Maverick Philosopher

More on Translating 'Something Exists' and a Response to Brightly

I issued the following challenge: translate 'Something exists' into standard first-order predicate logic with identity. This is the logic whose sources are Frege and Russell. So I call it Frege-Russell logic, or, to be cute, 'Fressellian' logic.  My esteemed commenters don''t see much of a problem here.  So let me first try to explain why I see a problem.  I then  consider David Brightly's proposal.

1. First of all, 'Something exists' cannot be rendered as 'For some x, x exists.'  This is because 'exist(s)' is not an admissible first-level predicate in Frege-Russell logic.  The whole point of the Fressellian approach is to make 'exist(s)' disappear into the machinery of quantification. There is no such propositional function as 'x exists.'  'For some x, x exists' is gibberish, syntactic nonsense in Frege-Russell logic. 

2. But the following is not gibberish: 'For some x, x = x.'  So one will be tempted to say that 'Something exists' can be rendered as 'For some x, x = x,' ('Something is self-identical') and 'Everything exists' as 'For all x, x = x' ('Everything is self-identical'). 

But this won't work either.  It is true that everything that exists is self-identical, and vice versa.  But it doesn't follow, nor is it true, that existence is self-identity. Here is one consideration.  When I say of Tom that he exists, I am not saying that he is self-identical. Suppose I hear a false rumour to the effect that Tom is no more.  But then I encounter him in the flesh.  I exclaim, "You still exist!"  Clearly, "You are still self-identical" does not mean the same.  If I said that, Tom might retort, "What the hell, man, were you worried that I had become legion?"  In some circumstances, that a man should continue in existence is surprising.  But we are never surprised by a man's continuing in self-identity.

Furthermore, when Tom ceases to exist, he does not become self-diverse.  Loss of existence is not loss of self-identity.  To put the point in formal mode, after his demise 'Tom' continues to refer to one and the same individual, Tom.  The bearer of the name is gone, but not the reference. Otherwise it could not be true that Tom is gone.  There is also a modal consideration.  Tom is a contingent being: he exists but he might not have existed.  If existence is self-identity, then Tom's possible nonexistence is Tom's possible self-diversity -- which is absurd.  It makes prima facie sense to say of an individual that it might not have existed or that it no longer exists; but it make no sense at all to say of an individual that it might not have been self-identical or that it is no longer self-identical.  If Tom might not have existed, then it is Tom who might not have existed.  But if Tom might not have been self-identical, then it is not Tom who might not have been self-identical.

So, even if everything that exists is self-identical and conversely, existence is not self-identity.  When we say that something exists we are not saying that something is self-identical, and when we say that everything exists we are not saying that everything is self-identical.  I conclude that 'Something exists' is not expressible in the terms of the Frege-Russell system.  As for 'Everything exists,' it is surely a presupposition of the whole Frege-Russell approach: the approach presupposes that Meinong was wrong to speak of nonexistent objects.  But this presupposition cannot be expressed, cannot be 'said,' in Fressellian terms.

We are in the following curious predicament.  Something that must be true if if the Fresselian system is to be tenable -- that everything exists, that there are no nonexistent objects -- is not expressible within the system.

3. David Brightly accepts my challenge to give a Frege-Russell translation of 'Something exists.'  He writes:

And as a Fressellian I accept the challenge. That property is Individual aka Object, the concept at the root of the Porphyrean tree. We can say 'Something exists' with ∃x.Object(x), ie, there is at least one object. Likewise ∀x.Object(x) (which is always true, even when the box is empty) says 'Everything exists' and its negation (which is always false) says 'Some thing is not an object'. But both these last are unenlightening---because always true and always false, respectively, they convey no information, make no distinction, are powerless to change us.

I asked: which property  is it whose instantiation is the existence of something?  David's answer is that it is the property or concept Individual or Object.  And so I take David to be saying something like the following. "Just as the existence of cats is the being-instantiated of the concept cat, the existence of something is the being-instantiated of the concept Object."

David mentions the tree of Porphyry:

David speaks of the 'root' of the tree where I speak of its apex. No matter.  However we visualize it, upside down or right side up, David's suggestion is that Object or Substance (as above) is a summum genus, a supreme genus. It is a concept superordinate to every concept, a concept under which everything falls.

Operating with a scheme like this, we can, in the spirit of Frege's dialogue with the illustrious Puenjer, reduce every existential proposition (or at least every general existential proposition) to a predication by climbing Porphyry's tree.  Thus:

Cats exist --> Some mammal is a cat
Mammals exist --> Some animal is a mammal
Animals exist --> Some  living thing is an animal
Living things exist --> Some  body is a living thing
Bodies exist --> Some  substance is a body
Substances exist --> Some Objects are substances.

The point of these translations is to dispense with 'existst(s)' by showing how propositions of the form Fs exist can be replaced salva veritate with propositions of the form Some G is a F, where G is superordinate to F.  This amounts to the elimination of existence in favor of the logical quantity, someness.

We have now climbed to the tippy-top of the tree of Porphyry. We have ascended to a concept superordinate to every concept (except itself) a genus generalissimum, a most general genus.  And what concept might that be? Such a concept must have maximal extension and so will have minimal intension. It will be devoid of all content, abstracting as it does from all differences. Frege in his dialog with Puenjer suggests something identical with itself as the maximally superordinate concept. 'There are men' and 'Men exist' thus get rendered as 'Something identical with itself is a man.' (63)  Something identical with itself is equivalent to Brightly's Object.

4. Now why can't I accept the Frege-Brightly view? Well, I've already shown that 'Everything exists' cannot be translated as 'Everything is self-identical.'  But this is tantamount to having established that the concept whose instantiation is the existence of everything cannot be the concept self-identical something or the concept Object.

Another way to see this is by considering two individuals at the very bottom of the Porphyrean tree.  So consider my cats, Max and Manny.  In respect of being cats, mammals, beasts, animals, living things, material substances, and self-identical somethings, they do not differ.  They do not differ quidditatively.  But they do differ: they differ in their very existence.  Each has his own existence.  Max is not Manny, and Manny is not Max.  That is not a mere numerical difference; it is a numerical-existential difference.  Since each cat has its own existence, the existence of either cannot be the being-instantiated of any quidditative concept. All such concepts abstract from existence.  The same goes for all individuals.  Individuals exist.  But the existence of individuals is not the being-instantiated of any concept. If you want, you can think of existent (self-identical something) as a highest genus, but Existence -- that in virtue of which things  exist and are not nothing -- is not a highest genus.  And it is Existence that is the topic.  There are no instances of Existence.  Existing things are not a kind of thing.

The Frege-Russell theory fails utterly as a theory of Existence.

As sure as I am sitting here, I am sure that I will not convince the Londonistas.  That fact is more grist for the (meta)philosophical mill.

On Translating 'Some Individual Exists' Fressellianly

An astute reader comments:

You write:

2. But can this presupposition be expressed (said) in this logic? Here is a little challenge for you Fressellians: translate 'Something exists' into standard logical notion. You will discover that it cannot be done. Briefly, if existence is instantiation, which property is it whose instantiation is the existence of something? Same problem with 'Nothing exists.' If existence is instantiation, which property is it whose non-instantiation is the nonexistence of anything? Similarly with 'Everthing exists' and 'Something does not exist.'

But couldn't we translate those expressions this way (assuming  we have only two properties: a, b)?
1. "something exists" -> "there is an x that instantiates either a or b or ab"
2. "everything exists" -> "there is an x that instantiates a and there is a y that instantiates b and there is a z that instantiates ab"
3. "nothing exists" -> 1 is false
4. "something doesn't exist" -> 2 is false

I am afraid that doesn't work.   We need focus only on on 'Some individual exists.'  The reader's proposal could be put as follows.  Given the properties F-ness and G-ness,

What 'Some individual exists' says is exactly what 'Either F-ness is instantiated or G-ness is instantiated' says.

I would insist however that they do not say the same thing, i.e., do not have the same meaning.  The expression on the left says that some individual or other, nature unspecified, exists.  The expression on the right, however, makes specific reference to the 'natures' F-ness and G-ness.  Surely, 'Some individual exists' could be true even if there are are no individuals that are either Fs or Gs. 

Note that it is not a matter of logic what properties there are.  This is an extralogical question.

On the Frege-Russell treatment of existence, 'exist(s)' is a second-level predicate, a predicate of concepts, properties, propositional functions and cognate items.  It is never an admissible  predicate of individuals.  Thus in this logic every affirmation of existence must say of some specified concept or property that it is instantiated, and every denial of existence must say of some specified concept or property that it fails of instantiation.

This approach runs into trouble when it comes to the perfectly meaningful and true 'Something exists' and 'Some individual exists.'  For in these instances  no concept or property can be specified whose instantiation is the existence of things or the existence of individuals.  To head off an objection: self-identity won't work.

That there are individuals is a necessary presupposition of the Frege-Russell logic in that without it one cannot validly move from 'F-ness is instantiated' to 'Fs exist.'  But it is a necessary presupposition that cannot be stated in the terms of the system.  This fact, I believe, is one of the motivations for Wittgenstein's distinction between the sayable and the showable.  What cannot be said, e.g., that there are individuals, is shown by the use of such individual variables as 'x.'

The paradox, I take it, is obvious.  One cannot say  that 'There are individuals' is inexpressible without saying 'There are individuals.'  When Wittgenstein assures us that there is the Inexpressible, das Unaussprechliche,  he leaves himself open to the retort: What is inexpressible? If he replies, 'That there are individuals,' then he is hoist by his own petard.

Surely it is true that there are individuals and therefore expressible, because just now expressed.

"The suicide of a thesis," says Peter Geach (Logic Matters, p. 265), "might be called Ludwig's self-mate . . . . "  Here we may have an instance of it.

The Philosophical Foundations of Slackerdom

Ludwig Wittgenstein took a dim view of Bertrand Russell's nontechnical writings.  They would include such provocative pieces as In Praise of Idleness.

Why Wittgenstein was a Better Man than Russell

Russell worried about logic.  Wittgenstein worried about logic and his sins.

The Wit and Wisdom of Bertrand Russell

Ludwig Wittgenstein sometimes shot his mouth off in summary judgment of men of very high caliber. He once remarked to M. O'C. Drury, "Russell's books should be bound in two colours: those dealing with mathematical logic in red -- and all students of philosophy should read them; those dealing with ethics and politics in blue -- and no one should be allowed to read them." (Recollections of Wittgenstein,* ed. R. Rhees, Oxford 1984, p. 112.)

Here is a passage from Russell's The Conquest of Happiness (Liveright 1930, p. 24) whose urbanity, wit, and superficiality might well have irritated the self-tormenting Wittgenstein:

I do not myself think that there is any superior rationality in being unhappy. The wise man will be as happy as circumstances permit, and if he finds the contemplation of the universe painful beyond a point, he will contemplate something else instead.

This observation ties in nicely with my remarks on short views and long views.  If middle-sized happiness is your object, then short views are probably best.  But some of us want more.

 __________

*This title is delightfully ambiguous. Read as an objective genitive, it refers to recollections about Wittgenstein, while read as a subjective genitive, it denotes Wittgenstein's recollections. The book, consisting as it does of both, is well-titled.

An Argument of Russell Against Mental Acts

Bertrand Russell's (1872-1970) The Analysis of Mind first appeared in 1921.  Lecture I contains a discussion of Brentano, Meinong, and mental acts.  He quotes the famous Brentano passage from the 1874 Psychology From an Empirical Standpoint, and then confesses that until very lately he believed "that mental phenomena have essential reference to objects . . .'" but that he no longer believes this. (p. 5)  One of Russell's arguments against acts is contained in the following passage:

. . . the act seems unnecessary and fictious. [. . .] Empirically, I cannot discover anything corresponding to the supposed act; and theoretically I cannot see that that it is indispensable.  We say: "I think so-and-so," and this word "I" suggests that thinking is the act of a person.  Meinong's "act" is the ghost of the subject, or what once was the full-blooded soul.  It is supposed that thoughts cannot just come and go, but need a person to think them. (p. 6)

Russell is making three claims.  The first is phenomenological: acts are not given to introspection.  The second is dialectical:  there are no arguments or considerations that make plausible the positing of acts.  The third is genetic:  the reason some believe that there are acts is because they have been bamboozled by the surface grammar of sentences like 'I want a unicorn' or 'I see at tree' into the view that when thinking takes place there is an agent who performs an act upon an object. 

The Phenomenology of the Situation

What is involved in the awareness of the lamp on my desk?  Phenomenologically, as it seems to me, there is awareness of (i) the lamp and of (ii) being aware of the lamp.  At a bare minimum, then,  we need to distinguish between the object of awareness and the awareness of the object.  Both items are phenomenologically accessible.  There is straightforward awareness of the lamp if it is seen or imagined or remembered, whereas the awareness of the lamp is given to introspection.  Of course, the awareness does not appear alongside the lamp as a separate object.  Being aware of the awareness of a lamp is not like being aware of a lamp being next to a clock.  And yet, phenomenologically, there is awareness of the lamp and awareness of the awareness of the lamp. Notice that I didn't smuggle in any ego or subject of awareness in my description.  So far, then, we are on solid phenomenological ground: there are objects of awareness, there is awareness of objects, and there is awareness that the two are different.  This is the phenomenological bare minimum.

But of course this does not show that there are mental acts.  For the bit of phenomenology that I have just done is consistent with the subjectlessness of awareness. If awareness is subjectless, as Sartre et al. have maintained against Husserl et al., then it cannot be articulated into individual acts of awareness  unless some individuating/differentiating factor can be specified.  But there seems to be no phenomenological evidence of such a factor. 

Well, let's see.  There is awareness of the lamp; there is awareness of the clock; there is awareness of the books piled up on the desk, etc.  But awareness appears 'diaphanous,' to borrow a word from G. E. Moore's 1903 "The Refutation of Idealism."  The diaphanousness of awareness is a phenomenological feature of it.  This being so, there is no phenomenological evidence of any act-articulation on the side of awareness.  All the articulation and differentiation appear on the side of the object.  But aren't there differences among seeing a lamp, imagining a lamp, and remembering a lamp?  No doubt, but why must they be act-differences?  It is consistent with the phenomenology of the situation that these differences too fall on the side of the object.  Instead of saying that there are acts of imagination and acts of memory, one could say that there are imaginal objects and memorative objects.

The point, then, is that phenomenology alone cannot justify the positing of mental acts. So Russell does have a point with respect to his first claim.   Phenomenology needs dialectical supplementation.

The Dialectics of the Situation

Being aware of a centaur and being aware of a mermaid are of course different.  This difference is phenomenologically evident.  But what differentiates them if there are no mental acts?  Not the objects, since they don't exist, and not the awarenesses since they are one and not two on the assumption that there are no mental acts.  And if there are no mental acts, then there are no subjects of mental acts.  And yet there must be something that accounts for the difference between awareness of a centaur and awareness of a unicorn.  The denier of acts seems at this point forced to embrace a Meinongian theory of beingless items.  He could say that the centaur-awareness and the mermaid-awareness are numerically different in virtue of the fact that a centaur and a mermaid are distinct denizens of Meinong's realm of Aussersein.

To this I respond that there are no beingless items.  The realm of Aussersein is empty.  (The arguments cannot be trotted out here.)  Hence there is no Meinongian way out.  I conclude that we are justified in positing mental acts to account for the difference.  I gave this argument already in more detail in my recent reconstruction  of an argument from Laird Addis for mental acts.

I conclude that Russell is wrong in his second claim.  If the argument I gave is sound, then acts are theoretically indispensable. 

Russell's Genetic Claim

This is fairly weak inasmuch as Russell seems not to appreciate the distinction between a mental act and a mental action.  An action is the action of an agent  who performs the action.  But a mental act is merely an occurrent episode of intentional awareness.  As such, it needn't be anchored in a substantial self.  One could reject substance ontologies as Bergmann does while admitting mental acts.  There is nothing in the notion of a mental act that requires that the subject of the act be a substance that exists self-same over time. 

Bertrand Russell on Arabic Philosophy

The following passage is from Bertrand Russell, A History of Western Philosophy (New York: Simon & Shuster, 1945), p. 427. I found it here, but without a link and without a reference. So, exploiting the resources of my well-stocked library, I located the passage, and verified that it had been properly transcribed. Whether Russell is being entirely fair to the Arabs is a further question.

Arabic philosophy is not important as original thought. Men like Avicenna and Averroes are essentially commentators. Speaking generally, the views of the more scientific philosophers come from Aristotle and the Neoplatonists in logic and metaphysics, from Galen in medicine, from Greek and Indian sources in mathematics and astronomy, and among mystics religious philosophy has also an admixture of old Persian beliefs. Writers in Arabic showed some originality in mathematics and in chemistry; in the latter case, as an incidental result of alchemical researches. Mohammedan civilization in its great days was admirable in the arts and in many technical ways, but it showed no capacity for independent speculation in theoretical matters. Its importance, which must not be underrated, is as a transmitter. Between ancient and modern European civilization, the dark ages intervened. The Mohammedans and the Byzantines, while lacking the intellectual energy required for innovation, preserved the apparatus of civilization, books, and learned leisure. Both stimulated the West when it emerged from barbarism; the Mohammedans chiefly in the thirteenth century, the Byzantines chiefly in the fifteenth. In each case the stimulus produced new thought better than that produced by the transmitters -- in the one case scholasticism, in the other the Renaissance (which however had other causes also).

Russell's Teapot: Does it Hold Water?

Here is a famous passage from Bertrand Russell's Is There a God?

Many orthodox people speak as though it were the business of sceptics to disprove received dogmas rather than of dogmatists to prove them. This is, of course, a mistake. If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.

One thing Russell is doing in this passage is making an unexceptionable point about burden of proof and/or the ad ignorantiam fallacy. If the existence of X has not been disproven, it does not follow that X exists, or even that it is reasonable to believe that X exists. So if anyone were to affirm the existence of something like Russell's celestial teapot or Edward Abbey's angry unicorn on the dark side of the moon, then the onus probandi would be on him to support his outlandish claims. The burden of proof would not rest on those who deny or dismiss such claims.

So far, so good. Russell is of course doing more than underscoring a couple of obvious points in the theory of argumentation. He is applying his points of logic to the God question. Here too I have no complaint. If the existence of God has not been disproven, it does not follow that God exists or even that it is reasonable to believe that God exists.

But the real appeal to atheists and agnostics of the Teapot passage rests on a third move Russell makes. He is clearly suggesting that belief in God (i.e., belief that God exists) is epistemically on a par with believing in a celestial teapot. Just as we have no reason to believe in celestial teapots, irate lunar unicorns (lunicorns?), flying spaghetti monsters, and the like, we have no reason to believe in God. But perhaps we should distinguish between a strong and a weak reading of Russell's suggestion:

S. Just as we cannot have any reason to believe that an empirically undetectable celestial teapot exists, we cannot have any reason to believe that God exists.

W. Just as we do not have any reason to believe that a celestial teapot exists, we do not have any reason to believe that God exists.

Now it seems to me that both (S) and (W) are plainly false: we have all sorts of reasons for believing that God exists. Here Alvin Plantinga sketches about two dozen theistic arguments. Atheists will not find them compelling, of course, but that is irrelevant. The issue is whether a reasoned case can be made for theism, and the answer is in the affirmative. Belief in God and in Russell's teapot are therefore not on a par since there are no empirical or theoretical reasons for believing in his teapot.

Another suggestion embedded in the Russell passage is the notion that if God existed, he would be just another physical thing in the physical universe. But of course this has nothing to do with anything maintained by any sophisticated theist. God is a purely spiritual being.

Another problem with the teapot analogy is that God as traditionally conceived in the West is not an isolani — to use a chess expression. He is not like an isolated pawn, unsupported and unsupporting. For if God exists, then God is the cause of the existence of every contingent being, and indeed, of every being distinct from himself. This is not true of lunar unicorns and celestial teapots. If there is a lunar unicorn, then this is just one more isolated fact about the universe. But if God exists, then everything is unified by this fact: everything has the ground of its being and its intelligibility in the creative activity of this one paradigmatic being.

This is connected with the fact that one can argue from general facts about the universe to the existence of God, but not from such facts to the existence of lunar unicorns and celestial teapots. Thus there are various sorts of cosmological argument that proceed a contingentia mundi to a ground of contingent beings. But there is no similar a posteriori argument to a celestial teapot. There are also arguments from truth, from consciousness, from apparent design, from desire, from morality, and others besides.

The very existence of these arguments shows two things. First, since they move from very general facts (the existence of contingent beings, the existence of truth) to the existence of a source of these general facts, they show that God is not a being among beings, not something in addition to what is ordinarily taken to exist. Second, these arguments give positive reason for believing in the existence of God. Are they compelling? No, but then no argument for any substantive philosophical conclusion is compelling.

People like Russell, Dawkins, and Dennett who compare God to a celestial teapot betray by so doing a failure to understand, and engage, the very sense of the theist's assertions. To sum up. (i) God is not a gratuitous posit in that there are many detailed arguments for the existence of God; (ii) God is not a physical being; (iii) God is not a being who simply exists alongside other beings. In all three respects, God is quite unlike a celestial teapot, a lunar uncorn, an invisible hippopotamus, and suchlike concoctions.

I am quite at a loss to explain why anyone should think the Teapot analogy any good. It leaks like a sieve.