Frege – Maverick Philosopher

Ray Monk on Frege, Russell, Patriotism and Prejudice

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.

This is a rich and fascinating topic, both intrinsically and especially for me, given my recent deep dive into the world of Carl Schmitt and his antecedents. I will be returning to him. But there is so bloody much else that clamors for my attention. I'm a scatter-shot man to my detriment. Quentin Smith detected that tendency in me way back when. How I miss that crazy guy.

Live long, old friends die, and new friends will never be old.

But Robert A. Heinlein is right: "Specialization is for insects." The trick is to be a jack of all trades but a master of one while running the risk of being a master of none.

Sorry Gottlob, Sorry Bertrand

Attributes are at the things to which they are attributed. Existence, then, is in a broad sense an attribute of existing items despite adding nothing to the quiddity of the thing to which it is attributed apart from its capacity to have a quiddity.

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.

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.

Ray Monk on Frege

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.

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.

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.

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?

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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.

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.

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.)

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.

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?