Maverick Philosopher

Notes on Idealism, Realism, Frege, and Prichard

Ed Buckner sent me a pdf the first couple pages of which I reproduce below. Bibliographical data here. Emphases added. My commentary is in blue. 

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Twentieth Century Oxford Realism

Mark Eli Kalderon and Charles Travis

1 Introduction

This is a story of roughly a century of Oxford philosophy told by two outsiders.
Neither of us has ever either studied or taught there. Nor are we specially privy to
some oral tradition. Our story is based on texts. It is, moreover, a very brief, and
very highly selective, story. We mean to trace the unfolding, across roughly the
last century, of one particular line of thought—a sort of anti-idealism, and also a
sort of anti-empiricism. By focussing in this way we will, inevitably, omit, or give
short shrift to, more than one more than worthwhile Oxford philosopher. We will
mention a few counter-currents to the main flow of 20th century Oxford thought.
But much must be omitted entirely.

Our story begins with a turn away from idealism. Frege’s case against idealism, so far as it exists in print, was made, for the most part, between 1893 (in the preface to Grundgesetze volume 1) and 1918-1919 (in “Der Gedanke”). Within that same time span, at Oxford, John Cook Wilson, and his student, H.A. Prichard, developed, independently, their own case against idealism (and for what might
plausibly be called—and they themselves regarded as—a form of “realism”). Because of the way in which Cook Wilson left a written legacy it is difficult at best to give exact dates for the various components of this view. But the main ideas were probably in place by 1904, certainly before 1909, which marked the publication of Prichard’s beautiful study, “Kant’s Theory of Knowledge”. It is also quite probably seriously misleading to suggest that either Cook Wilson or Prichard produced a uniform corpus from the whole of their career—uniform either in content or in quality. But if we select the brightest spots, we find a view which overlaps with Frege’s at most key points, and which continued to be unfolded in the main lines of thought at Oxford for the rest of the century.

Frege’s main brief against idealism could be put this way: It placed the scope of experience (or awareness) outside of the scope of judgement. In doing that, it left us nothing to judge about. A central question about perception is: How can it make the world bear on what one is to think—how can it give me what are then my reasons for thinking things one way or another? The idealist answer to that, Frege showed, would have to be, “It cannot”.

BV: This is not at all clear. An example would be nice. Let me supply one. I see a tree. The seeing is a perceiving and this perceiving is a mental state of  me, the perceiver.  I see that the tree is green.  Seeing that the tree is green I come  to think that the tree is "one way or another," e.g., green as opposed to not green.  The authors seem to be asking the following question: How can perceiving something -- a tree in my example -- make the world give me the perceiver a reason for thinking the tree to be "one way or another," green for example?

This is a very strange question, one that has no clear sense.  Or at least I don't know what the authors are asking. If the question has no clear sense, then the supposedly idealist answer has no clear sense either. The authors are presumably defending some sort of realism about the objects of sense perception. If so, then it is not my perceiving that makes the world do anything. Their question ought to be: how do physical things in the external world, things that exist and have (most of) the properties they have independently of my or anyone's perceivings, make our perceivings of these things have the content that they in fact have? How does the green tree over there bring it about that I am now having an experience as of a green tree? Or is this perhaps the very question the authors are trying to ask their convoluted way?

But let's read on.

What, in Frege’s terms, “belongs to the contents of my consciousness”—what, for its presence needs someone to be aware of it, where, further, that someone must be me—cannot, just in being as it is, be what might be held, truly, to be thus and so. (This is one point Prichard retained throughout his career, and which, later on, he directed against others who he termed “sense-datum theorists”. It is also a point Cook Wilson directed, around 1904, against Stout (see section 4).

BV:  There is a solid point here, but it needs to be put clearly. The tree is in space and is green. No content of consciousness is in space or is green. Therefore, the tree is not a content of consciousness. This syllogism refutes a form of subjective or psychological idealism. But who holds it? Certainly not Kant. But let's leave Kant out of the  discussion for now. More important than Koenigsbergian exegesis is the deep and fascinating question of idealism versus realism.

What I said in the preceding paragraph needs a bit of refining. If I see a tree, then I am aware of something. That awareness-of or consciousness-of is an episode in my conscious, mental life.  So it is appropriately referred to as a 'content of consciousness.' Now consider that awareness-of just as such.  (Of course, you cannot consider my awareness, but you can consider your own similar but numerically different awareness.) Is it green? No. It is colorless. The awareness-of, as such, is not the sort of 'thing' that could have a color.  

The awareness of green is not a green awareness.  If it were green it would have to be extended in space. No color without extension. But the awareness-of, though it is in time, is not in space.  So here we have a content of consciousness that is neither colored nor in space. 

We should all will agree, then,  that a perceiving as of a green tree is not a green perceiving. This is so even if the perceiving is not merely as of the tree, but of it in the sense that implies that there exists a tree that is being perceived. Again, all colors are extended in space. But no mental act is extended in space. Ergo, no mental act is colored. A fortiori if mental acts  are as G. E. Moore once said, "diaphanous."  

What about the content of a mental act? It too is a 'content of consciousness.' Macbeth had an hallucinatory visual experience as of a dagger. The dagger-appearance is what I am now calling the content. It is clearly distinct (though not separable) from the hallucinatory experiencing.  The hallucinatory act/experiencing is not spatially extended.  What about the dagger-appearance?  Did it not seem extended to Macbeth? Don't pink rats look to be extended in space by that drunks who hallucinate them? Yes they do.  What we can say here is that while the dagger-appearance is phenomenologically extended, it is not extended in objective space. 

But there is a deeper reason for opposing subjective idealism. This I believe to be the solid point that Prichard makes.

If I judge a tree to be green, I judge it to be green whether or not I or anyone so judge it.  So if the tree is green, it is green in itself whether or not there are any perceivers.  The point is quite general: to judge of anything x that it is F is to judge that it is F in itself whether or not there are any judgers. It doesn't matter whether the judgment is true or false: a judgment that x is F purports to lay bare the way things are independently of judgers, whether or not in fact things are as the judgment states. 

So if I say that the perceiving is green, I thereby commit myself to saying that the perceiving is green in itself whether or not there are any perceivers.  But it is contradictory to maintain that something that can exist only as a content of consciousness, and thus cannot exist in itself, can also exist in itself apart from any consciousness.

What I am calling 'the solid point 'puts paid to any form of idealism that identifies physical objects with contents of consciousness if those contents exist only in contingent minded organisms such as human animals.   If there exists a tree that I perceive, it is as little in my consciousness as it is inside my head. But please note that the point just made presupposes the reality of the external world and thus begs the question against those forms of idealism that avoid the mistakes that subjective/psychological idealists make.

So, in particular, it was crucial to Frege that a thought could not be an idea (“Vorstellung”), in the sense of “idea” in which to be one is to belong to someone’s consciousness. The positive sides of these coins are: all there is for us to judge about—all there is which, in being as it is might be a way we could judge it to be—is that environment we all jointly inhabit; to be a thought is, intrinsically, to be sharable and communicable. All these are central points in Cook Wilson’s, and Prichard’s, Oxford realism. So, as they both held (early in the century), perception must afford awareness of, and relate us to, objects in our cohabited environment.

BV: The authors seem to be saying that it is not about ideas, Vorstellungen, contents of consciousness, etc. that we make judgments, but about the common physical environment in which we human animals live.  This remains vague, however, if we aren't told what "the environment" is.  Do they mean particular things in the physical world, or are they referring to the physical world as a whole? And while it is true that thoughts (either Frege's Gedanken or something very much like them) are communicable and thus sharable -- unlike contents of consciousness that are numerically different for numerically different people -- what does this have to do with "the environment"? Fregean and Frege-like thoughts are abstract objects; hence, not to be found in the physical "environment."  Of course, for Frege, thoughts/propositions are not contents of consciousness; it does not follow, however, they are in the "environment."  There are in Frege's third realm, that of abstracta. (I promise to avoid tasteless jokes about the supposedly anti-Semitic Fege and the Third Reich.) 

There is another point which Prichard, at least, shared with Frege. As Prichard
put it:

There seems to be no way of distinguishing perception and conception
as the apprehension of different realities except as the apprehension
of the individual and the universal respectively. Distinguished in this
way, the faculty of perception is that in virtue of which we apprehend
the individual, and the faculty of conception is that power of reflection
in virtue of which a universal is made the explicit object of thought.
(Prichard, 1909, 44)

Compare Frege:

A thought always contains something which reaches out beyond the
particular case, by means of which it presents this to consciousness as
falling under some given generality. (1882: Kernsatz 4) But don’t we see that the sun has set? And don’t we also thereby see that this is true? That the sun has set is no object which emits rays which arrive in our eyes, is no visible thing like the sun itself. That the sun has set is recognized as true on the basis of sensory input. (1918: 64)

For the sun to have set is a way for things to be; that it has set is the way things are according to a certain thought. A way for things to be is a generality, instanced
by things being as they are (where the sun has just set). Recognizing its instancing
is recognizing the truth of a certain thought; an exercise of a faculty of thought.

By contrast, what instances a way for things to be, what makes for that thought’s
truth, does not itself have that generality Frege points to in a thought—any more
than, on a different level, which Frege calls “Bedeutung”, what falls under a (first-level) concept might be the sort of thing things fall under. What perception affords is awareness of the sort of thing that instances a way for things to be. Perception’s role is thus, for Frege, as for Prichard, to bring the particular, or individual, in view—so as, in a favorable case, to make recognizable its instancing (some of) the ways for things to be it does. The distinction Prichard points to here is as fundamental both to him and to Frege as is, for Frege, the distinction between objects and concepts.

BV: Now things are now getting interestingly 'aporetic.' How do I know that the sun has set? I see the sun, and I see the horizon, but I don't literally see (with my eyes) that the sun has set. If the italicized words pick out an entity, it is an invisible one. As Frege says, "That the sun has set is no object that emits rays . . . ."

How do I know that the tree is green? I see the tree, and I see green at the tree, but I don't see that the tree is green. Why not? Well, 'That tree is green' is logically equivalent to 'That green tree exists.' So if I can see that the tree is green, then I can see that the green tree exists. But existence is not empirically detectable. I can sense green, but I cannot sense existence. So I cannot see that the green tree exists.  Therefore, I cannot see that the tree is green.  Existence and property-possession are invisible. More generally, they are insensible, and not because of our sensory limitations, but because existence and property-possession are not empirically detectable by any manner of critter or by any device. 

And yet I know that the tree is green and I know that the sun has set. But how? Frege's answer, "on the basis of sensory input" is lame.  Sure, there has to be sensory input for me  to know what I know in these cases, but how does it work? Such input is necessary, but it cannot be sufficient.  Here is what Frege says in Der Gedanke:

Das Haben von Sinneseindruecken ist zwar noetig zum Sehen der Dinge, aber nicht hinreichend. Was noch hinzukommen muss, ist nichts Sinnliches. (Logische Untersuchungen, 51)

To be sure, the having of sensory impressions is necessary for seeing things, but not sufficient. What yet must be added is nothing sensory.

Necessary, because seeing (with the eyes) is a sensory function that cannot occur without sensory data, which is to say, sensory givenness, sensory input. Not sufficient, because what I need to know to know that that the tree is green, is that the physical individual/object does in reality instantiate the concept/property. The problem is that I cannot see the copulative linkage in the green tree any more than I can see the existence of the green tree. For again, to see either the linkage or the existence I would have to be able to sense them when there is no sensory awareness of either.  

What Frege adds that is not sensory is the thought/proposition. But this item is off by itself in a platonic topos ouranios. How on Earth or in Plato's Heaven can Fregean thoughts avail anything for the solution of our problem? To know that the tree is green in reality I need to know the sublunary unity of thing and property here below. How is that knowledge aided by the positing of a 'ouranic' item, the thought/proposition, whose subject constituent is an abstract item as abstract as the thought itself? The Fregean thought brings together a subject-constituent, a sense, with a predicate-constituent, also a sense.  It does not bring together the concrete tree and its properties.

What the authors say above on behalf of Frege and Prichard is thus no answer at all. We are told, "Perception’s role is thus, for Frege, as for Prichard, to bring the particular, or individual, in view—so as, in a favorable case, to make recognizable its instancing (some of) the ways for things to be it does."  Are they joking?  This glides right past the problem.  What I need to know to know that the tree is green is the linkage or togetherness of individual and property in the thing in the external world. The thing is a this-such or a something-which. You cannot split the this from the such.  You cannot split perception from conception assigning to the first the job of supplying bare individuals and assigning to the second the job of providing universals.  For the problem, again, is 'methectical,' a problem of methexis: how do sensory individual and  intelligible universal meet to form the sublunary this-such?

Kant has an answer (whatever you think of it): the synthesis of individual and property/concept is achieved by the transcendental unity of apperception! 

I will have more to say about this in a later post.

Defending Barry Miller against Herman Philipse: Existence as a First-Level Property, Part II

This is the second in a series. Here is the first installment. Read it for context and references. We are still examining only the first premise of Barry Miller's cosmological argument, as sketched by Philipse:

1) Existence is a real first-level accidental property of contingent individuals.

Philipse gave two arguments contra. In my first entry I refuted the weaker of the two. Philipse argued that Kant in 1781 had already put paid to the proposition that existence is a "real predicate," i.e., a real property of individuals.  I showed that Philipse confuses two different senses of 'real.'  When the Sage of Koenigsberg tells us that Offenbar, Sein ist kein reales Praedikat, he is telling us that it is obvious that being or existence is not a first-level quidditative determination.  This is true, whether or not it is obvious.  But when Miller tells us that existence is a real property of individuals, he is telling us that it is a non-Cambridge property of individuals.  Philipse confuses 'real' in the sense of 'quidditative' with 'real' in the sense of 'non-Cambridge,' and on the basis of this confusion takes Kant to have refuted Miller.  The ineptitude of Philipse's 'argument' takes the breath away.

The other argument Philipse gives is not so easily blown out of the water, if it can be so blown at all. He writes:

It is not necessary to discuss here all the attempted refutations Miller puts forward, for the simple reason that if he fails to refute convincingly only one plausible argument to the effect that existence is not a real predicate, his negative strategy is shipwrecked.

Let me take the so-called absurdity objection as an example (pp. 21-23). According to this objection, if existence is an accidental real first-order property of individual entities, so must non-existence be, but this would imply an absurdity. For in order to attribute truly a real property to a specific individual, we must be able to refer successfully to that individual by using a proper name, a pronoun, or by pointing to it, etc. However, we can refer successfully to an individual only if that individual exists or at least has existed, so that non-existence cannot be a real property. Hence existence cannot be an accidental real first-level property of individuals either.

The absurdity objection can be put like this:

a) Existence is a (real, non-Cambridge) property of individuals if and only if nonexistence is also a (real, non-Cambridge) property of individuals.

b) Non-existence cannot be a property of individuals: if an individual exists, then it cannot have the property of nonexistence. 

Therefore

c) Existence is not a property of individuals.

This is an argument that cannot be dismissed as resting on an elementary confusion. But let's take a step back and formulate the problem as an aporetic triad or antilogism the better to reconnoiter the conceptual terrain.

a) Existence is a (real, non-Cambridge) property of individuals if and only if nonexistence is also a (real, non-Cambridge) property of individuals.

b) Non-existence cannot be a property of individuals: if an individual exists, then it cannot have the property of nonexistence. 

c*) Existence is a property of individuals.

Each of these three propositions is individually plausible. And yet they cannot all be true on pain of logical contradiction. Individually plausible, but collectively inconsistent. So, if we adhere to the law of non-contradiction,  one of the propositions must be rejected.  Which will it be?

A. The Fregean will reject (c*).  A Fregean or Fressellian for present purposes is someone who, first, holds that 'exist(s)' is univocal in sense and second, has only one admissible sense: as a second-level predicate.  Thus the general existential 'Cats exist' is logically kosher because it can be read as predicating of the first-level property of being a cat the second-level property of being instantiated.  But the singular existential 'Max exists' is not logically kosher and is indeed meaningless in roughly the way 'Max is numerous' is meaningless.  For if 'exists' is univocal and means 'is instantiated,' then one cannot meaningfully say of Max that he exists for the simple reason that it is meaningless to say of an individual that it is instantiated.  Max could conceivably have an indiscernible twin, but that would not be an instance of him. By definition, the only instantiable items are properties, concepts, and the like.  Some will say that the Fregean analysis can be made to work for singular existentials if there are such haecceity properties as identity-with-Max, 'Maxity' to give it a name.   Suppose that there are.  Then 'Max exists' is analyzable as 'Maxity is instantiated.'  But this does not alter the fact that 'exist(s)' is a second-level predicate, and existence a second-level property.

B. The Meinongian will reject (b).  A Meinongian for present purposes is someone who denies that everything exists, and holds instead that some items exist and some do not.  For the Meinongian, existence is a classificatory principle: it partitions a logically prior domain of items into those that exist and those that do not.  For the Meinongian, both existence and non-existence are first-level properties. Existence cannot be classificatory for the Fregean because, for the Fregean, everything exists.  And so for the Fregean, there cannot be a property of non-existence.

C. The Millerian -- to give him a name -- rejects (a).  A Millerian for present purposes is one who holds, against the Meinongian, that there are no nonexistent items, and against the Fregean that existence is a genuine, non-relational  property predicable of individuals.  Holding that everything exists, the Millerian cannot admit that non-existence is a real (i.e., non-Cambridge) property of individuals.  

In Part III of this series, I will examine Philipse's atempted rebuttal of Miller's rejection of (a).  For now I will merely point out that the Meinongian and Fregean positions are open to powerful objections and therefore cannot be used to refute the Millerian view.  They merely oppose it. To oppose a theory T with a questionable theory T* is not to refute T.  'Refute' is a verb of success. To refute a theory is to prove that it is untenable. Note also that the Fregean and the Meinongian are at profound loggerheads, which fact undermines both positions. After all, deep thinkers have supported each.  

My point, then, is that Philipse hasn't refuted Miller; he has merely opposed him from the point of view of the Fregean theory which is fraught with difficulties.  One cannot refute a theory with a theory that is itself open to powerful objections as the Fregean theory is.

Intentionality for Third-World Entities?

Commenter John and I are having a very productive discussion about intentionality.  I thank him for helping me clarify my thoughts about this fascinating topic.  I begin with some points on which (I think) John and I agree.

a) There is a 'third world' or third realm and it is the realm of abstracta.   (I promise: no jokes about Frege's Third Reich. But I can't promise not to speak of Original Sinn and Original Sinn-ers.) Fregean senses, whether propositional or sub-propositional, are abstracta, but not all abstracta are reference-mediating senses. John and I are operating with a provisional tripartite or tri-categorial ontology comprising the mental, the physical, and the abstract.

b) There are instances of intrinsic intentionality. Neither of us is an eliminativist about intentionality in the manner, say, of Alexander Rosenberg. (See Could Intentionality be an Illusion?)

c) There is no intentionality without intrinsic or original intentionality: it cannot be that all intentionality is derivative or a matter of ascription, pace Daniel Dennett.  (See Original and Derived Intentionality, Circles, and Regresses.)

d) Nothing physical qua physical is intrinsically intentional, although some physical items are derivatively intentional.  (Combine this true proposition with the false proposition that all mental states are physical, and you have an unsound but valid argument for the eliminativist conclusion that there is no intrinsic intentionality.)

Agreement on the foregoing points leaves open the question whether there could be intrinsically intentional abstract items.  I tend to think that there are no intrinsically intentional abstract items.  John's position, assuming I understand it, is that some abstract items are intrinsically intentional, and that some  intrinsically intentional items are not abstract, mental states being examples of the latter.

The bare bones of the debate between John and I may be set forth as an aporetic triad:

1) Fregean senses are intrinsically intentional items. 

2) Only conscious items are intrinsically intentional.

3) Fregean senses are not conscious. 

It is easy to see that this threesome is not logically consistent: the propositions cannot all be true. John and I assume that the Law of Non-Contradiction holds across the board: we are not dialetheists.  So something has to give. Which limb of the triad should we reject?  (3) is not in dispute and presumably will be accepted by all: no abstract item is conscious, and senses are abstract.  'Abstract' was defined in earlier entries, and John and I agree on its meaning. The dispute concerns (1) and (2). I reject (1) while accepting the other two propositions; John rejects (2) while accepting the other two propositions.

I argue from the conjunction of (2) and (3) to the negation of (1), while John argues from the conjunction of (1) and (3) to the negation of (2).

My rejection of (1) entails that there are no Fregean senses (Sinne).  This is because Fregean senses, by definition, are intrinsically intentional. It follows that they are essentially intrinsically intentional. So if they can't be intrinsically intentional, then they can't exist. Why are senses essentially intrinsically intentional?  Well, as platonica, senses are necessarily existent: they exist in all metaphysically possible worlds. It follows that they exist in worlds in which there are no finite minds.* Now a sense, by definition, is a mode of presentation (Darstellungsweise) of its object.  It mediates between minds and things.  Reference, whether thinking reference or linguistic reference, is routed though sense. The (re)presentational power of a sense is essential to it, and it has this power even in worlds in which there are no words to express the sense, no things to be presented by  the sense, and no minds to refer to things via senses.  For example, consider a possible world W in which there are no languages, no minds, and no planet Venus. In W the sense that 'Phosphorus' -- 'Morning Star,' Morgenstern -- expresses in our world exists (because it exists in every world) and has its (re)presentational power there in W. Thus its intentionality is intrinsic to it and does not depend on any relations to words or to things or to minds.  It (re)presents non-linguistically and non-mentally and without the need for physical embodiment.

I think it follows that there is no distinction in reality -- although there is one notionally -- between the power of a Fregean sense to represent and its exercise of this power.  There is, in other words, no distinction in reality between the power of a sense to represent and its actually representing.  I say this because the existence of what an intrinsically intentional item is of or about has no effect whatsoever on the aboutness of the item.  Suppose I am thinking about the Washington monument, but that while I am thinking about it, it ceases to exist. That change in objective reality in no way affects the aboutness of the intentional state.  Thus the power of an intrinsically intentional item to represent does not need an external, objectively real, 'trigger' to actualize the power.  The extramental existence of the Washington monument is not  a necessary condition of the aboutness of my thinking about it.  The content and aboutness of my thinking is exactly the same whether or not the monument exists 'outside the mind.' The same goes for senses. The sense of 'Phosphorus' presents Venus whether or not Venus exists. And the content of the sense is exactly the same whether or not Venus exists.

There is an important difference, however, between an intrinsically intentional mental state and a Fregean sense.   The occurrent mental state or 'act' -- in the terminology of Twardowksi, Husserl, et al. -- is the state of a mind. It is the act of a subject, the cogitatio of an ego, where the last three occurrences of 'of' all express the genitivus subjectivus.  This is essentially, not accidentally, the case.  There has to be an ego behind the cogitatio for the cogitatio to be a cogitatio of a cogitatum.  But there needn't be an ego 'behind' the sense for the sense to be a sense of or about a thing. If a Fregean sense mediates a reference between a mind and a thing, it is not essential to the mediation that there be a mind 'behind' the sense.

Here then is an argument against Fregean senses:

4) Every instance of intrinsic intentionality has both a subject and an object.
5) Some instances of reference-mediation by a sense do not have both a subject and an object.
Therefore
6) Some instances of reference-mediation by a sense are not instances of intrinsic intentionality.

When I reject the proposition that Fregean senses are intrinsically intentional items, I thereby reject the very existence of Fregean senses. I am not maintaining that Fregean senses exist but are derivatively intentional items.  I do hold, however, that there are derivatively intentional items, maps for example.  Maps get their meaning and aboutness from us original Sinn-ers. A map is not about a chunk of terrain just in virtue of the map's physical and geometrical properties. Consider the contour lines on a topographical map. The closer together, the steeper the terrain. But that closer together should mean steeper is a meaning assigned by the community of map-makers and map-users. This meaning is not intrinsic to the map qua physical object. Closer together might have meant anything, e.g., that the likelihood of falling into an abandoned mine shaft is greater.

So some things derive their referential and semantic properties from other things.  That is also true of language. Words and phrases don't mean anything in and of themselves. Mind is king: no minds, no meaning. I subscribe to the primacy of the intentional over the linguistic. 

John and I agree that Fregean senses, whether propositional or sub-propositional, are explanatory posits.  They are not 'datanic' as I like to say. Thus it is a pre-analytic or pre-theoretical datum that the sentences 'The sky is blue' and Der Himmel ist blau 'say the same thing' or can by used to say the same thing. But that this same thing is a Fregean proposition goes beyond the given and enters the explanatory realm.  One forsakes phenomenology for dialectics. Now what am I claiming exactly? That there is no need for these posits, that to posit senses is to 'multiply entities beyond necessity in violation of Occam's Razor: Entia non sunt multiplicanda praeter necessitatem?  Or am I saying something stronger, namely, that there cannot be any such items as Fregean senses? I believe my view is the latter, and not merely the former.  If senses cannot exist, then they cannot be reasonably posited either.  

John's view, I take it, is that both Fregean senses and some conscious items are intrinsically intentional or object-directed. He is not maintaining that only third-world entities (abstracta) are intrinsically intentional. By contrast, I maintain that only second-world entities (mental items, both minds and some of their occurrent states) are intrinsically intentional.

I assume that John intends 'intrinsically intentional' to be taken univocally and not analogically.  Thus he is not saying that Fregean senses are of or about first-world items in a manner that is analogous to the way second-world items are of or about first-world items.    

Fregean senses are intrinsically intentional, necessarily existent, abstract entities.  By its very nature a sense presents or represents something apart from itself, something that may or may not exist. It is a natural, not conventional, sign.  

Do I have a compelling argument against Fregean senses?  Above I mentioned the following argument:

2) Only conscious items are intrinsically intentional.

3) Fregean senses are not conscious. Therefore:

1) It is not the case that Fregean senses are intrinsically intentional.

But this argument appears to beg the question at (2).  Why can't there be intrinsically intentional items that are not conscious?  If there can be intentionality below the level of conscious mind in the form of dispositionality -- see Intentionality, Potentiality, and Dispositionality -- why con't there be intentionality above the level of conscious mind in platonica?

Nevertheless, there seems to me something incoherent about Fregean senses. They actually represent even in worlds in which there is nothing to represent and no one to whom to represent.  Consider again the sense of 'Phosphorus.'  It exists in every world including worlds in which Venus does not exist and no mind exists. In those worlds, the sense in question actually represents but does not represent anything to anyone.  It is therefore a non-representing representation, and thus an impossibility.

_____________________

*A finite mind is the kind of mind that needs such intermediary items as Fregean senses or Husserlian noemata to mediate its reference (both thinking reference and linguistic reference) to things that it cannot get completely before its mind in all their parts, properties, and relations. An archetypal intellect such as the divine mind can get at the whole of the thing 'in one blow.'  As an infinite mind it has an infinite grasp of the infinitely-propertied thing.  An infinite mind has no need of senses. The existence of senses therefore reflects the finitude of our minds.  That the reflections of this finitude should be installed in Plato's heavenly place (topos ouranos) seems strange.  It looks to be an illict hypostatization. But this thought needs a further post for its adequate deployment.

'Platonic' Propositions: A Consideration Contra. The Argument from Intrinsic Intentionality

Commenter John put the following question to me:

Which Platonist theories of propositions did you have in mind in your original post, and what are the problems involved in accepting such views?

I had in mind a roughly Fregean theory.  One problem with such a view is that it seems to require that propositions possess intrinsic intentionality.  Let me explain.

Propositions: A Broadly Fregean Theory Briefly Sketched

On one approach, propositions are abstract items. I am not suggesting that propositions are products of abstraction.  I am using 'abstract' in the (misconceived) Quinean way to cover items that are not in space, or in time, and are not causally active or passive.  We should add  that no mind is an abstract item.  Abstracta, then, are neither bodies nor minds. They comprise a third category of entity. Besides propositions, numbers and (mathematical) sets are often given as candidate members of this category. But our topic is propositions.

For specificity, we consider Frege's theory of propositions. He called them Gedanken, thoughts, which is a strangely psychologistic terminological choice for so anti-psychologistic a logician, but so be it.  Like its German counterpart, the English 'thought' is ambiguous. It could refer to an act of thinking, a mental act, or it it could refer to the intentional object or accusative of such an act.  Some use the word 'content,' but it has the disadvantage of suggesting something contained in the act of thinking.  But when I think of the river Charles, said river is not literally contained in my act of thinking.  A fortiori for Boston's Scollay Square which I am now thinking about: it no longer exists and so cannot be contained in anything.  The same is true when I think that the Charles is polluted or that Scollay Square was a magnet for sailors on shore leave. Those propositions are not  psychological realities really contained in my or anyone's acts of thinking.  And of course they are not literally in the head.  You could say that they are in the mind, but only if you mean that they are before the mind.

A proposition for Frege is the sense (Sinn) of a certain sort of sentence in the indicative mood, namely, an indicative sentence from which all indexical elements, if any, such as the tenses of verbs, have been extruded. Consider the following sentence-tokens each of which features a tenseless copula:

1. The sea is blue.
2. The sea is blue.
3. Die See ist blau.
4. Deniz mavidir.

(Since Turkish is an agglutinative language, the copula in the Turkish sentence is the suffix 'dir.')

The (1)-(4) array depicts four sentence-tokens of three sentence-types expressing exactly one proposition. Intuitively, the four sentences say the same thing, or to be precise, can be used by people to say the same thing. That 'same thing' is the proposition they express, or to be precise, that people express by (assertively) uttering them or otherwise encoding them.  The proposition is one to their many.  (I have just sounded a Platonic theme.) And unlike the sentence-tokens, the proposition is nonphysical, which has the epistemological consequence that it, unlike the sentence-tokens, cannot be seen with the eyes or heard with the ears. It is 'seen' (understood) with the mind. Herewith, a second Platonic theme. Frege is a sort of latter-day Platonist.  

So one reason to introduce propositions is to account for the fact that the same meaning-content or sense can be expressed by different people using different sentences of different languages.  We also need to account for the fact that the same thought can be expressed by the same person at different times in the same or different languages. Another reason to posit propositions is to have a stable entity to serve as vehicle of the truth-values. It is the proposition that is primarily either true or false. Given that a proposition is true, then any sentence expressing it is derivatively true.  Similarly with judgments and beliefs: they are derivatively true if true.   For Frege, propositions are the primary truth bearers or vehicles of the truth-values.  

There is quite a lot to be said for the view that a sentence-token cannot be a primary truth-bearer. For how could a string of marks on paper, or pixels on a screen, be either true or false? Nothing can be either true or false unless it has meaning, but how could mere physical marks (intrinsically) mean anything? Merely physical marks, as such, are meaningless. Therefore, a string of marks cannot be either true or false.  It is the office of minds to mean. Matter means nothing. 

One could agree that a string of marks  or a sequence of noises cannot, as such, attract a truth-value, but balk at the inference that therefore propositional meanings (senses) are self-subsistent, mind-independent abstract items.  One might plump for what could be called an 'Aristotelian' theory of propositions according to which a sentence has all the meaning it needs to attract a truth-value in virtue of its being thoughtfully uttered or otherwise tokened by someone with the intention of making a claim about the world.  The propositional sense would then be a one-IN-many and not a Platonic one-OVER-many.  The propositional sense would be a unitary sense but not a sense that could exist on its own apart from minds or mean anything apart from minds.

But how would the Aristotelian account for necessary truths, including the truths of logic, which are true in worlds in which there are no minds?  Here the Platonist has an opportunity for rejoinder.  Fregean propositions are especially useful when it comes to the necessary truths expressed by such sentences as '7 is prime.' A necessary truth is true in all possible worlds, including those worlds in which there are no minds and/or nothing physical and so no means of physically expressing truths. If truth is taken to be a property of physical items or any contingent item, then it might be difficult to account for the existence of necessary truths. The Fregean can handle this problem by saying that propositions, as abstract objects, exist in all possible worlds, and that necessarily true ones have the property of being true in all possible worlds. The Fregean can also explain how there can be necessary truths in worlds in which there is nothing physical and nothing mental either.

Propositions also function as the accusatives of the so-called 'propositional attitudes' such as belief. To believe is to believe something. One cannot just believe. One way to construe this is de dicto: to believe is to stand in a relation to a proposition or dictum. Thus if I believe that the river Charles is polluted, then the intentional object of the occurrent belief state is the proposition expressed by 'The river Charles is polluted.' (Of course, there is also a de re way of construing the belief in question: To believe that the Charles is polluted is to believe, of the river Charles, that is is polluted.)

A Consideration Contra

Well, suppose one endorses a theory of propositions such as the one just sketched. You have these necessarily existent Platonic entities called propositions some of which are true and some of which are false. There are all of these entities that there could have been.  Each necessarily exists although only some are necessarily true.  As necessarily existent and indeed necessarily existent in themselves and from themselves, they have no need of minds to 'support' them.  Hence they are not mere accusatives of mental acts.  They are apt to become accusatives but they are not essentially accusatives. They can exist without being accusatives of any mind. To borrow a phrase from Bernard Bolzano, they are Saetze an sich.  They are made for the mind, and transparent to mind, but they don't depend for their existence on any mind, finite or infinite.

Even more salient for present purposes is that these Platonic propositions are not only existent in themselves but also meaningful in themselves: they do not derive their meaning from minds.  It follows that they possess intrinsic intentionality.  At this juncture an aporetic tetrad obtrudes itself.

A. Fregean propositions are non-mental representations: they are intrinsically representative of state of affairs in the world.

B. Fregean propositions are abstract items.

C. No abstract item possesses intrinsic representational power.

D. Fregean propositions exist.

The limbs of the tetrad cannot all be true.  One can therefore reasonably argue from the conjunction of the first three to the negation of the fourth.

Kenny, Geach, and the Perils of Reading Frege into Aquinas

Here at Maverick Philosopher: Strictly Philosophical.

Atomic Sentences and Syncategorematic Elements

The Ostrich tells me that Frege has no copula. That's not wrong, but there is a nuance that muddies the waters. Suppose Al is fat. The symbolization as Fa suggests the absence of a copula and thus the absence of a syncategorematic element. There appears to be only two categorematic elements, a and F. Well, let's see.

......................................

According to Fred Sommers (The Logic of Natural Language, Oxford UP, 1982, 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:

In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements.  In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)

Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.'  Examples of syncategorematic (logical) expressions are 'not,' 'every,' and  'and.'  As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions.  Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164) 

At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts.  Consider the atomic sentence  'Al is fat.' It is symbolized thusly: Fa.  'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand).  Both expressions are categorematic or 'non-logical.'  Neither is syncategorematic.  And there are supposed to be no syncategorematic elements in the sentence:  there is just 'F' and 'a.'

But wait a minute!  What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing.  It conveys something.  It conveys that the referent of 'a' falls under the referent of 'F'.  It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element.  If this is right, then it is false that atomic sentences lack all syncategorematic elements.

Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.'  So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick.  The syncategorematic element is precisely the juxtaposition.

Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all.  A sentence is not a list.  The sentence 'Fa' is not the list 'F, a.'  A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn).  And it has a reference (Bedeutung), namely a truth value (Wahrheitswert).  No list of words (or of anything else) expresses a thought or has a truth value.  So a sentence is not a list of its constituent words.  A sentence depends on its constituent words, but it is more than them.  It is their unity. 

We here touch upon the ancient problem of the unity of the proposition first descried by the immortal Plato.

So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence.  There is need of a copulative element to tie together subject and predicate.  It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.

Note what I am NOT saying.  I am not saying that the copulative element in a sentence must be a separate sign such as 'is.'  There is no need for the copulative  'is.'  In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible.  My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate.  There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.

At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt).  They are 'gappy' or incomplete unlike objects.  The incompleteness of concepts is reflected in the incompleteness of predicate expressions.  Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap.  We can thus say that for Frege the copula is imported into the predicate.  It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.

But this would be a mistake.  For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence.  The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid.  (If there were a third thing, then Bradley's regress would be up and running.)  But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name.  There is need of a syncategorematical element in the sentence.

So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.

The Ostrich tells me that Frege has no copula. That's not wrong, but there is a nuance that muddies the waters. Suppose Al is fat. The symbolization as Fa suggests the absence of a copula and thus the absence of a syncategorematic element. There appears to be only two categorematic elements, a and F. Well, let's see.

......................................

According to Fred Sommers (The Logic of Natural Language, Oxford UP, 1982, 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:

In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements.  In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)

Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.'  Examples of syncategorematic (logical) expressions are 'not,' 'every,' and  'and.'  As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions.  Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164) 

At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts.  Consider the atomic sentence  'Al is fat.' It is symbolized thusly: Fa.  'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand).  Both expressions are categorematic or 'non-logical.'  Neither is syncategorematic.  And there are supposed to be no syncategorematic elements in the sentence:  there is just 'F' and 'a.'

But wait a minute!  What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing.  It conveys something.  It conveys that the referent of 'a' falls under the referent of 'F'.  It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element.  If this is right, then it is false that atomic sentences lack all syncategorematic elements.

Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.'  So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick.  The syncategorematic element is precisely the juxtaposition.

Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all.  A sentence is not a list.  The sentence 'Fa' is not the list 'F, a.'  A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn).  And it has a reference (Bedeutung), namely a truth value (Wahrheitswert).  No list of words (or of anything else) expresses a thought or has a truth value.  So a sentence is not a list of its constituent words.  A sentence depends on its constituent words, but it is more than them.  It is their unity. 

We here touch upon the ancient problem of the unity of the proposition first descried by the immortal Plato.

So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence.  There is need of a copulative element to tie together subject and predicate.  It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.

Note what I am NOT saying.  I am not saying that the copulative element in a sentence must be a separate sign such as 'is.'  There is no need for the copulative  'is.'  In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible.  My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate.  There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.

At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt).  They are 'gappy' or incomplete unlike objects.  The incompleteness of concepts is reflected in the incompleteness of predicate expressions.  Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap.  We can thus say that for Frege the copula is imported into the predicate.  It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.

But this would be a mistake.  For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence.  The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid.  (If there were a third thing, then Bradley's regress would be up and running.)  But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name.  There is need of a syncategorematical element in the sentence.

So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.

Did Kepler Die in Misery?

Either he did or he didn't. Suppose I say that he did, and you say that he didn't. We both presuppose, inter alia, that there was a man named 'Kepler.'  Now that proposition that we both presuppose, although entailed both by Kepler died in misery and Kepler did not die in misery is no part of what I assert when I assert that Kepler died in misery.

Why not?

Well, to proceed by reductio, if what I assert when I assert that Kepler died in misery is that (there was a man named 'Kepler' & he died in misery), then what you assert when you contradict  me is that (either there was no man named 'Kepler' or that he did not die in misery). But the latter is not what you assert, and the former is not what I assert.  That is because we take it for granted that there was a man who rejoiced under the name 'Johannes Kepler.'

What I assert is that Kepler died in misery, and what you assert is that Kepler did not die in misery.  But we both presuppose that there was a man named 'Kepler.'  The proposition that we both presuppose, while entailed by what we each assert, is not part of what we each assert.

That, I take it, is Frege's famous argument in Ueber Sinn und Bedeutung.

It seems pretty good to me.

Half-Way Fregeanism About Existence: Questions for Van Inwagen

 In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two sub-theses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being instantiated.  We can therefore call the Fregean account of existence an instantiation account.  A concept is instantiated just in case it has one or more instances.  So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated.  This seems to imply, and was taken by Frege and Russell to imply that 'Cats exist' is not about cats, but about a non-cat, a concept or propositional function, and what it says about this concept or propositional function is not that it (singularly) exists, but that it is instantiated!  (Frege: "has something falling under it"; Russell: "is sometimes true.") A whiff of paradox? Or more than just a whiff?

The paradox, in brief, is that 'Cats exist' which one might naively take to be about cats, is in reality about a non-cat, a concept or propositional function. 

Accordingly, as Russell in effect states, 'Cats exist' is in the same logical boat with 'Cats are numerous.' Now Mungojerrie is a cat; but no one will infer that Mungojerrie is numerous. That would be the fallacy of division. On the Fressellian view, one who infers that Mungojerrie exists commits the same fallacy.  'Exist(s)' is not an admissible first-level predicate.

My concern in this entry is the logical relation between the above two sub-theses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true. 

Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or of identifying existence with instantiation, or even of eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different.  But I make this point only to move on.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean sub-theses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.  One can go half-way with Frege without going  all the way.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation, that of robbing,  and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.)  What I don't understand are van Inwagen's examples of variably polyadic predicates.  Consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  I do understand that some hooved animals have one hoof per foot, some two hooves per foot, and so on, which implies variability in the number of hooves that hooved animals have. What I don't understand is the polyadicity. It seems to me that 'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental(e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

As I understand it,  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 or Antifa thugs have the building surrounded, it does not follow that each such nimrod or thug 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.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example -- which is a collective predication -- when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) does not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

Frege's Horse Paradox, Bradley's Regress, and the Problem of Predication

The concept horse is not a concept.  Thus spoke Frege, paradoxically.  Why does he say such a thing?  Because the subject expression 'the concept horse' refers to an object.  It names an object.  Concepts and objects on his scheme are mutually exclusive. No concept is an object and conversely.   Only objects can be named.  No concept can be named. Predicates are not names.  If you try to name a concept you will fail.  You will succeed only in naming an object.  You will not succeed in expressing the predicativity of the concept.  Concepts are predicable while objects are not. It is clear that one cannot predicate Socrates of Socrates. We can, however, predicate wisdom of Socrates.  It is just that wisdom is not an object.

But now we are smack in the middle of the paradox. For to explain Frege's view I need to be able to talk about the referent of the gappy predicate ' ___ is wise.'  I need to be able to say that it is a predicable entity, a concept.  But how can I do this without naming it, and thus objectifying it?  Ineffability may be the wages of Frege's absolute object-concept distinction.

To savor the full flavor of the paradox, note that the sentence 'No concept can be named'  contains the general name 'concept.'  It seems we, or rather the Fregeans, cannot say what we or they mean.  But if we cannot say what we mean, how do we know that we mean anything at all?  Is an inexpressible meaning a meaning?  Are there things that cannot be said but only shown? (Wittgenstein) Perhaps we cannot say that concepts are concepts; all we can do is show that they are by employing open sentences or predicates such as '___ is tall.'  Unfortunately, this is also paradoxical.  For I had to say what the gappy predicate shows. I had to say that concepts are concepts and that concepts are what gappy predicates (predicates that are not construed as names) express.

Why can't concepts be named?  Why aren't they a kind of higher-order object? Why can't they be picked out using abstract substantives?  Why can't we say that, in a sentence such as 'Tom is sad,' 'Tom' names an object while 'sad' names a different sort of object, a concept/property?  Frege's thought seems to be that if concepts are objects, then they cannot exercise their predicative function.  Concepts are essentially and irreducibly predicative, and if you objectify them -- think or speak of them as objects -- then you destroy their predicative function. A predicative proposition is not a juxtaposition of two objects.  If  there is Tom and there is sadness, it doesn't follow that sadness is true of Tom. What makes a property true of its subject?  An obvious equivalence: if F-ness is true of a, then *a is F* is true.  So we might ask the questions this way: What makes *a is F* true?

The Problem of the Unity of the Proposition and the Fregean Solution

We are brought back to the problem of the unity of the proposition. It's as old as Plato. It is a genuine problem, but no one has ever solved it. (Of course, I am using 'solve' as a verb of success.)

A collection of two objects is not a proposition.  The mereological sum Tom + sadness is neither true nor false; propositions are either true or false.  The unity of a proposition is a type of unity that attracts a truth value, whereas the unity of a sum does not attract a truth value.  The unity of a proposition is mighty puzzling even in the simplest cases.   It does no good to say that the copula 'is' in 'Tom is sad' refers to the instantiation relation R and that this relation connects the concept/property to the object, sadness to Tom, and in such a way as to make sadness true of Tom.  For then you sire Mr Bradley's relation regress.  It's infinite and it's vicious.  Note that if the sum Tom + sadness can exist without it being true that Tom is sad, then the sum Tom + R + sadness can also exist without it being true that Tom is sad. 

Enter Frege with his obscure talk of the unsaturatedness of concepts. Concepts exist whether or not they are instantiated, but they are  'gappy':  if a first-level concept is instantiated by an object, there is no need for a tertium quid to connect concept and object. They fit together like plug and socket, where the plug is the object and the concept the socket.  The female receptacle accepts the male plug without the need of anything to hold the two together.

On this approach no regress arises.  For if there is no third thing that holds concept and object together, then no worries can arise as to how the third thing is related to the concept on the one side and the object on the other.  But our problem about the unity of the proposition remains unsolved.  For if the concept can exist uninstantiated, then both object and concept, Tom and sadness, can exist without it being true that Tom is sad. 

The dialectic continues on and on. Philosophia longa, vita brevis. Life is brief; blog posts ought to be.

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Excerpt:

The single thing I can imagine Russell finding most shocking would be Frege’s endorsement of patriotism as an unreasoning prejudice. The absence of political insight characteristic of his times, Frege says, is due to “a complete lack of patriotism.” He acknowledges that patriotism involves prejudice rather than impartial thought, but he thinks that is a good thing: “Only Feeling participates, not Reason, and it speaks freely, without having spoken to Reason beforehand for counsel. And yet, at times, it appears that such a participation of Feeling is needed to be able to make sound, rational judgments in political matters.” These are surely surprising views for “an absolutely rational man” to express. The man who wanted to set mathematics on surer logical foundations, was content for politics to be based on emotional spasms.

Related: For Veteran's Day, 2015: Patriotism versus Jingoism

The Function-Argument Schema in the Analysis of Propositions, Part II

A second installment from the Ostrich of London. 

Another difficulty with the function-argument theory is staring us in the face, but generally unappreciated for what it is. As Geach says, the theory presupposes an absolute category-difference between names and predicables, which comes out in the choice of ‘fount’ [font] for the schematic letters corresponding to name and predicable. For example ‘Fa’, where the upper case ‘F’ represents the predicable, as Geach calls it, and lower case ‘a’ the name. As a direct result, there is only one negation of the proposition, i.e. ‘~Fa’, where the tilde negates whatever is expressed by ‘Fa’. But ‘F’ is a function mapping the referent of ‘a’ onto the True or the False, so ‘~Fa’ says that a does not map onto the True. The object a is there all right, but maps to a different truth-value. Thus ‘Fa’ implies ExFx, ‘~Fa’ implies Ex~Fx, and excluded middle (Fa or ~Fa) implies that something, i.e. a, does or does not satisfy F. The function-argument account has the bizarre consequence that the name always has a referent, which either does or does not satisfy the predicable. There is no room for the name not being satisfied. Indeed, the whole point of the function theory is to distinguish the idea of satisfaction, which only applies to predicables, from reference, which is a feature of proper names only. As Frege points out here:

The word 'common name' is confusing .. for it makes it look as though the common name stood under the same, or much the same relation to the objects that fall under the concept as the proper name does to a single object. Nothing could be more false! In this case it must, of course, appear as though a common name that belongs to an empty concept were as illegitimate as a proper name that designates [bezeichnet] nothing.

The scholastic two-term account, by contrast, allows for the non-satisfaction of the proper name. ‘Frodo is a hobbit’ is true if and only if something satisfies both ‘hobbit’ and ‘Frodo’. It is essential to Aristotle’s theory of the syllogism, as Geach notes, that the middle term (the one which appears in both premisses) can be subject in one premiss, predicate in another. The notion of ‘satisfaction’ or ‘supposition’ applies to both subject and predicate, even if the subject is a proper name like ‘Frodo’. Thus the negation of ‘Frodo is a hobbit’ can be true in two ways. Either some individual satisfies ‘Frodo’ but does not satisfy ‘hobbit’. We express this in English by so-called predicate negation ‘Frodo is not a hobbit’, where the negative is placed after the copula. Or no individual satisfies ‘Frodo’, which we can express by placing the negation before the whole proposition, ‘it is not the case that Frodo is a hobbit’. So the scholastic theory neatly accounts for empty proper names. Not so for the function-argument theory, a difficulty which was recognised early on. Frege developed a complex and (in my view) ultimately incoherent theory of sense and reference. Russell thought that proper names were really disguised descriptions, which is actually a nod to the scholastic theory.

Of course there is a separate problem for the two term theory, of making sense of a proper name not being ‘satisfied’. What concept is expressed by the proper name that is satisfied or not satisfied, and which continues to exist as a concept even if the individual ceases to exist? Bill and I have discussed this many times, probably too many times for his liking.

BV: What is particularly interesting here is the claim that Russell's theory of proper names is a nod to to the scholastic theory.  This sounds right, although we need to bear in mind that Russell's description theory is a theory of ordinary proper names. Russell also allows for logically proper names, which are not definite descriptions in disguise.  The Ostrich rightly points out that that for Frege there there is an absolute categorial difference between names and predicables.  I add that this is the linguistic mirror of the absolute categorial difference in Frege between objects and concepts (functions). No object is a concept, and no concept is an object.  No object can be predicated, and no concept can be named. This leads directly to the Paradox of the Horse:  The concept horse is not a concept. Why not? Because 'the concept horse' is a name, and whatever you name is an object. 

This is paradoxical and disturbing because it imports ineffability into concepts and thus into logic. If concepts cannot be named and objectified, then they are not wholly graspable.  This is connected with the murky notion of the unsaturatedness of concepts. The idea is not that concepts cannot exist uninstantiated; the idea is that concepts have a 'gappy' nature that allows them to combine with objects without the need for a tertium quid to tie them together.   Alles klar?

Now it seems to me that Russell maintains the absolute categorial difference between logically proper names and predicates/predicables. ('Predicable' is a Geachian term and it would be nice to hear how the Ostrich defines it.) Correct me if I am wrong, but this presupposition of an absolute categorial difference between logically proper names and predicates/predicables is a presupposition of all standard modern logic.  It is 1-1 with the assumption that there are atomic propositions.

Here is one problem.  On the Russellian and presumably also on the scholastic theory, an ordinary proper name stands to its nominatum in the same relation as a predicate to the items that satisfy it.  Call this relation 'satisfaction.'  Socrates satisfies 'Socrates' just as he and Plato et al. satisfy 'philosopher.' Now if an item satisfies a term, then it instantiates the concept expressed by the term. But what is the concept that 'Socrates' expresses?  One candidate is: the unique x such that x is the teacher of Plato. Another is: the greatest philosopher who published nothing. 

Notice, however, that on this approach singularity goes right out the window. 'Socrates' is a singular term. But 'the greatest philosopher who published nothing' is a general term despite the fact that the latter term, if satisfied, can be satisfied by only one individual in the world that happens to be actual. It is general because it is satisfied by different individuals in different possible worlds. Without prejudice to his identity, Socrates might not have been the greatest philosopher to publish nothing.  He might not have been a philosopher at all. So a description theory of names cannot do justice to the haecceity of Socrates. What makes Socrates precisely this individual cannot be some feature accidental to him. Surely the identity of an individual is essential to it.

If we try to frame a concept that captures Socrates' haecceity, we hit a brick wall.  Concepts are effable; an individual's haeceity or thisness is ineffable.  Aristotle says it somewhere, though not in Latin: Individuum ineffabile est.  The individual as such is ineffable. There is no science of the particular qua particular.  There is no conceptual understanding of the particular qua particular because the only concepts we can grasp are general in the broad way I am using 'general.'  And of course all understanding is conceptual involving as it does the subsumption of particular under concepts.

Some will try the following move.  They will say that 'Socrates' expresses the concept, Socrateity, the concept of being Socrates, or being identical to Socrates. But this haecceity concept is a pseudo-concept.  For we had to bring in the non-concept Socrates to give it content.

There are no haecceity concepts. As the Ostrich appreciates, this causes trouble for the scholastic two-name theory of predication according to which 'Socrates' and 'wise' are both names, and the naming relation is that of satisfaction.  It makes sense to say that the concept wise person is uninstantiated. But it makes no sense to say that the concept Frodoity is uninstantiated for the simple reason that there cannot be any such concept.

It looks like we are at an impasse. We get into serious trouble if we go the Fregean route and hold that names and predicates/predicables are radically disjoint and that the naming/referring relation is toto caelo different from the satisfaction relation.  But if we regress to the scholastic two-name theory, then we have a problem with empty names. 

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The Function-Argument Schema in the Analysis of Propositions

The Function-Argument Schema in the Analysis of Propositions

The Ostrich of London sends the following to which I add some comments in blue.

Vallicella: ‘One of Frege's great innovations was to employ the function-argument schema of mathematics in the analysis of propositions’.  

Peter Geach (‘History of the Corruptions of Logic’, in Logic Matters 1972, 44-61) thinks it actually originated with Aristotle, who suggests (Perihermenias 16b6) that a sentence is composed of a noun (ὄνομα) and a verb (ῥῆμα), and the verb is a sign of something predicated of something else. According to Geach, Aristotle dropped this name-predicate theory of the proposition later in the Analytics, an epic disaster ‘comparable only to the fall of Adam’, so that logic had to wait more than two thousand years before the ‘restitution of genuine logic’ ushered in by Frege and Russell. By ‘genuine logic’ he means modern predicate logic, which splits a simple proposition into two parts, a function expression, roughly corresponding to a verb, and an argument expression, roughly corresponding to a noun. ‘To Frege we owe it that modern logicians almost universally accept an absolute category-difference between names and predicables; this comes out graphically in the choice of letters from different founts [fonts] of type for the schematic letters of variables answering to these two categories’.

The Fregean theory of the proposition has never seemed coherent to me. Frege began his studies (Jena and Göttinge, 1869–74) as a mathematician. Mathematicians naturally think in terms of ‘functions’ expressing a relation between one number and another. Thus

            f(3)  =  9

where ‘3’ designates the argument or input to the function, corresponding to Aristotle’s ὄνομα, ‘f()’ the function, here y=x², corresponding to Aristotle’s ῥῆμα, and ‘9’ the value of the function. The problem is the last part. There is nothing in the linguistic form of the proposition which corresponds to the value in the linguistic form of the mathematical function. It is invisible. Now Frege thinks that every propositional function or ‘concept’ maps the argument to one of two values, either the True or the False. OK, but this is a mapping which, unlike the mathematical mapping, cannot be expressed in language. We can of course write

            ___ is wise(Socrates) = TRUE

but then we have to ask whether that equality is true or false, i.e. whether the function ‘is_wise(--) = TRUE’ itself maps Socrates onto the true or the false. The nature of the value (the ‘truth value’) always eludes us. There is a sort of veil beyond which we cannot reach, as though language were a dark film over the surface of the still water, obscuring our view of the Deep.

BV: First a quibble. There is no need for the copula 'is' in the last formula since, for Frege, concepts (which are functions) are 'unsaturated' (ungesaettigt) or incomplete.  What exactly this means, of course, is  a separate problem.  The following suffices:

___wise(Socrates) = TRUE.

The line segment '___' represents the gappiness or unsaturatedness of the concept expressed by the concept-word (Begriffswort).

Quibbling aside, the Ostrich makes two correct interrelated points, the first negative, the second positive.

The first is that while 'f(3) = 9' displays the value of the function for the argument 3, namely 9, a sentence that expresses a (contingent) proposition does NOT display its truth-value. The truth-value remains invisible. I would add that this is so whether I am staring at a physical sententional inscription or whether I am contemplating a proposition with the eye of the mind.  The truth or falsity of a contingent proposition is external to it.  No doubt, 'Al is fat' is true iff Al is fat.' But this leaves open the question whether Al is fat.  After all the biconditional is true whether or not our man is, in fact, obese.

The second point is that there has to be something external to a contingent proposition (such as the one expressed by 'Socrates is wise') that is involved in its being true, but this 'thing,' -- for Frege the truth-value -- is ineffable.  Its nature eludes us as the Ostrich correctly states.  I used the somewhat vague phrase 'involved in its being true' to cover two possibilities. One is the Fregean idea that declarative sentences have both sense and reference and that the referent (Bedeutung) of a whole declarative sentence is a truth-value.  The other idea, which makes a lot more sense to me, is that a sentence such as 'Socrates is wise' has a referent, but the referent is a truth-making fact or state of affairs, the fact of Socrates' being wise.

Now both of these approaches have their difficulties.  But they have something sound in common, namely, the idea that there has to be something external to the contingent declarative sentence/proposition involved in its being true rather than false.  There has to be more to a true proposition than its sense.  It has to correspond to reality.  But what does this correspondence really come to? Therein lies a major difficulty.  

How will the Ostrich solve it? My impression is that he eliminates the difficulty by eliminating reference to the extralinguistic entirely. 

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Half-Way Fregeanism About Existence

Another subtle existence entry to flummox and fascinate the Londonistas.  Hell, this Phoenician is flummoxed by it himself.  Ain't philosophy grand?

....................

In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated.  We can therefore call the Fregean account of existence an instantiation account.  A concept is instantiated just in case it has one or more instances.  So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated.  This implies, of course, that 'Cats exist' is not about cats, but about a non-cat, a concept, and what it says about this concept is not that it (singulatly) exists, but that it is instantiated!  A whiff of paradox? Or more than just a whiff?

My concern in this entry is the logical relation between the above two subtheses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true.  Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different.  But I make this point only to move on.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.  One can go half-way with Frege without going 'whole hog' or all the way.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.)  What I don't understand are van Inwagen's examples of variably polyadic predicates.  Consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

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.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) does not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

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In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated.  We can therefore call the Fregean account of existence an instantiation account.  A concept is instantiated just in case it has one or more instances.  So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated.  This implies, of course, that 'Cats exist' is not about cats, but about a non-cat, a concept, and what it says about this concept is not that it (singulatly) exists, but that it is instantiated!  A whiff of paradox? Or more than just a whiff?

My concern in this entry is the logical relation between the above two subtheses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true.  Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different.  But I make this point only to move on.

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.  One can go half-way with Frege without going 'whole hog' or all the way.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.)  What I don't understand are van Inwagen's examples of variably polyadic predicates.  Consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

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.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) does not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

Kenny, Geach, and the Perils of Reading Frege Back Into Aquinas

London Ed has informed me of the passing of Peter Geach.  May he find the Unchanging Light that he sought through his long and productive life of  truth-seeking in these shadowlands.  One honors a thinker best by thinking his thoughts, sympathetically, but critically.  Here is one of my attempts. Others referenced below.

............

I have been studying Anthony Kenny, Aquinas on Being (Oxford 2002).  I cannot report that I find it particularly illuminating.  I am troubled by the reading back of Fregean doctrines into Aquinas, in particular in the appendix, "Frege and Aquinas on Existence and Number." (pp. 195-204)  Since Kenny borrows heavily from Peter Geach, I will explain one of my misgivings in connection with a passage from Geach's important article, "Form and Existence" in God and the Soul.  Geach writes,

Frege, like Aquinas, held that there was a fundamental distinction in rebus answering to the logical distinction between subject and predicate -- the distinction between Gegenstand (object) and Begriff (concept). [. . .] And for Frege the Begriff, and it alone, admits of repetition and manyness; an object cannot be repeated -- kommt nie wiederholdt vor. (45-46)

So far, so good.  Geach continues:

Understood in this way, the distinction between individual and form is absolutely sharp and rigid; what can be sensibly said of one becomes nonsense if we try to say it of the other. [. . .] Just because of this sharp distinction, we must reject the Platonic doctrine that what a predicate stands for is is some single entity over against its many instances, hen epi pollon. On the contrary:  the common nature that the predicate 'man' (say) stands for can be indifferently one or many, and neither oneness nor manyness is a mark or note of human nature itself.  This point is made very clearly by Aquinas in De Ente et Essentia.  Again we find Frege echoing Aquinas; Frege counts oneness or manyness (as the case may be) among the properties (Eigenschaften) of a concept, which means that it cannot at the same time be one of the marks or notes (Merkmalen) of that concept. (46)

I smell deep confusion here.  But precisely because the confusion runs deep I will have a hard time explaining clearly wherein the confusion consists.  I will begin by making a list of what Geach gets right.

1. Objects and individuals are unrepeatable. 
2. Concepts and forms are repeatable.
3. Setting aside the special question of subsistent forms, no individual is a form, and no object is a concept.
4. Frege distinguishes between the marks of a concept and the properties of a concept. The concept man, for example, has the concept animal as one of its marks.  But animal is not a property of man, and this for the simple reason that no concept is an animal.  Man has the property of being instantiated.  This property, however, is not a mark of man since it is not included within the latter's conceptual content:  one cannot by sheer analysis of the concept man determine whether or not there are any men.  So there is a sense in which "neither oneness nor manyness is a mark or note of human nature itself."  This is true if taken in the following sense: neither being instantiated singly nor being instantiated multiply is a mark of the concept man.

But how do these points, taken singly or together, support Geach's rejection of "the Platonic doctrine that what the predicate stands for is some single entity over against its many instances"?  They don't!

It seems obvious to me that Geach is confusing oneness/manyness as the relational property of single/multiple instantiation with oneness/manyness as the monadic property of being one or many.  It is one thing to ask whether a concept is singly or multiply instantiated.  It is quite another to ask whether the concept itself  is one or many.  It is also important to realize that a Fregean first-level concept, when instantiated, does not enter into the structure of the individuals that instantiate it.  Aquinas is a constituent ontologist, but Frege is not.  This difference is deep and causes a world of trouble for those who attempt to understand Aquinas in Fregean terms.  For Frege, concepts are functions, and no function enters into the structure of its argument.  The propositional function x is a man is not a constituent of Socrates.  What's more, the value of the function for Socrates as argument is not a state of affairs with Socrates and the function as constituents. The value of the function for Socrates as argument is True; for Stromboli as argument, False.  And now you know why philosophers speak of truth-values.  It's mathematical jargon via Frege the mathematician.

The Fregean concept man is one, not many.  It is one concept, not many concepts.  Nor is it neither one nor many.  It can have one instance, or many instances, or no instance.   The Thomistic form man, however, is, considered in itself, neither one nor many.  It is one in the intellect but (possibly) many in things.  In itself, however, it is neither.  And so it is true to say that the form is not "some single entity over against its many instances."  It is not a single entity because, considered in itself, it is neither single nor multiple.

But this doesn't follow from point (3) above.  And therein consists Geach's mistake.  One cannot validly move from the "sharp distinction" between individuals/objects and forms/concepts  to the conclusion that what a predicate stands for is not a single entity.  Geach makes this mistake because of the confusion  exposed two paragraphs supra.  The mutual exclusion of objects and concepts does not entail that concepts cannot be single entities.

There is another huge problem with reading Frege back into Aquinas, and that concerns modes of existence (esse).  A form in the intellect exists in a different way than it does in things.  But if Frege is right about existence, there cannot be modes of existence.  For if existence is instantiation, then there cannot be modes of existence for the simple reason that there cannot be any modes of instantiation.

I'll say more about this blunder in another post.  It rests in turn on a failure to appreciate  the radically different styles of ontology practiced by Aquinas and Frege.  In my jargon, Aquinas is a constituent ontologist while Frege is a nonconstituent ontologist.  In the jargon of Gustav Bergmann, Aquinas is a compex ontologist while Frege is a function ontologist.

Related articles

Aquinas Meets Frege: Analysis of an Argument from De Ente et Essentia

Geach on the Real Distinction I

Defending the Distinctio Realis Against Anthony Kenny

Stanislav Sousedik and the Circularity Objection to the Thin Theory

Stanislav Sousedik's "Towards a Thomistic Theory of Predication"

Enough of politics, back to some hard-core technical philosophy.  If nothing else, the latter offers exquisite escapist pleasures not unlike those of chess. Of course I don't believe that technical philosophy is escapist; my point is a conditional one: if it is, its pleasures suffice to justify it as a form of recuperation from  this all-too-oppressive world of 'reality.'  It's what I call a 'fall-back position.'

I have been commissioned to review the collection of which the above-captioned article is a part.  The collection is entitled Metaphysics: Aristotelian, Scholastic, Analytic (Ontos Verlag 2012) and includes contributions by Peter van Inwagen, Michael Loux, E. J. Lowe, and several others.  My review article will address such topics as predication, truth-makers, bare particulars, and the advantages and liabilities of constituent ontology.  I plan a series of posts in which I dig deep into some of the articles in this impressive collection.

Stanislav Sousedik argues for an "identity theory of predication" according to which a predicative sentence such as 'Peter is a man' expresses an identity of some sort between the referent of the subject 'Peter' and the referent of the predicate 'man.'  Now to someone schooled in modern predicate logic (MPL) such an identity  theory will appear wrongheaded from the outset.  For we learned at Uncle Gottlob's knee to distinguish between the 'is' of identity ('Peter is Peter') and the 'is' of predication ('Peter is a man').

But let's give the Thomist theory a chance.  Sousedik, who is well aware of Frege's distinction, presents an argument for the identity in some sense of subject and predicate.  He begins by making the point that in the declarative 'Peter is a man' and the vocative 'Peter, come here!' the individual spoken about is (or can be) the same as the individual addressed.  But common terms such as 'man' can also be used to address a person.  Instead of saying,  'Peter, come here!' one can say 'Man, come here!'  And so we get an argument that I will put as follows:

1. Both 'Peter' and 'man' can be used to refer to the same individual. Therefore

2. A common term can be used to refer to an individual.  But

3. Common terms also refer to traits of individuals.  Therefore

4. The traits must be identical in some sense to the individuals.  E.g., the referent of 'Peter' must be in some sense identical to the referent of 'man.'

But in what sense are they identical?  Where Frege distinguishes between predication and identity, Sousedik distinguishes between weak and strong identity. 'Peter is Peter' expresses strong identity while 'Peter is a man' expresses weak identity.  "Strong identity is reflexive, symmetric, and transitive, weak identity has none of these formal properties." (254)  It thus appears that strong identity is the same as what modern analytic philosophers call (numerical) identity.  It is clear that 'Peter is a man' cannot be taken to express strong identity. But what is weak identity?

S. is a constituent ontologist.  He holds that ordinary substances such as Peter have what he calls "metaphysical parts."  Whereas Peter's left leg is a physical part of him, his traits are metaphysical parts of him.  Thus the referents of the common terms 'man,' 'animal,' living thing,' etc. are all metaphysical parts of Peter.  Clearly, these are different traits of Peter.  But are they really distinct in Peter?  S. says that they are not: they are really identical in Peter and only "virtually distinct" in him.  The phrase is defined as follows.

(Def. 1)  Between x, y there is a virtual  distinction iff (i) x, y are really identical; (ii) x can become an object of some cognitive act Φ without y being the object  of the same act Φ . . . . (251)

For example, humanity and animality in Peter are really identical but virtually distinct in that humanity can be the intentional object of a cognitive act without animality being the object of the same act.  I can focus my mental glance so to speak on Peter's humanity while leaving out of consideration his animality even though he is essentially both a man and an animal and even though animality is included within humanity. 

The idea, then, is that Peter has metaphysical parts (MPs) and that these items are really identical in Peter but virtually distinct, where the virtual distinctness of any two MPs is tied to the possibility of one of them being the object of a cognitive act without the other being the object of the same act.

Is S. suggesting that virtual distinctness is wholly mind generated?   I don't think so.  For he speaks of a potential distinction of MPs in concrete reality, a distinction that becomes actual when the understanding grasps them as distinct.  (253) And so I take the possibility mentioned in clause (ii) of the above definition to be grounded not only in the mind's power to objectify and abstract but also in a real potentiality in the MPs in substances like Peter.

One might be tempted to think of weak identity as a part-whole relation.  Thus one might be tempted to say that 'Peter' refers to Peter and 'man' to a property taken in the abstract that is predicable not only of Peter but of other human beings as well.  'Peter is a man' would then say that this abstract property is a metaphysical part of Peter.  But this is not Sousedik's or any Thomist's view.  For S. is committed to the idea that "Every empirical individual and every part or trait of it is particular." (251)  It follows that no metaphysical part of any concrete individual is a universal.  Hence no MP is an abstract property.  So weak identity is not a part-whole relation.

What is it then?

First of all, weak identity is a relation that connects a concrete individual such as Peter to a property taken abstractly.  But in what sense is Peter identical to humanity taken abstractly?   In this sense:  the humanity-in-Peter and the humanity-in-the-mind have a common constituent, namely, humanity taken absolutely as common nature or natura absoluta or natura secundum se.  (254)  What makes weak identity identity is the common constituent shared by the really existing humanity in Peter and the intentionally existing  humanity in the mind of a person who judges that Peter is human.

So if we ask in what sense the referent of 'Peter' is identical to the referent of 'man,' the answer is that they are identical in virtue of the fact that Peter has a proper metaphysical part that shares a constituent with the objective concept referred to by 'man.'  Sousedik calls this common constituent the "absolute subject."  In our example, it is human nature taken absolutely in abstraction from its real existence in Peter and from its merely intentional existence in the mind.

Critical Observations

I am deeply sympathetic to Sousedik's constituent-ontological approach, his view that existence is a first-level 'property,' and the related view that there are modes of existence. (253)  But one of the difficulties I  have with S.'s  identity theory of predication is that it relies on common natures, and I find it difficult to make sense of them as I already spelled out in a previous post.    Common natures are neither one nor many, neither universal nor particular.  Humanity is many in things but one in the mind.  Hence taken absolutely it is neither one nor many.  It is this absolute feature that allows it be the common constituent in humanity-in-Peter and humanity-in-the-mind.  And as we just saw, without this common constituent there can be no talk of an identity between Peter and humanity.  The (weak) identity 'rides on' the common constituent, the natura absoluta.  Likewise, humanity is particular in particular human beings but universal in the mind (and only in the mind).  Hence taken absolutely it is neither particular nor universal. 

But it also follows that the common nature is, in itself and taken absolutely, neither really existent nor intentionally existent.  It enjoys neither esse naturale (esse reale) nor esse intentionale.  Consequently it has no being (existence) at all. This is not to say that it is nonexistent.  It is to say that it is jenseits von Sein und Nichtsein to borrow a phrase from Alexius von Meinong, "beyond being and nonbeing." 

The difficulty is to understand how there could be a plurality of distinct items that are neither universal nor particular, neither one nor many, neither existent nor nonexistent.  Note that there has to be a plurality of them: humanity taken absolutely is distinct from animality taken absolutely, etc.  And what is the nature of this distinctness?  It cannot be mind-generated.  This is because common natures are logically and ontologically prior to mind and matter as that which mediates between them. They are not virtually distinct.  Are they then really distinct?  That can't be right either since they lack esse reale.

And how can these common or absolute natures fail to be, each of them, one, as opposed to neither one nor many?  The theory posits a plurality of items distinct among themselves.  But if each is an item, then each is one.  An item that is neither one nor many is no item at all.

There is also this consideration.  Why are common natures more acceptable than really existent universals as constituents of ordinary particulars such as Peter?    The Thomists allow universals only if they have merely intentional existence, existence 'in' or rather for a mind.  "Intentional existence belongs to entities which exist only in dependence upon the fact that they are objects of our understanding." (253)  They insist that, as S. puts it,  "Every empirical individual and every part or trait of it is particular." (251)  S. calls the latter an observation, but it is not really a datum, but a bit of theory.  It is a datum that 'man' is predicable of many different individuals.  And it is a datum that Peter is the subject of plenty of essential predicates other than 'man.'  But it is not a clear datum that Peter is particular 'all the way through.'  That smacks of a theory or a proto-theory, not that it is not eminently reasonable.

One might 'assay' (to use G. Bergmann's term) an ordinary particular as a complex consisting of a thin or 'bare'  particular instantiating universals.  This has its own difficulties, of course, but why should a theory that posits common natures be preferrable to one that doesn't but posits really existent universals instead?  Either way problems will arise.

The main problem in a nutshell is that it is incoherent to maintain that some items are such that they have no being whatsoever.  'Some items are such that they have no being whatsoever' is not a formal-logical contradiction, pace van Inwagen, but it is incoherent nonetheless.  Or so it seems to me. 

Aquinas Meets Frege: Analysis of an Argument from De Ente et Essentia

The other day I expressed my reservations as to the coherence of the Thomistic notion of a common nature.  Let's plunge a little deeper by considering the argument from Chapter 3 of Thomas Aquinas, On Being and Essence (tr. Robert T. Miller, emphasis added):

The nature, however, or the essence thus understood can be considered in two ways.
First, we can consider it according to its proper notion, and this is to consider it absolutely. In this way, nothing is true of the essence except what pertains to it absolutely: thus everything else that may be attributed to it will be attributed falsely. For example, to man, in that which he is a man, pertains animal and rational and the other things that fall in his definition; white or black or whatever else of this kind that is not in the notion of humanity does not pertain to man in that which he is a man. Hence, if it is asked whether this nature, considered in this way, can be said to be one or many, we should concede neither alternative, for both are beyond the concept of humanity, and either may befall the conception of man. If plurality were in the concept of this nature, it could never be one, but nevertheless it is one as it exists in Socrates. Similarly, if unity were in the notion of this nature, then it would be one and the same in Socrates and Plato, and it could not be made many in the many individuals. Second, we can also consider the existence the essence has in this thing or in that: in this way something can be predicated of the essence accidentally by reason of what the essence is in, as when we say that man is white because Socrates is white,
although this does not pertain to man in that which he is a man.

The argument may be set forth as follows:

1. A nature can be considered absolutely or according to the being it has in this or that individual.

2. If a nature is considered absolutely, then it is not one.  For if oneness were included in the nature of humanity, e.g., then humanity could not exist in many human beings.

3. If a nature is considered absolutely, then it is not many. For if manyness were included in the nature of humanity, e.g., then humanity could not exist in one man, say, Socrates.

Therefore

4. If a nature is considered absolutely, then it is neither one nor many, neither singular nor plural.

I find this argument intriguing because I find it extremely hard to evaluate, and because I find the conclusion to be highly counterintuitive.  It seems to me obvious that a nature or essence such as humanity is one, not many, and therefore not neither one nor many!

The following is clear.  There are many instances of humanity, many human beings.  Therefore, there can be many such instances. It follows that there is nothing in the nature of humanity to preclude there being many such instances.  But there is also nothing in the nature of humanity to require that there be many instances of humanity, or even one instance.  We can express this by saying that the nature humanity neither requires nor precludes its being instantiated. It allows but does not entail instantiation.  This nature, considered absolutely, logically allows multiple instantiation, single instantiation, and no instantiation.  It logically allows that there be many men, just one man, or no men.

That much is crystal clear.  But surely it does not follow that the nature humanity is neither one nor
many.  What Aquinas is doing above is confusing what Frege calls a mark (Merkmal) of a concept with a property (Eigenschaft)  of a concept.  (See Foundations of Arithmetic, sec. 53, first publ. 1884)  The marks of a concept are the subconcepts which are included within it.  Thus man has animal and rational as marks.  But these are not properties (Eigenschaften) of the concept man since no concept is an animal or is rational.  Being instantiated is an example of a property of man, a property that cannot be a mark of man.   If being instantiated were a mark of man, then the concept man could not fail to be instantiated.  In general, the marks of a concept are not properties thereof, and vice versa. 

A couple more examples.  Three-sided is a mark of the concept triangle, but is is not a property of this concept for the simple reason that no concept is three-sided. Male is a mark of the concept bachelor, but not a property of it since no concept is male.

Aquinas has an insight which can be expressed in Fregean jargon as follows.  Being singly instantiated -- one in reality --  and being multiply instantiated -- many in reality -- are not marks (Merkmale) of the nature humanity.  But because he (along with everyone else prior to 1884) confuses marks with properties (Eigenschaften), he concludes that the nature itself cannot be either one or many.  But surely the nature itself is one, nor many.  That is consistent with holding that the nature admits of single instantiation, multiple instantiation, or no instantiation.

To put it another way, Aquinas confuses the 'is' of predication ('Socrates is a man') with the 'is' of subordination ('Man is an animal').  Man is predicable of Socrates, but animal is not predicable of man, pace Aristotle, Categories 3b5: no concept or nature is an animal.  Socrates falls under man; Animal falls within man.  Falling-under and falling-within are different relations.  Animal is superordinate to man while man is subordinate to animal. But that is not to say that animal is predicable of man.  Both animal and man are predicable of Socrates, which is to say: Socrates falls under both concepts.  But man does not fall under animal, animal falls within man.  If man fell under animal, then the concept man would be an animal, which is absurd.

For these reasons I do not find the argument from De Ente et Essentia compelling.  It is based on confusions that the great logician Gottlob Frege was the first to sort out. But perhaps there is a good Thomist response.

Still Trying to Understand Van Inwagen's Half-Way Fregeanism about Existence

In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that

. . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)

Frege is here advancing a double-barreled thesis that splits into two subtheses.

ST1. Existence is analogous to number.

ST2. Existence is a property (Eigenschaft) of concepts and not of objects.

In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal).  Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it.  The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts.  And so one cannot validly argue from the concept of God to the existence of God.

Existence as a property of concepts is the property of being-instantiated.  We can therefore call the Fregean account of existence an instantiation account.

My concern in this entry is the logical relation between the subtheses.  Does the first entail the second or are they logically independent?  There is a clear sense in which (ST1) is true.  Necessarily, if horses exist, then the number of horses is not zero, and vice versa.  'So 'Horses exist' is logically equivalent to 'The number of horses is not zero.'  This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects.  But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications.  So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. 

(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.'  My question is whether (ST1) entails (ST2).  Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:

I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero.  Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero.  'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate.  But so are many predicates that can hardly be regarded as predicates of concepts.  The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates.  When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse.  ("Being, Existence, and Ontological Commitment," pp. 483-484)

It is this passage that I am having a hard time understanding.   It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second.  One can hold that existence is denial of the number zero without  holding that existence is a property of concepts.

But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is  'variably polyadic' and the examples van Inwagen employs.  'Robbed a bank together' is an example of a variably polyadic predicate.  It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments.  For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on.  (Example from Chris Swoyer and Francesco Orilia.) 

Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse.  What I don't understand is why van Inwagen says that 'the number of . . . is not zero' is a variably polyadic predicate. As far as I can see, it is not even polyadic, let alone variably polyadic.  What is the relation that the predicate expresses, and why is that relation multigrade?  I grant that there are indefinitely many ways the number of horses could be not zero: there could be one horse, two, three, and so on.  But what is the relation between or among horses that this supposedly polyadic predicate expresses? 

'. . .exist(s)' is monadic.  It expresses no relation.  Why not say the same about 'such that their number is not zero'?

Now consider 'are ungulates.'  If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic.  'Are hooved mammals' is monadic.

The other example is 'Horses have an interesting evolutionary history.'  This sentence is clearly not about the concept horse. But it is not about any individual horse either.  Consider Harry the horse.  Harry has a history.  He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age.  He went through all sorts of changes.  But Harry didn't evolve, and so he had no evolutionary history.  No individual evolves; populations evolve:

Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.

'Horses have an interesting evolutionary history,' then, is not about the concept horse or about any individual horse.  The predicate in this sentence appears to be non-distributive or collective.  It is like the predicate in 'Horses have been domesticated for millenia.'  That is certainly not about the concept horse.  No concept can be ridden or made to carry a load.  But it is also not about any individual horse.  Not even the Methuselah of horses, whoever he might be, has been around for millenia.

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.

My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evlutionary history' example when he is committed to saying that each horse exists.  His view , I take it, is that 'exist(s)' is a first-level non-distributive predicate.  'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate.  Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?

Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent.  I incline toward the latter.  He is trying to show that (ST1) doe not entail (ST2).  He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic.  But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evilutionary history.'  'Horses exist,' however, cannot be non-distributive.  If some horses exist, then each of them exists.  And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.

The ComBox is open if there is anyone who knows this subject and has read PvI's paper and can set me straight. 

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. 

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.

Transitivity of Predication?

I dedicate this post to London Ed, who likes sophisms and scholastic arcana.

Consider these two syllogistic arguments:

A1. Man is an animal; Socrates is a man; ergo, Socrates is an animal.
A2. Man is a species; Socrates is a man; ergo, Socrates is a species.

The first argument is valid.  On one way of accounting for its validity, we make two assumptions.  First, we assume that each of the argument's constituent sentences is a predication.  Second, we assume the principle of the Transitivity of Predication: if x is predicable of y, and y is predicable of z, then x is predicable of z.  This principle has an Aristotelian pedigree.  At Categories 3b5, we read, "For all that is predicated of the predicate will be predicated also of the subject." So if animal is predicable of man, and man of Socrates, then animal of Socrates.  

Something goes wrong, however, in the second argument.  The question is: what exactly?  Let's first of all see if we can diagnose the fallacy while adhering to our two assumptions.  Thus we assume that each occurrence of 'is' in (A2) is an 'is' of predication, and that predication is transitive.  One suggestion  -- and I take this to be the line of some Thomists -- is that (A2) equivocates on 'man.'  In the major, 'man' means 'man-in-the-mind,' 'man as existing with esse intentionale.'  In the minor, 'man' means 'man-in-reality,' 'man as existing with esse naturale.'  We thus diagnose the invalidity of (A2) by saying that it falls afoul of quaternio terminorum, the four-term fallacy.  On this diagnosis, Transitivity of Predication is upheld: it is just that in this case the principle does not apply since there are four terms.

But of course there is also the modern Fregean way on which we abandon both of our assumptions and locate the equivocation in (A2) elsewhere.  On a Fregean diagnosis, there is an equivocation on 'is' in (A2) as between the 'is' of inclusion and the 'is' of predication.  In the major premise, 'is' expresses, not predication, but inclusion: the thought is that the concept man includes within its conceptual content the subconcept species.  In the minor and in the conclusion, however, the 'is'  expresses predication: the thought is that Socrates falls under the concepts man and species.  Accordingly, (A2) is invalid because of an equivocation on 'is,' not because of an equivocation on 'man.'

The Fregean point is that the concept man falls WITHIN but not UNDER the concept animal, while the object Socrates falls UNDER but not WITHIN the concepts man and animal.  Man does not fall under animal because no concept is an animal.  Animal is a mark (Merkmal) not a property (Eigenschaft) of man.  In general, the marks of a concept are not its properties.  But concepts do have properties.  The property of being instantiated, for example, is a property of the concept man.  But it is not a mark of it.  If it were a mark, then man by its very nature would be instantiated and it would be a conceptual truth that there are human beings, which is false.

Since on the Fregean scheme the properties of concepts needn't be properties of the items that fall under the concepts, Transitivity of Predication fails.  Thus, the property of being instantiated is predicable of the concept philosopher, and the concept philosopher is predicable  of Socrates; but the property of being instantiated is not predicable of Socrates. 

Frege Meets Aquinas: A Passage from De Ente et Essentia

Here is a passage from Chapter 3 of Thomas Aquinas, On Being and Essence (tr. Robert T. Miller, emphasis added):

The nature, however, or the essence thus understood can be considered in two ways. First, we can consider it according to its proper notion, and this is to consider it absolutely. In this way, nothing is true of the essence except what pertains to it absolutely: thus everything else that may be attributed to it will be attributed falsely. For example, to man, in that which he is a man, pertains animal and rational and the other things that fall in his definition; white or black or whatever else of this kind that is not in the notion of humanity does not pertain to man in that which he is a man. Hence, if it is asked whether this nature, considered in this way, can be said to be one or many, we should concede neither alternative, for both are beyond the concept of humanity, and either may befall the conception of man. If plurality were in the concept of this nature, it could never be one, but nevertheless it is one as it exists in Socrates. Similarly, if unity were in the notion of this nature, then it would be one and the same in Socrates and Plato, and it could not be made many in the many individuals. Second, we can also consider the existence the essence has in this thing or in that: in this way something can be predicated of the essence accidentally by reason of what the essence is in, as when we say that man is white because Socrates is white, although this does not pertain to man in that which he is a man.

What intrigues me about this passage is the following argument that it contains:

1. A nature can be considered absolutely (in the abstract) or according to the being it has in this or that individual.
2. If a nature is considered absolutely, then it is not one.  For if oneness were included in the nature of humanity, e.g., then humanity could not exist in many human beings.
3. If a nature is considered absolutely, then it is not many. For if manyness were included in the nature of humanity, e.g., then humanity could not exist in one man, say, Socrates.
Therefore
4. If a nature is considered absolutely, then it is neither one nor many, neither singular nor plural.

I find this argument intriguing because I find it extremely hard to evaluate, and because I find the conclusion to be highly counterintuitive.  It seems to me obvious that a nature or essence such as humanity is one, not many, and therefore not neither one nor many!

The following is clear.  There are many instances of humanity, many human beings.  Therefore, there can be many such instances. It follows that there is nothing in the nature of humanity to preclude there being many such instances.  But there is also nothing in the nature of humanity to require that there be many instances of humanity, or even one instance.  We can express this by saying that the nature humanity neither requires nor precludes its being instantiated. This nature, considered absolutely, logically allows multiple instantiation, single instantiation, and no instantiation.  It logically allows that there be many men, just one man, or no men.

But surely it does not follow that the nature humanity is neither one nor many.  What Aquinas is doing above is confusing what Frege calls a mark (Merkmal) of a concept with a property (Eigenschaft)  of a concept.  The marks of a concept are the subconcepts which are included within it.  Thus man has animal and rational as marks.  But these are not properties of the concept man since no concept is an animal or is rational.  Being instantiated is an example of a property of man, a property that cannot be a mark of man.   In general, the marks of a concept are not properties thereof, and vice versa.  Exercise for the reader:  find a counterexample, a concept which is such that one of its marks is also a property of it.

Aquinas has an insight which can be expressed in Fregean jargon as follows.  Being singly instantiated -- one in reality --  and being multiply instantiated -- many in reality -- are not marks (Merkmale) of the nature humanity.  But because he (along with everyone else prior to 1884) confuses marks with properties (Eigenschaften), he concludes that the nature itself cannot be either one or many.

To put it another way, Aquinas confuses the 'is' of predication ('Socrates is a man') with the 'is' of subordination ('Man is an animal').  Man is predicable of Socrates, but animal is not predicable of man, pace Aristotle, Categories 3b5: no concept or nature is an animal.  Socrates falls under man; Animal falls within man.  Animal is superordinate to man while man is subordinate to animal.

For these reasons I do not find the argument from De Ente et Essentia compelling.  But perhaps there is a good Thomist response.

Kenny, Geach, and the Perils of Reading Frege Back Into Aquinas

I have been studying Anthony Kenny, Aquinas on Being (Oxford 2002).  I cannot report that I find it particularly illuminating.  I am troubled by the reading back of Fregean doctrines into Aquinas, in particular in the appendix, "Frege and Aquinas on Existence and Number." (pp. 195-204)  Since Kenny borrows heavily from Peter Geach, I will explain one of my misgivings in connection with a passage from Geach's important article, "Form and Existence" in God and the Soul.  Geach writes,

Frege, like Aquinas, held that there was a fundamental distinction in rebus answering to the logical distinction between subject and predicate -- the distinction between Gegenstand (object) and Begriff (concept). [. . .] And for Frege the Begriff, and it alone, admits of repetition and manyness; an object cannot be repeated -- kommt nie wiederholdt vor. (45-46)

So far, so good.  Geach continues:

Understood in this way, the distinction between individual and form is absolutely sharp and rigid; what can be sensibly said of one becomes nonsense if we try to say it of the other. [. . .] Just because of this sharp distinction, we must reject the Platonic doctrine that what a predicate stands for is is some single entity over against its many instances, hen epi pollon. On the contrary:  the common nature that the predicate 'man' (say) stands for can be indifferently one or many, and neither oneness nor manyness is a mark or note of human nature itself.  This point is made very clearly by Aquinas in De Ente et Essentia.  Again we find Frege echoing Aquinas; Frege counts oneness or manyness (as the case may be) among the properties (Eigenschaften) of a concept, which means that it cannot at the same time be one of the marks or notes (Merkmalen) of that concept. (46)

I smell deep confusion here.  But precisely because the confusion runs deep I will have a hard time explaining clearly wherein the confusion consists.  I will begin by making a list of what Geach gets right.

1. Objects and individuals are unrepeatable. 
2. Concepts and forms are repeatable.
3. Setting aside the special question of subsistent forms, no individual is a form, and no object is a concept.
4. Frege distinguishes between the marks of a concept and the properties of a concept. The concept man, for example, has the concept animal as one of its marks.  But animal is not a property of man, and this for the simple reason that no concept is an animal.  Man has the property of being instantiated.  This property, however, is not a mark of man since it is not included within the latter's conceptual content:  one cannot by sheer analysis of the concept man determine whether or not there are any men.  So there is a sense in which "neither oneness nor manyness is a mark or note of human nature itself."  This is true if taken in the following sense: neither being instantiated singly nor being instantiated multiply is a mark of the concept man.

But how do these points, taken singly or together, support Geach's rejection of "the Platonic doctrine that what the predicate stands for is some single entity over against its many instances"?  They don't!

It seems obvious to me that Geach is confusing oneness/manyness as the relational property of single/multiple instantiation with oneness/manyness as the monadic property of being one or many.  It is one thing to ask whether a concept is singly or multiply instantiated.  It is quite another to ask whether the concept itself  is one or many.  It is also important to realize that a Fregean first-level concept, when instantiated, does not enter into the structure of the individuals that instantiate it.  Aquinas is a constituent ontologist, but Frege is not.  This difference is deep and causes a world of trouble for those who attempt to understand Aquinas in Fregean terms.  For Frege, concepts are functions, and no function enters into the structure of its argument.  The propositional function x is a man is not a constituent of Socrates.  What's more, the value of the function for Socrates as argument is not a state of affairs with Socrates and the function as constituents. The value of the function for Socrates as argument is True; for Stromboli as argument, False.  And now you know why philosophers speak of truth-values.  It's mathematical jargon via Frege the mathematician.

The Fregean concept man is one, not many.  It is one concept, not many concepts.  Nor is it neither one nor many.  It can have one instance, or many instances, or no instance.   The Thomistic form man, however, is, considered in itself, neither one nor many.  It is one in the intellect but (possibly) many in things.  In itself, however, it is neither.  And so it is true to say that the form is not "some single entity over against its many instances."  It is not a single entity because, considered in itself, it is neither single nor multiple.

But this doesn't follow from point (3) above.  And therein consists Geach's mistake.  One cannot validly move from the "sharp distinction" between individuals/objects and forms/concepts  to the conclusion that what a predicate stands for is not a single entity.  Geach makes this mistake because of the confusion  exposed two paragraphs supra.  The mutual exclusion of objects and concepts does not entail that concepts cannot be single entities.

There is another huge problem with reading Frege back into Aquinas, and that concerns modes of existence (esse).  A form in the intellect exists in a different way than it does in things.  But if Frege is right about existence, there cannot be modes of existence.  For if existence is instantiation, then there cannot be modes of existence for the simple reason that there cannot be any modes of instantiation.

I'll say more about this blunder in another post.  It rests in turn on a failure to appreciate  the radically different styles of ontology practiced by Aquinas and Frege.  In my jargon, Aquinas is a constituent ontologist while Frege is a nonconstituent ontologist.  In the jargon of Gustav Bergmann, Aquinas is a compex ontologist while Frege is a function ontologist.

Morning Star and Evening Star

London Ed of Beyond Necessity does a good job patiently explaining the 'morning star' - 'evening star' example to one of his uncomprehending readers.  But I don't think Ed gets it exactly right.  I quibble with the following:

Summarising:
(1) The sentence “the morning star is the evening star” has informational content.
(2) The sentence “the morning star is the morning star” does not have informational content.
(3) Therefore, the term “the morning star” does not have the same informational content as “the evening star”.

One quibble is this.  Granted, the two sentences differ in cognitive value, Erkenntniswert.  (See "On Sense and Reference" first paragraph.) The one sentence expresses a truth of logic, and thus a truth knowable a priori.  The other sentence expresses a factual truth of astronomy, one knowable only a posteriori.  But note  that Frege says that they differ in cognitive value, not that the one has it while the other doesn't.  Ed says that the one has it while the other doesn't -- assuming Ed is using 'informational content' to translate Erkenntniswert.  There is some annoying slippage here.

More importantly, I don't see how cognitive value/informational content can be had by such subsentential items as 'morning star' and 'evening star.'  Thus I question the validity of the inference from (1) & (2) to (3). Neither term gives us any information.  So it cannot be that they differ in the information they give.  Nor can they be contrasted in point of giving or not giving information.  Information is conveyable only by sentences or propositions.

I say this:  neither of the names Morgenstern (Phosphorus) or Abendstern (Hesperus) have cognitive value or informational content.  (The same holds, I think, if they are not proper names but definite descriptions.)  Only indicative sentences (Saetze) and the propositions (Gedanken) they express have such value or content.  As I see it, for Frege, names have sense (Sinn) and reference (Bedeutung), and they may conjure up  subjective ideas (Vorstellungen) in the minds of their  users.  But no name has cognitive value.  Sentences and propositions, however, have sense, reference, and cognitive value.  Interestingly, concept-words (Begriffswoerter)  or predicates also have sense and reference, but no cognitive value.

I also think Ed misrepresents the Compositionality Principle.  Frege is committed to compositionality of sense (Sinn),  not compositionality of informational content/cognitive value.  So adding the C. P. to his premise set will not validate the  above inference.

The Difference Between a Truth-Bearer and a Truth-Maker

Frege makes the point that the being of a proposition cannot be identical to its being true.  This I find obvious.  There are true propositions and there are false propositions.  Therefore, for propositions (the senses of context-free declarative sentences) it cannot be the case that to be = to be true.  Furthermore, a given proposition that is contingently true is possibly such as not to be true, whence it follows that its being and its being true cannot be identical.  (Whether Frege does or would give the second argument, I don't know; but I think it is correct.)

As Frege puts its, "The being of a thought [Gedanke, proposition] thus does not consist in its being true." (Near the beginning of his essay, "Negation.")  One can grasp a proposition without knowing whether or not it is true. To grasp a proposition is not to accept it as true, to reject it as false, or to suspend judgment as to its truth-value.  To grasp a proposition is merely to have it before one's mind, to understand it.  A Fregean proposition is a sense, and no such propositional sense has as part of its sense its being true.  That's Frege's point and it strikes me as rock-solid.

Our London sparring-partner Ed now demonstrates that he still does not understand what a truth-maker is:

I wonder if a ‘truthmaker’ as understood by the advocates of truthmaking is the same sort of thing as Frege’s marvelous but impossible thought. Something that if we perceived it for what it was, would simultaneously communicate to us the truth of what it includes.

Ed is obviously confusing truth-bearers such as Fregean propositions with truth-makers.  Truth-bearers are representations; truth-makers are not.  That's one difference.  Truth-bearers are either true or false; truth-makers are not since, not being representations,  they cannot be said to be true, nor can they be said to be false.  That's a second difference.  Truth-bearers are 'bipolar,' either true or false; truth-makers are 'unipolar':  all of them obtain.  That's a third difference.  Truth-bearers are such that their being or existence does not entail their being true; truth-makers are such that their being or existence does entail their obtaining.  I am assuming that truth-makers are facts.  If a fact obtains then it exists; there are no non-obtaining facts.  That's a fourth difference.

There is no point in criticizing a doctrine one misrepresents.  First represent it fairly, then lodge objections.  And as I have said, there are reasonable objections one can bring.

So far Ed has not lodged one clear objection. 

Frege's Regress

Some of us of a realist persuasion hold that at least  some truths have need of worldly correlates that 'make them true.' This notion that (some) truths need truthmakers  is a variation on the ancient theme that truth implies a correspondence of what-is said or what-is-thought with what-is.  You all know the passages in Aristotle where this theme is sounded.

Example. Having just finished my drink, the thought expressed by an assertive utterance of 'My glass is empty' is true. But the thought is not just true; it is true because of the way things are 'outside' my mind. The glass (in reality) is (in reality) empty. So the realist says something like this: the thought (proposition, judgmental content, etc.) is true in virtue of the obtaining of a truthmaking state of affairs or fact. The thought is true because the fact obtains or exists, where 'because' does not have a causal sense but expresses the asymmetrical relation of truthmaking. The fact is the ontological ground (not the cause) of the thought's being true.

One might wonder whether this realist theory of truth leads to an infinite regress, and if it does, whether the regress is vicious. Some cryptic remarks in Gottlob Frege's seminal article, "The Thought: A Logical Inquiry," suggest a regress argument against the correspondence theory of truth.

For Frege, a thought (Gedanke) or proposition is the sense (Sinn) of a context-free declarative sentence. 'Snow is white' and its German translation Schnee ist weiss are examples of context-free declarative sentences. 'Context-free' means that all indexical elements have been extruded including verb tenses.  When we say that a sentence such as 'Snow is white' is true, what we are really saying is that the sense of this sentence is true.  The primary truth-vehicles are propositions, sentences being truth-bearers only insofar as they express true propositions.

Now could the being-true of a sentential sense consist in its correspondence to something else? Frege rejects this notion: "In any case, being true does not consist in the correspondence of this sense with something else, for otherwise the question of truth would reiterate itself to infinity." (Philosophical Logic, ed. Strawson, p. 19) A little earlier, Frege writes,

For what would we then have to do to decide whether something were true? We should have to enquire whether it were true that an idea and a reality, perhaps, corresponded in the laid-down respect. And then we should be confronted by a question of the same kind and the game could begin again. So the attempt to explain truth as correspondence collapses. And every other attempt to define truth collapses too. (Ibid.)

What exactly is Frege's argument here? We begin by noting that

1. Necessarily, for any proposition p, it is true that p iff p.

This equivalence, which I hope nobody will deny, gives rise to an infinite regress, call it the truth regress. For from (1) we can infer that if snow is white, then it is true that snow is white, and
iterating the operation, if it is true that snow is white, then it is true that it is true that snow is white, and so on without end. This is an infinite regress all right, but it is obviously benign. For if
we establish the base proposition, Snow is white, then we ipso facto establish all the iterations. Our establishing that snow is white does not depend on a prior establishing that it is true that snow is white. In general, our establishing of any proposition in the infinite series does not depend on having first established the next proposition in the series. The truth regress, though infinite, is benign.

Note that if the truth-regress were vicious, then the notion of truth itself would have been shown to be incoherent. For the truth-regress is a logical consequence of the equivalence principle (1) above, a principle that simply unpacks our understanding of 'true.' So if the truth-regress were vicious, then (1) would not be unproblematic, as it surely is.

It follows that if Frege's Regress is to amount to a valid objection to the definition of truth as correspondence, "and [to] every other attempt to define truth," then Frege's Regress must be different from the truth regress. In particular, it must be a vicious regress. Only vicious infinite regresses have the force of philosophical refutations.  But then what is Frege's Regress? Consider

2. Necessarily, for any p, it is true that p iff *p* corresponds to reality.

One can think up counterexamples to (2), but the precise question before us is whether (2) issues in a vicious infinite regress. Now what would this regress (progress?) look like? Let 'T(p)' abbreviate
'it is true that p.' And let 'C*p*' abbreviate '*p* corresponds to reality.' (The asterisks function like Quine's corners.) The regress, then, looks like this:

3. p iff T(p) iff C*p* iff T(C*p*) iff C(T(C*p*)) iff T(C(T(C*p*) iff C(T(C(T(C*p*)) . . .
   
Is (3) a vicious regress? It would be vicious if one could establish T(p) only by first establishing C*p* and so on. But if these two terms have the same sense, in the way that the first and second terms have the same sense, then (3) will be as benign as the truth regress.  Suppose that 'It is true that p' and '*p* corresponds to reality' have  the same sense. Suppose in other words that the correspondence theory of truth is the theory that the sense or meaning of these distinct sentences is the same. It would then follow that to establish that it is true that p and to establish that *p* corresponds to reality would come to the same thing, whence it would follow that the regress is benign.

For the regress to be vicious, the second and third terms must differ in sense. For again, if the second and third terms do not differ in sense, then to establish one is to establish the other, and it would not be case that to establish that it is true that p one would first have to establish that *p* corresponds to reality or to some chunk of reality. But if the second and third terms do not differ in sense, then it appears that the regress doesn't get started at all. For the move from the second term to the third to be valid, the entailment must be grounded in the sense of the second term: the third term must merely unpack the sense of the second term. If, however, the two terms are not sense-connected, then no infinite regress is ignited.

My interim conclusion is that it is not at all clear that Frege's Regress is either benign, or not a regress at all, and therefore not at all clear that it constitutes a valid objection to theories of truth, in particular to the theory that truth resides in correspondence.

REFERENCE: Peter Carruthers, "Frege's Regress," Proc. Arist. Soc., vol. LXXXII, 1981/1982, pp. 17-32.
 

Atomic Sentences and Syncategorematic Elements

According to Fred Sommers (The Logic of Natural Language, p. 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:

In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements.  In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)

Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.'  Examples of syncategorematic (logical) expressions are 'not,' 'every,' and  'and.'  As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions.  Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164) 

At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts.  Consider the atomic sentence  'Al is fat.' It is symbolized thusly: Fa.  'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand).  Both expressions are categorematic or 'non-logical.'  Neither is syncategorematic.  And there are supposed to be no syncategorematic elements in the sentence:  there is just 'F' and 'a.'

But wait a minute!  What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing.  It conveys something.  It conveys that the referent of 'a' falls under the referent of 'F'.  It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element.  If this is right, then it is false that atomic sentence lack all syncategorematic elements.

Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.'  So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick.  The syncategorematic element is precisely the juxtaposition.

Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all.  A sentence is not a list.  The sentence 'Fa' is not the list 'F, a.'  A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn).  And its has a reference (Bedeutung), namely a truth value (Wahrheitswert).  No list of words (or of anything else) expresses a thought or has a truth value.  So a sentence is not a list of its constituent words.  A sentence depends on its constituent words, but it is more than them.  It is their unity. 

So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence.  There is need of a copulative element to tie together subject and predicate.  It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.

Note what I am NOT saying.  I am not saying that the copulative element in a sentence must be a separate sign such as 'is.'  There is no need for the copulative  'is.'  In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible.  My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate.  There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.

At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt).  They are 'gappy' or incomplete unlike objects.  The incompleteness of concepts is reflected in the incompleteness of predicate expressions.  Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap.  We can thus say that for Frege the copula is imported into the predicate.  It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.

But this would be a mistake.  For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence.  The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid.  (If there were a third thing, then Bradley's regress would be up and running.)  But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name.  There is need of a syncategorical element in the sentence.

So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.

Nota Notae Est Nota Rei Ipsius and the Ontological Argument

(By popular demand, I repost the following old Powerblogs entry.)

"The mark of a mark is a mark of the thing itself." I found this piece of scholasticism in C. S. Peirce. (Justus Buchler, ed., Philosophical Writings of Peirce, p. 133) It is an example of what Peirce calls a   'leading principle.'

Let's say you have an enthymeme:

   Enoch was a man
   -----
   Enoch died.

Invalid as it stands, this argument can be made valid by adding a premise. (Any invalid argument can be made valid by adding a premise.) Add 'All men die' and the argument comes out valid. Peirce writes:

     The leading principle of this is nota notae est nota rei ipsius.
     Stating this as a premiss, we have the argument,

     Nota notae est nota rei ipsius
     Mortality is a mark of humanity, which is a mark of Enoch
     -----
     Mortality is a mark of Enoch.

But is it true that the mark of a mark is a mark of the thing itself? There is no doubt that mortality is a mark of humanity in the following sense: The concept humanity includes within its conceptual content the superordinate concept mortal, which implies that, necessarily, if anything is human, then it is mortal. But mortality is not a mark, but a property, of Enoch. I am alluding to Frege's distinction between a Merkmal and an Eigenschaft. Frege explains this distinction in various places, one being The Foundations of Arithmetic, sec. 53. But rather than quote Frege, I'll explain the distinction in my own way using a totally original example.

Consider the concept bachelor. This is a first-order or first-level concept in that the items that fall under it are not concepts but objects. The marks of a first-order concept are properties of the objects that fall under the concept. Now the marks of bachelor are unmarried, male, adult, and not a member of a religious order. These marks are themselves concepts, concepts one can extract from bachelor by analysis. Given that Tom falls under bachelor, he has these marks as properties. Thus unmarried, etc. are not marks of Tom, but properties of Tom, while unmarried, etc. are not properties of bachelor but marks of bachelor.

To appreciate the Merkmal (mark)-Eigenschaft (property) distinction, note that the relation between a concept and its marks is entirely different from the relation between a concept and its instances. A first-order concept includes its marks without instantiating them, while an object instantiates its properties without including them.

This is a very plausible line to take. It makes no sense to say of a concept that it is married or unmarried, so unmarried cannot be a property of the concept bachelor. Concepts don't get married or remain single. But it does make sense to say that a concept includes certain other concepts, its marks. On the other hand, it makes no sense to say of Tom that he includes certain concepts since he could do such a thing only if he were a concept, which he isn't. But it does make sense to say of Tom that he has such properties as being a bachelor, being unmarried, being an adult, etc.

Reverting to Peirce's example, mortality is a mark of humanity, but not a mark of Enoch. It is a property of Enoch. For this reason the scholastic formula is false. Nota notae NON est nota rei ipsius. The mark of a mark is not a mark of the thing itself but a property of the thing itself.

No doubt commenter Edward the Nominalist will want to wrangle with me over this slight to his scholastic lore, and I hope he does, since his objections will aid and abet our descent into the labyrinth of this fascinating cluster of problems. But for now, two quick applications.

One is to the ontological argument, or rather to the ontological argument aus lauter Begriffen as Kant describes it, the ontological argument "from mere concepts." So we start with the concept of God and analyze it. God is omniscient, etc. But 'surely' existence is also contained in the concept of God. For a God who did not exist would lack a perfection, a great-making property; such a God would not be id quo maius cogitari non posse. He would not be that than which no greater can be conceived. To conceive God, then, is to conceive an existing God, whence it follows that God exists! For if you are conceiving a nonexistent God, then you are not conceiving God.

Frege refutes this version of the OA -- not the only or best version I hasten to add -- in one sentence: Weil Existenz Eigenschaft des Begriffes ist, erreicht der ontologische Beweis von der Existenz Gottes sein Ziel nicht. (Grundlagen der Arithmetik, sec. 53)  "Because existence is a property of concepts, the ontological argument for the existence of God fails to attain its goal." What Frege is saying is that the OA "from mere concepts" rests on the mistake of thinking of existence as a mark of concepts as opposed to a property of concepts.  No concept for Frege is such that existence is included within it. Existence is rather a property of concepts, the property of having an instance.

The other application of my rejection of the scholastic formula above is to the logical question of the correct interpretation of singular propositions. The scholastics treat singulars as if they are generals as I explained fully in previous posts. But if Frege is right, this is a grave logical error since it rides roughshod over the mark/property distinction. To drag this all into the full light of day will take many more posts.

Being as the Apotheosis of the Copula: Frege's Eliminativism in his Dialogue with Pünjer on Existence

Some time before 1884, Gottlob Frege had a discussion about existence with the Protestant theologian Bernard Pünjer (1850-1885). A record of the dialogue was found in Frege's Nachlass, and an English translation is available in Gottlob Frege: Posthumous Writings, eds. Hans Hermes et al., University of Chicago Press, 1979. Herewith, some critical commentary on part of the dialogue.

1. We have often discussed  'thin' or deflationary approaches to Being or existence. On a thin approach, existence is not a metaphysical or ontological topic, but a merely logical one. Consider the general   existential, 'Cats exist.' For Frege, the content of such a general existential does not lie in 'exist' but "in the form of the particular judgment." (63) Frege uses the good old 19th century term 'judgment' (Urteil) but the point could also be put, with minor adjustments, in terms of  indicative sentences, statements, and propositions. Particular judgments are the I- and O-judgments of the Square of Opposition: those of the form Some S is P and Some S is not P.

Frege's contention, then, is that the content of affirmative general existentials lies in the logical form: Some S is P. But how do we put 'Cats exist' into this form? We need a concept superordinate to the   concept cat, say, the concept mammal. We can then write, 'Some mammals are cats.' If we acquiesce in the natural anti-Meinongian presupposition that there are no nonexistent items, then 'Cats exist' is true if and only if  'Some mammals are cats' is true.

This translation illustrates what Frege means when he says that the content of affirmative general existentials does not lie in 'exist'  but in the [logical] form of the particular judgment. The logical form is Some S is P, which is just a bit of syntax, whence we are to conclude that 'exists' is bare of semantic content, whether sense or reference, and merely functions as a stylistic variant of 'Some ___ is    ---.'

Those who take a deflationary tack, therefore, can be dubbed someists.  We who resist deflation can then be called existentialists.

By showing that 'exist(s)' and cognates are eliminable, Frege thinks he has eliminated those hoary metaphysical subjects Being or existence which fascinate Thomists, Heideggerians, and such other 'thicks' as your humble correspondent.

2. But does Frege's schedule of elimination really work? We saw how 'Cats exist' can be rendered as 'Some mammals are cats.' But what about 'Mammals exist'? This in turn needs elimination. Assuming that the domain of quantification is a domain of existents, this can be translated salva veritate as 'Some animals are mammals.' And so on up the tree of Porphyry, or, if you deem that to be barking up the  wrong tree, then supply some other scheme of classification. 'Animals exist' becomes 'Some living things are animals.' 'Living things exist'  becomes 'Some bodies are living things.' 'Bodies exist' gets translated as 'Some substances are bodies.'

Clearly, we either now or very soon must call a halt to the ascent by resting in "a concept superordinate to all concepts." (p. 63) Superordinate to all concepts except itself, of course. 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 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)

3. In ordinary language, the role of maximally superordinate concept, a "concept without content," (63) is played by an hypostatization of the copula. In 'The sea is blue' the content of the predicate lies in   'blue': 'is' is contentless. But from the copulative 'is'  we form a quasi-concept -- 'being' -- without content since its  extension is unlimited. This makes it possible to say: men = men  that have being; 'There are men' is the same as 'Some men are' or 'Something that has being is a man.' Thus here the real content of  what is predicated does not lie in 'has being' but in the form of  the particular judgment. Faced with an impasse, language has simply created the word 'being' in order to enable the form of the particular judgment to be employed. When philosophers speak of  'absolute being,' that is really an apotheosis of the copula. (64)

This is an excellent statement of the thin or deflationary or eliminativist line: there is in reality no such 'thing' as Being or existence. Being (as a metaphysical topic) is a result of an illicit reification or hypostatization of the copula, an apotheosis (deification) of the copula.

4. Now why can't I accept this? We saw that to eliminate existence in all cases and make it disappear into the logical form Some S is P we must ascend a classificatory tree at the apex of which is a concept or "quasi-concept" unlimited in extension and empty in intension. This is the concept a being, an existent, something self-identical. Using this concept we can translate salva veritate every sentence of the form Fs exist into a sentence of the form Some being is an F. The availability of such translations seems to strip 'exist(s)' and cognates of all semantic content.

The problem with this was appreciated by Aristotle long ago when he argued that Being is not a summum genus, a highest genus, or a genus generallisimum, a most general genus. (See Metaphysics 998b22 and   Posterior Analytics 92b14). Being, as that which makes beings be, does not abstract from the differences among beings. But a concept  superordinate to every quidditative concept, which is what the concept a being and the concept something self-identical are, does abstract from the differences among beings. To put it another way, Being, as that which constitutes beings as beings, is not superordinate to every  quidditative concept since it belongs to a different order entirely, the non-quidditative order of existence. The Being of a being is its thatness, not its whatness.

The mistake that Frege makes is to think that Being is a highest quidditative determination, a highest what-determination. The concept a being, ens, is such a concept, but this concept is not Being, esse.

In sum: Frege's elimination of existential judgments by translation into copulative judgments works only if Being (esse, das Sein) is a maximally abstract quidditative concept, the concept a being (ens, das  Seiende). But this is precisely what Being is not. Ergo, etc.