from the re-assembly of the wooden planks? After all, it consists of the original matter arranged in the original way. Since the resultant wooden and aluminum ships are numerically distinct, they cannot both be identical to the original ship.

Van Inwagen makes short work of the puzzle: "There are no ships, and hence there are no puzzles about the identities of ships." (128) One way van Inwagen supports this bizarre solution is by re-telling the story in language that does not make even apparent reference to ships. Here is his retelling:

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (128-129)

If I understand what van Inwagen is claiming here, it is that there is nothing in the standard telling of the story, a version of which I presented above, that is not captured in his re-telling. But since there is no mention of any ships in the re-telling, no puzzle about ship-identity can arise. Perhaps van Inwagen's point could be put by saying that the puzzle about identity is an 'artifact' of a certain way of talking that can be paraphased away. Instead of talking about ships, we can talk about shipwise arrangements of planks. The planks do not then compose a ship, he thinks, and so there is no whole of which they are proper parts, and consequently no question about how this whole maintains its diachronic identity under replacement of its parts.

What are we to say about van Inwagen's dissolution of the puzzle? What I find dubious is van Inwagen's claim that ". . . at no time do two or more of these planks compose anything, and no plank is a proper part of anything." (129) This strikes me as plainly false. If the First Planks are arranged shipwise, then there is a distinction beween the First Planks and their shipwise arrangement. The latter is the whole ship and the former are its proper parts. So how can van Inwagen claim that the planks do not compose a ship? Van Inwagen seems to think that if the planks were parts of a whole, and there were n planks, then the whole would be an n + 1 th entity. Rejecting this extreme, he goes to the other extreme: there is no whole of parts. If there were ships, they would be wholes of parts, but there are no artifactual wholes of parts, so there are no ships. The idea seems to be that when we build an artifact like a ship we are not causing something new to come into existence; we are merely re-arranging what already exists. If so, then although a ship's planks exist, the ship does not exist. Consider what van Inwagen says on p. 35:

If I bring two cubes into contact so that the face of one is conterminous with the face of the other, have I thereby brought into existence a solid that is twice as long as it is wide? Or have I merely rearranged the furniture of the earth without adding to it?

Van Inwagen seems to be saying that when it comes to artifacts, there is only rearrangement, no 'addition to existence.' As a general thesis, this strikes me as false. A ship is more than its planks, and van Inwagen seems to concede as much with his talk of a shipwise arrangement of planks; but this shipwise arrangement brings something new into being, namely, a thing that has causal powers that its constituents do not have. For example, a boat made of metal planks properly arranged will float, while the planks themselves will not float.

Sets and the Number of Objects: An Antilogism

Commenter Jan, the Polish physicist, gave me the idea for the following post.

An antilogism is an aporetic triad, an array of exactly three propositions which are individually plausible but collectively inconsistent.  For every antilogism, there are three corresponding syllogisms, where a syllogism is a deductive argument with exactly two premises and one conclusion.  Here is the antilogism I want to discuss:

1. Possibly, the number of objects is finite.
2. Necessarily, if sets exist, then the number of objects is not finite.
3. Sets exist.

The modality at issue is 'broadly logical' and sets are to be understood in the context of standard (ZFC) set theory. 'Object' here just means entity.  An entity is anything that is. (Latin ens, after all, is the present participle of the infinitive esse, to be.)

Corresponding to the above antilogism, there are three syllogisms. The first, call it S1, argues from the conjunction of (1) and (2) to the negation of (3).  The second, call it S2, argues from the conjunction of (2) and (3) to the negation of (1).  The third, call it S3, argues from (1) and (3) to the negation of (2). 

Note that each syllogism is valid, and that the validity of each reflects the logical inconsistency of the the antilogism. Note also that for every antilogism there are three corresponding syllogisms, and for every syllogism there is one corresponding antilogism.  A third thing to note is that S3 is uninteresting inasmuch as it is surely unsound.  It is unsound because (2) is unproblematically true. 

This narrows the field to S1 which argues to the nonexistence of (mathematical) sets and S2 which argues to the impossibility of the number of objects (entities) being finite.  Our question is which of these two syllogisms we should accept.  Obviously, both are valid, but both cannot be sound.  Do we have good reason to prefer one over the other?

Here are our choices.  We can say that there is no good reason to prefer S1 over S2 and vice versa; that there is good reason to prefer S1 over S2; or that there is good reason to prefer S2 over S1.

Being an aporetician, I incline toward the first option.  Peter Lupu, being less of an aporetician and more of dogmatist, favors the third option.  Thus he thinks that the antilogism is best solved by rejecting (1).  Peter writes:

(a) If there are infinitely many numbers, then (1) is false. Are there infinitely many numbers? Very few would deny this. How could they, for then they would have to reject most of mathematics. [. . .]

To keep it simple, let's confine ourselves to the natural numbers and the mathematics of natural numbers. (The naturals are the positive integers including 0.)  If there are infinitely many naturals, then there are infinitely many objects.  If so, then presumably this is necessarily so, whence it follows that (1) is false. 

I fail to see, however, why there MUST be infinitely many naturals.  I am of course not denying the obvious: for any n one can  add 1 to arrive at n + 1.  With a sidelong glance in the direction of Anselm of Canterbury: there is no n that fits the description 'that than which no greater can be computed.'   In plain English:  there is no greatest natural number.  But this triviality does not require that all of the results of possible acts of +1 computation actually be 'out there' in Plato's heaven.  When I drive along a road, I come upon milemarkers that are already out there before I come upon them.  But why must we think of that natural number series like this?  I don't bring the road and its milemarkers into being by driving.  But what is to stop us from viewing the natural number series along Brouwerian (intuitionistic) lines?  One can still maintain that the series is infinite, but the infinity is potential not actual or completed.  Peter's first argument, as it stands, is not compelling.  (Compare:  Everyone will agree that every line segment is infinitely divisible.  But it does not follow that every line segment is infinitely divided.)

(b) If propositions exist, then there are infinitely many propositions. Are there propositions? Kosher-nominalists obviously will have to deny that propositions exist. Sentences do not express propositions. But, then, what do they express?

I am on friendly terms with Fregean (not Russellian) propositions myself. And I grant that it is very plausible to say that if there is one proposition then there is an actual infinity of them.  Consider for example the proposition *p* expressed by 'Peter has a passion for philosophy.'  *P* entails *It is true that p* which entails *It is true that it is true that p,* and so on infinitely.  But again, why can't this be a potential infinity? 

The following three claims are consistent: (i) Declarative sentences express propositions; (ii)Propositions are abstract; (iii) Propositions are man-made. Karl Popper's World 3 is a world of abstracta.  It is a bit like Frege's Third Reich (as I call it), except that the denizens of World 3 are man-made.

I am agreeing with Peter and against the illustrious William that there are (Fregean) propositions, understood as the senses of context-free declarative sentences.  I simply do not understand how a declarative sentence-token could be a vehicle of a truth-value.  But why can't I say that propositions are mental constructs?  (This diverges from Frege, of course.)

(c) Are there sentence types? A nominalist will have to deny the existence of sentence types. But, then, it is difficult to see how any linguistic analysis can be done.

Peter may be conflating two separate questions.  The first is whether there are any abstract objects, sentence types for example. The second is whether there is an actual infinitity of them.  He neeeds the latter claim as a countrerexample of (1).  So again I ask:  why couldn't there be a finite number of abstract objects:  a finite number of sets, propositions, numbers, sentence types, etc.  This would make sense if items of this sort were Popperian World 3 items.

I conclude that, so far, there is no knock-down refutation of (1).  But there is also no knock-down refutation of (3) either, as Peter will be eager to concede.  So I suggest that the rational course is to view my (or my and Jan's) antilogism as a genuine intellectual knot that so far has not been definitively solved.

 

Presentism and Existence-Entailing Relations: An Aporetic Tetrad

It is plausibly maintained that all relations are existence-entailing. To illustrate from the dyadic case: if R relates a and b, then both a and b exist.   A relation cannot hold unless the things between which or among which it holds all exist.  A weaker, and hence even more plausible, claim is that all relations are existence-symmetric: if R relates a and b, then either both relata exist or both do not exist. Both the stronger and the weaker claims rule out the possibility of a relation that relates an existent and a nonexistent. (So if Cerberus is eating my cat, then Cerberus exists. And if I am thinking about Cerberus, then, given that Cerberus does not exist, my thinking does not relate me to Cerberus.  This implies that  intentionality is not a relation, though it is, as Brentano says, relation-like (ein Relativliches).)

But if presentism is true, and only temporally present items exist, then no relation connects a present with a nonpresent item. This seems hard to accept for the following reason.

I ate lunch  an hour ago. So the event of my eating (E) is earlier than the event of my typing (T). How can it be true that E bears the earlier than relation to T, and T bears the later than relation to E, unless both E and T exist? But E is nonpresent. If presentism is true, then E does not exist.  And if E does not exist, then E does not stand in the earlier than relation to T.  If, on the other hand, there are events that exist but are nonpresent, then presentism is false.

How will the presentist respond? Since E does not exist on his view, while T does, and E is earlier than T, he must either (A) deny that all relations are existence-symmetric, or deny (B) that earlier than is a relation. He must either allow the possibility of genuine relations that connect nonexistents and existents, or deny that T stands in a temporal relation to E.

To  fully savor the problem we  cast it in the mold of an aporetic tetrad:

1. All relations are either existence-entailing or existence-symmetric.

2. Earlier than is a relation.

3. Presentism: only temporally present items exist.

4. Some events are earlier than others.

Each limb of the tetrad is exceedingly plausible.  But they cannot all be true:  any three, taken together, entail the negation of the remaining limb.  For example, the first three entail the negation of the fourth.  To solve the problem, we must reject one of the limbs.  Now (4) cannot be rejected because it is a datum.

Will you deny (1) and say that there are relations that are neither existence-entailing nor existence-symmetric?  I find this hard to swallow because of the following argument.  (a) Nothing can have properties unless it exists.  Therefore (b) nothing can have relational properties unless it exists. (c) Every relation gives rise to relational properties:  if Rab, then a has the property of standing in R to b, and b has the property of standing in R to a.  Therefore, (d) if R relates a and b, then both a and b exist.

Will you deny (2) and say that earlier than is not a relation?  What else could it be?

Will you deny presentism and say that that both present and nonpresent items exist?  Since it is obvious that present and nonpresent items cannot exist in the present-tense sense of 'exists,'  the suggestion has to be that present and nonpresent (past or future) items exist in a tenseless sense of 'exist.'  But what exactly does this mean?

The problem is genuine, but there appears to be no good solution, no solution that does not involve its own difficulties.

Frondizi on the Philosophical Attitude

Risieri Fondizi's What is Value? An Introduction to Axiology, tr. S. Lipp (Open Court, 1963) has stood up well since its English debut over forty five years ago. What follows is a noteworthy metaphilosophical observation of Frondizi's:

The philosophical attitude is basically problematic. He who is not capable of grasping the sense of problems and who prefers to seize upon the first solution that presents itself, and which offers him illusory stability, runs the risk of being submerged, together with his so-called solution, in a sea of difficulties. (p. 26)

'Problematic' can mean dubious. But what Frondizi intends is best rendered by 'problem-oriented.' A philosopher is someone who is sensitive to puzzles, problems, and mysteries. Or, as I like to say, the philospher is one who has the aporetic sense.   I once heard Roderick Chisholm say that one is not philosophizing until one has a puzzle. That's exactly right. But of course it's an old thought. At Theaetetus 155, Plato tells us that philosophy begins in wonder or perplexity, this being the characteristic feeling of the philosopher. Aristotle echoes the idea at Metaphysics 982b10.

Wilfrid Sellars once likened the philosopher's touch to that of King Midas. Whatever the king touched, turned into gold; whatever the  philosopher touches turns into a puzzle. The trouble with this comparison is that it suggests that philosophers create their difficulties. Not so: they discover them, or at least some of them. We could call the ones that are discovered the ground-level problems, distinguishing them from problems that arise as artifacts of theories proposed in solution of the ground-level problems. The ground-level problems are in a  certain sense 'out there' independent of our linguistic and conceptual operations. Pace Wittgenstein, they are not engendered by a  "bewtchment of our understanding by language" (eine Verhexung unseres  Verstandes durch die Sprache). Pace Rorty, they do not arise as artifacts of arbitrarily adopted ways of talking.

The problem of universals, for example, is a perennial problem. It may not interest you, or seem important, but it is there whether you like it or not, and it has repercussions for problems you probably will find important. We attribute properties to things, and sometimes the things to which we attribute the properties actually have them. But what are properties? Are they mental in nature, or perhaps linguistic? Or are properties independent of language and mind? If the latter, are they universals (repeatable entities) or particulars (unrepeatable entities such as sets or tropes)? If properties are universals, can they exist uninstantiated, or can they only exist when instantiated?  How are properties related to the things that have them. 

These are some of the questions that arise when we think about what is somewhat misleadingly called the problem of universals. 'The problem of properties' is perhaps a better moniker.

The onus probandi is on anyone who claims that this problem (or cluster of problems) is not genuine.

A Modal Aporetic Tetrad

Here is a four-limbed aporetic polyad:

1. The merely possible is not actual.

2. To be actual is to exist.

3. To exist is to be.

4. The merely possible is not nothing.

Each limb is plausible, but they cannot all be true.  The first three limbs, taken together, entail the negation of the fourth.  Indeed, any three, taken together, entail the negation of the remaining limb, as you may verify for yourself. 

Now which limb ought we reject in order to avoid logical inconsistency?  (1) is non-negotiable because purely definitional.  Everything actual is possible, but not everything possible is actual.  'Merely possible,' by definition, refers to that which is possible but not actual.  This leaves us three options.

(2)-Rejection.  One might reject the equivalence of the actual and the existent analogously as one might reject the equivalence of the temporally present and the existent.  Just as one might maintain that past events exist just as robustly as present events despite their pastness, one might maintain that merely possible items exist just as robustly as actual items.  David Lewis' extreme ('mad dog') modal realism is an example of (2)-rejection.  On his modally egalitarian scheme there is a plurality of possible worlds all on an ontological par.  Each is a maximal mereological sum of concreta.  Each of these worlds is actual at itself, but no one of these worlds is actual simpliciter.  For each world w, w is actual-at-w, but no world is actual, period.  Thus there is no such property as absolute actuality.  It is not the case that one of the worlds is privileged over all the others in point of being actual simpliciter.  What is true of a world is true of its occupants:  I enjoy no ontological privilege over that counterpart of me who is bald now and living in Boston.  Actuality is world-relative and 'actual' is accordingly an indexical term like 'now.' When I utter a token of 'now' I refer to the time of my utterance; likewise, on Lewis' theory, when I utter a token of 'actual,' I refer to the world I am in.

Having rejected (2), a Lewis-type philosopher could gloss the other limbs of the tetrad as follows.  To say that the merely possible is not actual is to say that merely possible objects (e.g. bald Bill the Bostonian) are denizens of worlds other than this one.  To say that to exist is to be is to say that there is no distinction between the existence of an object and its being in some world or other.  To say that the merely possible is not nothing is to say that objects which are not denizens of this world are denizens of some other world or worlds.

I am tempted to say that this solution, via rejection of (2), is worse than the problem.  For one has to swallow an infinity of equally real possible worlds.  Further, my possibly being bald is not some counterpart of mine's being bald in another possible world.  (This critique of course needs to be spelled out in detail.)

(3)-Rejection.  A second theoretical option is to reject the equivalence of being and existence, of that which is and that which exists.  Accordingly, there are things that are but do not exist.  They have Being but not Existence.  Everything is, but only some things exist.  The early Russell, in the Principles of Mathematics from 1903, toyed with this view although he rejected it later in his career.  If existents are a proper subset of beings, then one could locate merely possible items in among the beings that do not exist.  The merely possible would then have Being but  not Existence or Actuality.

This solution leads to an ontological population explosion much as the Lewis theory does. 

(4)-Rejection.  A third option is to deny (4) by affirming that the merely possible is nothing in reality, that it has no ontological status.   One might construe the merely possible as merely epistemic, as being merely parasitic on our ignorance, or as having no status outside our thought.   A view along these lines can be found in Spinoza. 

Intuitively, though, it seems mistaken to say that there are no genuine, mind-independent possibilities.  My writing desk, for example, is one inch from the wall, but it could have been two inches from the wall.  It is not just that I can imagine or conceive it being two inches from the wall; it really could be two inches from the wall even though this possible state of affairs was never actual and never will be actual. (Moreover, what I CAN imagine or conceive refers to real but unactual possibilities of imagination and conception; or will you say that these possibilities are themselves derivative from acts of imagining or conceiving?  If you do, then a vicious infinite regress is in the offing.))

Now suppose I had provided more rigorous and more convicing rejections of each of the three theoretical options.  Suppose that a strong case can be made that all four propositions must be accepted.  Then we would have four propositions each of which has a very strong claim on our acceptance, but which are collectively inconsistent.  (Assume that the inconsistency is demonstrable.) What might one conclude from that?  (A) One possibility is that we ought to abandon the Law of Non-Contradiction.  (B) A second is that one of the solutions must be right even though we have good reason to think that every solution is mistaken.  (C) A third is that the aporetic tetrad is an insoluble problem, a genuine intellectual knot that cannot be untied.

Note that (A), (B), and (C) form a meta-aporia.  Each of them has a claim on our acceptance, but they cannot all be true.

Suppose there are genuine but absolutely insoluble philosophical problems.  What would that show, if anything?

The Aporetics of Divine Simplicity

Thomist27 e-mails: 

Thank you first of all for a spectacular blog. I discovered Maverick Philosopher a few years ago and have been reading it regularly ever since. Through your blog, I learned that you wrote the SEP's article on divine simplicity, among similar things; I think, then, that you are qualified to answer my questions.  My questions concern divine simplicity and divine knowledge, two nuts that I've lately been making every effort to crack. First, do you think that theism can be salvaged without absolute divine simplicity? I know that there are many theists who don't believe that God is simple, but is such a concept of Deity coherent? I believe a case can be made, pace Alvin Plantinga and other theistic deniers of divine simplicity, that to deny the absolute ontological simplicity of God is to deny theism itself.  For what we mean by 'God' is an absolute reality, something metaphysically ultimate, "that than which no greater can be conceived." (Anselm)   Now an absolute reality cannot depend for its existence or nature or value upon anything distinct from itself.  It must be from itself alone, or a se.  Nothing could count as divine, or worthy of worship, or be an object of our ultimate concern, or be maximally great, if it lacked the property of aseity.  But the divine aseity, once it is granted, seems straightaway to entail the divine simplicity, as Aquinas argues in ST.  For if God is not dependent on anything else for his existence, nature, and value, then God is not a whole of parts, for a whole of parts depends on its parts to be and to be what it is.  So if God is a se, then he is not a composite being, but a simple being.  This implies that in God there is no real distinction between: existence and essence, form and matter, act and potency, individual and attribute, attribute and attribute.   In sum, if God is God, then God is simple.  To deny the simplicity of God is to deny the existence of God.  It is therefore possible for an atheist to argue:  Nothing can be ontologically simple, therefore, God cannot exist. A theist who denies divine simplicity might conceivably be taxed with idolatry inasmuch as he sets up something as God that falls short of the exacting requirements of deity.  The divine transcendence would seem to require that God cannot be a being among beings, but must in some sense be Being itself . (Deus est ipsum esse subsistens:  God is not an existent but self-subsisting Existence itself.)  On the other hand, a theist who affirms divine simplicity can be taxed, and has been taxed, with incoherence.  As an aporetician first and foremost, I seek to lay bare the problem in all its complexity under suspension of the natural urge for a quick solution. Second, if my understanding is correct, then according to the doctrine of divine simplicity, God has no intrinsic accidents. How is that compatible with divine freedom? I know it's trite, but I haven't seen a good answer to the question of how God could have properties such as having created mankind or having declined to create elves without their being just as necessary to Him as His benevolence and omnipotence (especially if He is what He does). This is indeed a problem. On classical theism, God is libertarianly free: although he exists in every metaphysically possible world, he does not create in every such world, and he creates different things in the different worlds in which he does create.  Thus the following are accidental properties of God:  the property of creating something-or-other, and the property of creating human beings.  But surely God cannot be identical to these properties as the simplicity doctrine seems to require.  It cannot be inscribed into the very nature of God that he create Socrates given that he freely creates Socrates.  Some writers have attempted to solve this problem, but I don't know of a good solution. Even if there's a solution to that problem, what's to be said about God's knowledge? Isn't His knowledge an intrinsic property of His? But, since the truth of a proposition like the planet Mars exists is contingent, isn't God's knowing it an accidental property, and, furthermore, an intrinsic accidental property? Well, this too is a problem.  If S knows that p, and p is contingent, then S's knowing that p is an accidental (as opposed to essential) property of S.  Now if God is omniscient, then he knows every (non-indexical) truth, including every contingent truth. It seems to follow that God has at least as many accidental properties as there are contingent truths.  Surely these are not properties with which God could be identical, as the simplicity doctrine seems to require.  Now there must be some contingent truths in consequence of the divine freedom; but this is hard to square with the divine simplicity.  And if it is in fact the case that God's knowledge is the cause of things, then how are we to understand His knowledge of the free actions of creatures? I know that God is supposed to be the final cause of these actions, as well as their ultimate efficient cause, but the issue is still unclear to me. This is also a problem.  The simplicity doctrine implies that God is identical to what he knows. It follows that what he knows cannot vary from world to world.   In the actual world A, Oswald shoots Kennedy at time t.  If that was a libertarianly free action, then there is a world W in which Oswald does not shoot Kennedy at t.  Since God exists in very world, and  knows what happens in every world, he knows that in A, Oswald shoots Kennedy at t and in W that Oswald does not shoot Kennedy at t. But this contradicts the simplicity doctrine, according to which what God knows does not vary from world to world.  The simplicity doctrine thus appears to collide both with divine and human freedom. I sincerely look forward to your addressing these questions. Thank you in advance for your consideration of these weighty matters. I have addressed them, but not solved them.  Solutions have been proffered, but they give rise to problems of their own -- something to be pursued in future posts.

The Aporetics of Reference to Past Individuals

'Ocham' responds: 

You say "Although Caesar no longer exists, he did exist, and so it is reasonable to take 'Caesar' as having a referent. " It would be correct to say that the proper name 'Caesar' *had* a referent. But does it *have* a referent? If it has (present tense) a referent, then there is a relation:

refers('Caesar', Caesar)

between the word and *something*. And if we accept that a *something* has to be an existing thing, we have the paradox that Caesar does not exist, but that 'Caesar' refers to *something*, and so he does exist after all.

The medievals were more conscious of this paradox because they were before Einstein. After Einstein, we have this sense that things that existed in the past are in some sense still existing, because time is a dimension of space, and because everything in space exists. So we don't see the problem of the referent of 'Caesar' in the way we see a problem with the referent of 'Zeus'.

I tend to side with the medievals. Einstein gives us no philosophical justification for the view that things do not *change* over time, which includes a change from existing to not existing. And if the referent of a proper name may cease to exist through being corrupted, how is it that a semantic relation can still exist between the name (which admittedly still exists) and the referent (which doesn't)?

This is an excellent objection and it shows that what I said is far from self-evident. The problem may be set forth as an aporetic triad:

1.  Reference is a relation that presupposes the existence of its relata.

2.  There is reference to past individuals.

3.  Presentism: The present alone exists; past and future items do not exist.

The limbs of this triad cannot all be true.  The conjunction of (1) and (2) entails the negation of (3).  The conjunction of (1) and (3) entails the negation of (2).  And the conjunction of  (2) and (3) entails the negation of (1). 

The triad is interesting because each of its limbs has a strong claim on our acceptance.  And yet they cannot all be true.  To solve the problem one must reject one of the limbs.  But which one?  It seems to me that (2) is the least rejectable of the three.  Surely we do refer to past individuals using proper names.  Boston's Scollay Square no longer exists.  But I nonetheless refer to it when I say 'My father visited Scollay Square while on shore leave during WWII.'  I should think that 'Scollay Square' is just as referential as 'Harvard Square.'  Since (2) is the most datanic of the three limbs, it is the least rejectable.  This leaves (1) and (2). 

One could reject (1) by maintaining that reference is a relation that presupposes the existence or the having existed of its relata.  Or one could reject (3) by adopting a B-theoryof time according to which past, present, and future items all enjoy tenseless existence.  Neither of these solutions is without difficulty.

Soul, Conceivability, and Possibility: An Aporetic Exercise

I am puzzling over the inferential move from X is conceivable to X is (metaphysically) possible. It would be very nice if this move were valid. But I am having trouble seeing how it could be valid.

I exist, and I have a body. But it is conceivable that I exist without a body. 'Conceivable' in this context means thinkable without broadly logical contradiction.   I distinguish between narrowly and broadly logical contradiction.  'Some cats are not cats' is NL-contradictory: it cannot be true in virtue of its very logical form.  (It is necessarily false, and its being necessarily false is grounded solely  in its logical form.) 'Some colors are sounds' is not NL-contradictory: the logical form of this sentence is such that some sentences of this form are true.  And yet 'Some colors are sounds' is contradictory in a broad sense of the term since it is necessarily the case that no color is a sound, where the necessity in question does not have a merely formal-logical ground but a 'material' one.

The Meno Paradox and the Difference Between Paradoxes and Arguments

S. C. e-mails:

I stumbled onto a question in my studies today that I am not sure how to resolve and you seem like just the person to ask. The question is this: what, exactly, makes a paradox different from a regular old argument? Consider: we tend to call paradoxes those arguments which seem sound and yet whose conclusions we are not inclined to accept. Hence, what one of my professors calls Meno’s Paradox is not a paradox in Meno’s eyes. For him it’s simply an argument that shows we can’t come to know things.  I think the same can be said for Zeno’s paradoxes. Zeno was not trying to conclude with contradictions for us to be puzzled over—he was trying to give reductio ad absurdum arguments against motion and time. If Zeno was right about time and motion then none of his arguments are paradoxes any more than the problem of evil is a paradox for the atheist. It seems to me that the only thing that makes a paradox a paradox is that the consumer is unwilling to accept its conclusion (or has independent reason to think the conclusion must be wrong). Am I missing something here?

What is the difference between a paradox and an argument?  An excellent question the answer to which depends on how 'paradox' and 'argument' are defined.  Following Nicholas Rescher, I would define a paradox as a set of individually plausible but collectively inconsistent propositions.   Meno's paradox, also known as the paradox of inquiry, is an example.  It can be cast in the form of the following aporetic tetrad: