Propositions – Maverick Philosopher

Token, Type, Proposition: Write-Up of Some of Yesterday’s Dialog

I am enjoying the pleasure of a three-day visit from Dr. Elliot Crozat who drove out yesterday from San Diego. The following expands upon one of the topics we discussed yesterday.

How many sentences immediately below, two or one?

Snow is white

Snow is white.

Both answers are plausible, and indeed equally plausible; but they can't both be right. There can't be both two sentences and one sentence. The obvious way to solve the problem is by distinguishing between token and type. We say: there are two tokens of the same type. One type, two tokens. That's a good proximate solution but not a good ultimate one. It is a stop-gap solution.

For the solution gives rise to problems of its own. And these may be expected to be as bad as, or worse than, the original one. We made a distinction between sentence-token and sentence-type to avoid contradiction. But what is a sentence-type and how is it related to its tokens? You see the tokens above but you do not see the type. The tokens are in space and bear spatial relations to each other and to other things. The type is not in space. It is obvious that the tokens came into being and will pass out of being. But that is not obviously the case with respect to sentence-types. Such types are arguably a species of platonica. The tokens exist contingently, but this is presumably not the case with respect to their type. The tokens are temporal items, but it doesn't follow that the type is. If the concrete is the causally active/passive, then the tokens are concrete whereas the type is not and is therefore abstract in the Quinean though not the traditional sense. If there are both abstracta and concreta, are both sorts of entity in time? Or only the abstracta?

Now consider:

Snow is white

Schnee ist weiss.

Here we have two different sentence-tokens of two different linguistic types. It is reasonable to maintain that such types are necessarily tied to their respective languages, English and German, in the sense that, were the languages not to exist, then neither would the types exist. But 'surely' human languages are contingent in their existence. If so, then the linguistic types are contingent in their existence, in contradiction to the strong tendency to view them as platonica, and thus as necessary beings.

Puzzles are erupting like weeds in Spring. I can't hope to catalog them all in one entry.

But let's throw a couple more into the mix. The two sentences lately displayed, the one in English, the other in German, express the same proposition or thought (Gedanke in Frege's lingo). Or at least they express the same proposition when assertively uttered or otherwise tokened by a speaker/writer competent in the language in question, a speaker/writer with the appropriate expressive intentions.

We now have token, type, and proposition to understand in their interrelatedness. It is obviously not enough to make distinctions; one must go on to inquire as to how the items distinguished gear into one another, fit together, are 'related.' To avoid this task would be unphilosophical.

One more set of questions. How do we become aware of types and propositions? We see with our eyes the sentence tokens on the page or we hear them with our ears when spoken. But we have no sense-acquaintance with abstracta. Do we 'see' them with the 'eye of the mind'? And how does that 'eye' hook up with the 'eye of the head'?

This ties in with another topic Elliot and I discussed yesterday evening: the difference between the literal and the metaphorical. Is talk of the 'eye of the mind' and of visio intellectualis metaphorical or is it literal? What does it mean to be literal? Is the literal the same as the physical? And what is the difference between metaphorical talk and analogical talk? Can food literally be healthy? Or is food healthy only metaphorically or figuratively? Some dead meat is good food. But no dead animal or its flesh is healthy. For an animal, being alive is a necessary condition of its being healthy.

Are analogical statements about God literally true?

Syntactic and Semantic Validity Again

Edward sends this interesting example:

Omnis homo est mortalis

Socrates is a man

Sokrates ist sterblich

Semantically valid, but not syntactically?

No, syntactically valid because the argument instantiates a valid argument-form, to wit:

Every F is a G
a is an F
Therefore
a is a G.

Validity is a matter of form. An argument is valid if it instantiates a valid argument-form. It is the form that is valid or invalid in the primary senses of these terms. The argument itself is valid or invalid in secondary senses. The argument inherits its validity from the form, so to speak. Or you could say that it is the validity of the form that is the ground of, and accounts for, the validity of the argument.

For me, and here is where Ed will disagree, a valid deductive argument such as the 'Socrates' syllogism above, is a sequence of propositions, not of sentences, that instantiates a valid argument-form.

A proposition is what a sentence in the indicative mood expresses. To be precise, a proposition is what is expressed by the tokening (whether by utterance, writing, or in some other way) of a sentence in the indicative mood. The following three sentences, each from a different language, can be used to express one and the same proposition or Fregean Gedanke (thought) :

Sokrates mortalis est.
Sokrates ist sterblich.
Socrates is mortal.

These three numerically different sentence tokens from three different languages express the same proposition when they are used to express a proposition. Sentences are linguistic entities. Propositions are extra-linguistic, and therefore not tied to particular languages as sentences are. Not tied in the sense that the same proposition can be expressed in different languages. Suppose that every English speaker is exterminated. Could it then be said that Socrates is mortal? Yes, though not in those words. One could say the same thing by uttering the corresponding German or French or Turkish sentence.

This is a reason to distinguish propositions from sentences.

Now glance back at Ed's example. It is linguistically hybrid. But logically it expresses the very same argument (sequence of propositions) that the following does:

Every man is mortal
Socrates is a man
Ergo
Socrates is mortal.

The argument expressed is syntactically valid because it is an instance of a valid argument-form.

Logical Form, Equivocation, and Propositions

A re-post with minor edits and additions from 4 September 2017.

………………………………..

Ed Buckner wants to re-fight old battles. I'm game. The following post of his, reproduced verbatim, just appeared at Dale Tuggy's site:

The concept of logical form is essential to any discussion of identity, and hence to any discussion of the Trinity. Here is a puzzle I have been discussing with the famous Bill Vallicella for many years.

(Argument 1) ‘Cicero is a Roman, therefore Cicero is a Roman’

(Argument 2) ‘Cicero is a Roman, therefore Tully is a Roman’

My puzzle [is] that the first argument is clearly not valid if the first ‘Cicero’ means the Roman, the second the American town, yet the argument seems to instantiate a valid form. Bill objects that if there is equivocation, then the argument really has the form ‘a is F, therefore b is F’, which fails to instantiate a valid form.

I then ask what is the form of. Clearly not of the sentences, since the sentences do not include the meaning or the proposition. Is it the form of the proposition expressed by the sentences? But then we have the problem of the second argument, where both ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid. But I think no one would agree that the second argument is valid.

So logical form does not belong to the sentences, nor to the propositions expressed by them. So what is it the form of?

My answer is that the logical form of the argument is the form of the Fregean propositions expressed by the sentences that make up the argument. Let me explain.

I agree with Ed that logical form is not the form of an array of sentence-tokens. It is rather the form of an array of propositions expressed by the sentences. (To be painfully precise: it is the form of an array of propositions expressed by the assertive utterance, and thus the tokening, of a series of sentence-types by a speaker or thinker on a given occasion. A sentence-token buried in a book does not express anything by itself!)

To solve Ed's puzzle we need to distinguish three views of propositions: the Aristotelian, the Fregean, and the Russellian. This would be a good topic for an extended post. Here I will be brief. Brevity is the soul of blog.

An Aristotelian proposition is an assertively uttered meaningful sentence in the indicative mood that expresses a complete thought. What makes such a proposition 'Aristotelian' as opposed to 'Platonic' is that the meaning of the sentence is not something that can subsist on its own apart from the assertive tokening of the sentence. The meaning of the sentence depends on its being expressed, whether in overt speech or in thought, by someone. And this expression must be thoughtfully done and not mindlessly like a parrot or a voice synthesizer. If there were no minds there would be no Aristotelian propositions. And if there were no languages there would be no Aristotelian propositions. In this sense, Aristotelian propositions are linguistic entities.

In brief: An Aristotelian proposition is just a declarative sentence in use together with its dependent sense or meaning. Suppose I write a declarative sentence on a piece of paper. The Aristotelian proposition is not the string of physical marks on the paper, nor it is the producing of the marks; it is the marks as produced by a minded organism on a particular occasion together with the meaning those marks embody where meaning is first in the mind and only then embodied in the marks.

A Fregean proposition is a nonlinguistic entity that subsists independently of minds and language. It is the sense (Sinn) of a declarative sentence (Satz) from which indexical elements have been extruded. For example, 'I am blogging' does not express a Fregean proposition because of the indexical 'I' and because of the present tense of the verb phrase. But 'BV blogs at 10:50 AM PST on 4 September 2017' expresses a Fregean proposition.

Fregean senses are extralinguistic and extramental 'abstract' or 'Platonic' items. They are not in time or space even when the objects they are about are in time and space. This is what makes Fregean propositions 'Platonic' rather than 'Aristotelian.' Fregean propositions are the primary truth-bearers; the sentences that express them are derivatively true or false. Likewise with the judgments whose content they are.

A Russellian proposition is a blurry, hybrid entity that combines some of the features of a Fregean truth-bearer and some of the features of a truth-maker. A Russellian proposition does not reside at the level of sense (Sinn) but at the level of reference (Bedeutung). It is out there in the (natural) world. It is what some of us call a fact or 'concrete fact' (as in my existence book) and others, e.g. D. M. Armstrong, a state of affairs.

Now consider a singular sentence such as 'Ed is happy.' For present purposes, the crucial difference between a Fregean proposition and a Russellian proposition is that, on the Fregean view, the subject constituent of Ed is happy is not Ed himself with skin and hair, but an abstract surrogate that represents him in the Fregean proposition, whereas in the Russellian proposition Ed himself is a constituent of the proposition!

We needn't consider why so many distinguished philosophers have opted for this (monstrous) view. But this is the view that seems to have Ed in its grip and that powers his puzzle above.

If we take the relatively saner (but nonetheless problematic) view that propositions are Fregean in nature, then the puzzle is easily solved.

Ed asks: What is the logical form the form of? He maintains, rightly, that it cannot be the form of an array of sentences. So it must be the form of an array of propositions. Right again. But then he falls into puzzlement:

. . . ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid.

The puzzlement disappears if we reject the Russsellian theory of propositions. A man cannot be contained in a proposition, and so it cannot be the same man in both propositions.

‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. Its form is: Rc, ergo Rt, which is an invalid form. If we adopt either an Aristotelian or a Fregean view of propositions we will not be tempted to think otherwise.

‘Cicero is a Roman, therefore Cicero is a Roman’ is plainly valid. ‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. The logical forms are different! If, on a Russellian theory of propositions, the forms are the same, then so much the worse for a Russellian theory of propositions!

‘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.

Truth-Bearers and Truth-Makers: Disjoint Classes?

Wesley C. writes,

Today I read your critique of Feser on presentism. I am curious about something you said: A truth-bearer cannot serve as a truth-maker.

If that's right, how would you handle obvious truths that are about propositions. Take the following: "The proposition that Humphreys Peak is the tallest in Arizona is true and believed by many."

That sentence would seem to express a proposition which has another proposition (the one about Humphreys Peak) as its truth-maker; it is about that proposition; that proposition, and nothing else, makes it true. But of course all propositions are truth-bearers. So it would seem that we have a case of some thing which bears truth and makes truth. How would you understand that sentence in a way that is consistent with the claim that a truth-bearer cannot serve a truth-maker?

As always, I enjoy your philosophical contributions.

I didn't go into this because it would have expanded and complicated an already long and difficult entry. But the point is well-taken: it seems that some truth-bearers are truth-makers. Let us assume that truth-bearers are abstract items, propositions in roughly Frege's sense.

In the typical case of truth-making, it is correct to say that if x makes-true y, then x is not a proposition, only y is. But if propositions exist, then doesn't the existence of any proposition make-true various propositions? The proposition expressed by 'The Earth has only one moon' exists. By its very existence it makes-true the proposition that there are propositions. So it seems that a proposition can serve as a truth-maker and that not every truth-maker is a non-proposition. One response is that it is not the Earth proposition qua true that makes-true the proposition that there are propositions, but the Earth proposition qua existent. But this response does not seem quite adequate. Perhaps the following works.

The intuition behind the truth-maker principle (TM) is that truth-makers are 'in the world' where the world is the totality of concrete extra-linguistic and extra-mental particulars (unrepeatables) including e.g. Socrates, and the concrete fact of Socrates' being wise. Representations are not part of the world in this sense. Representations are either mental or abstract. Mental representations are mind-dependent in the sense that they cannot exist except in or for minds as their contents or accusatives. Abstract representations are not dependent for their existence on finite minds, but they are accessible or graspable or understandable by such minds. Abstract propositions are representations in this sense. Thus the (abstract, Fregean) proposition expressed by 'Snow is white' represents snow as having a certain color. Abstract propositions are therefore not 'in the world' in the sense just defined. But truth-makers are. Therefore, abstract propositions are not truth-makers. And so truth-bearers and truth-makers form disjoint classes. But if course a lot depends on what we pack into the notion of a truth-maker.

The basic idea behind TM is that for every truth, or at least for every contingent truth, there must be at least one (though there could be more than one) item distinct from the truth that 'makes' it true, an item that is not itself a truth and is not some finite person's say-so. As Michael Dummett puts it in his 1959 article “Truth,” “. . . a statement is true only if there is something in the world in virtue of which it is true.” (Dummett 1980, 14) He tells us that this is “one important feature of the concept of truth.” (ibid.) TM implies a commitment to realism, as correspondence theories of truth do, but without sharing the specific commitments of the latter, where “Realism consists in the belief that for any statement there must be something in virtue of which either it or its negation is true . . . .” (ibid.) This something must be 'in the world,' which for present purposes means that it must be extra-mental, extra-linguistic, and extra-propositional, if propositions are abstract objects.

Truth and Falsity from a Deflationary Point of View

The following equivalence is taken by many to support the deflationary thesis that truth has no substantive nature, a nature that could justify a substantive theory along correspondentist, or coherentist, or pragmatic, or other lines. For example, someone who maintains that truth is rational acceptability at the ideal (Peircean) limit of inquiry is advancing a substantive theory of truth that purports to nail down the nature of truth. Here is the equivalence:

1) is true iff p.

The angle brackets surrounding a declarative sentence make of it a name of the proposition the sentence expresses. For example, <snow is white> – the proposition that snow is white — is true iff snow is white. (1) suggests that the predicate ' ___ is true' does not express a substantive property. We can dispense with the predicate and say what we want without it. It suggests that there is no such legitimate metaphysical question as: What is the nature of truth? Having gotten rid of truth, can we get rid of falsity as well?

A false proposition is one that is not true. This suggests that 'false,' as a predicate applicable to propositions and truth-bearers generally, is definable in terms of 'true' and 'not.' Perhaps as follows:

2) is false iff is not true.

From (2) we may infer

2*) is false iff ~( is true)

and then, given (1),

2**) is false iff ~p.

This suggests that if we are given the notions of 'proposition' and 'negation,' we can dispense with the supposed properties of truth and falsity. (1) shows us how to dispense with 'true' and (2**) show us how to dispense with 'false.'

But we hit a snag when we ask what 'not' means. Now the standard way to explain the logical constants employs truth tables. Here is the truth table for the logician's 'not' which is symbolized by the tilde, '~'.

$\vbox{\offinterlineskip \halign{& \vrule # & \strut \hfil \quad # \quad \hfil \cr \noalign{\hrule} height2pt & \omit & & \omit & \cr & P & & $\lnot P$ & \cr height2pt & \omit & & \omit & \cr \noalign{\hrule} height2pt & \omit & & \omit & \cr & T & & F & \cr height2pt & \omit & & \omit & \cr \noalign{\hrule} height2pt & \omit & & \omit & \cr & F & & T & \cr height2pt & \omit & & \omit & \cr \noalign{\hrule} }}$

But now we see that our explanation is circular. We set out to explain the meaning of 'false' in terms of 'not' only to find that 'not' cannot be explained except in terms of 'false.' We have moved in a circle.

The Ostrich has a response to this:

. . . we can define negation without reaching for the notions of truth and falsity. Assume that the notion of ‘all possible situations’ is coherent, and suppose it is coherent for any proposition ‘p’ to map onto a subset of that set. Then ‘not p’ maps onto the complement. The question is whether the very idea of a complement of a subset covertly appeals to the concept of negation. But then that suggests that negation is a primitive indefinable concept, rather than what you are claiming (namely that it is truth and falsity which are primitive).

So let's assume that there is a set S of possible worlds,and that every proposition (except impossible propositions) maps onto to an improper or a proper subset of S. The necessary propositions map onto the improper subset of S, namely S itself. Each contingent proposition p maps onto a proper subset of S, but a different proper subset for different propositions. If so, ~p maps onto the complement of the proper subset that p maps onto. And let's assume that negation can be understood in terms of complementation.

The most obvious problem with the Ostrich response is that it relies on the notion of a proposition. But this notion cannot be understood apart from the notions of truth and falsity. Propositions are standardly introduced as the primary vehicles of the truth-values. They alone are the items appropriately characterizable as either true or false. Therefore, to understand what a proposition is one must have an antecedent grasp of the difference between truth and falsity.

To understand the operation of negation we have to understand that upon which negation operates, namely, propositions, and to understand propositions, we need to understand truth and falsity.

A second problem is this. Suppose contingent p maps onto proper subset T of S. Why that mapping rather than some other? Because T is the set of situations or worlds in which p is true . . . . The circularity again rears its ugly head.

The Ostrich, being a nominalist, might try to dispense with propositions in favor of declarative sentences. But when we learned our grammar back in grammar school we learned that a declarative sentence is one that expresses a complete thought, and a complete thought is — wait for it — a proposition or what Frege calls ein Gedanke: not a thinking, but the accusative of a thinking.

Truth and falsity resist elimination.

Battling the Bad Ostrich over Assertion

BV said:

I will now pose a problem for the view that assertion = proposition. Suppose I give the following valid argument, an instance of modus ponens. By 'give an argument,' I mean that I assert its premises, and I assert its conclusion as following from the premises, and this in the presence of one or more interlocutors. Thus the argument is to be taken in concreto, not in abstracto.

If Tom is drunk, then Tom ought not drive
Tom is drunk
—–
Tom ought not drive.

If the argument is valid, as it plainly is, then, in both of its occurrences, the sentence 'Tom is drunk' must express the same proposition. But this cannot be the case if a proposition is identical to an assertion. For the proposition Tom is drunk occurs unasserted in the major, but asserted in the minor. (To assert a conditional is not thereby to assert either its antecedent or its consequent.) Since one and the same proposition can occur unasserted in one context and asserted in another, we must distinguish between a proposition and an assertion.

The Ostrich responds:

I deny that the sentence ‘Tom is drunk’ in the major expresses a proposition at all. It expresses a proposition in the minor, I agree. I also claim that both sentences must have the same content in major and minor. But having the same content is not the same as expressing the same proposition. Perhaps we should rewrite the major as follows:

That Tom is drunk implies that Tom ought not drive.

We connect a name for contents, using a that-clause, with the connector ‘entails’. Thus we express the whole argument as follows

It is the case (that Tom is drunk implies that Tom ought not drive)
It is the case that Tom is drunk
It is the case that Tom ought not drive.

BV counter-responds:

The Ostrich carelessly leaves out the parentheses in the minor and in the conclusion of his re-write of the original argument. His re-write should look like this:

It is the case (that Tom is drunk implies that Tom ought not drive)
It is the case (that Tom is drunk)
It is the case (that Tom ought not drive).

'That Tom is drunk' is not a sentence but a nominal phrase. In the major, it names a proposition, the proposition expressed in English by a tokening of 'Tom is drunk.' It has to name a proposition because the implication relation connects propositions to propositions. In the minor 'that Tom is drunk' also expresses a proposition. It has to if the argument is to be valid.

So one and the same proposition — the one named by 'that Tom is drunk' — occurs in both the major and the minor. It is just that in the major it is not asserted, whereas in the minor it is. Therefore, a proposition is not the same as an assertion — which was my claim all along. (Not original with me, of course. From Frege via Peter Geach.)

So the Ostrich re-write is useless rigmarole. Consider the following re-write:

That Tom is drunk implies that Tom ought not drive
Tom is drunk
Tom ought not drive.

This is valid. In the major, 'That Tom is drunk' names but does not assert a proposition. In the minor 'Tom is drunk' asserts the very same proposition. So one and the same proposition can be both asserted and left unasserted. Therefore, a proposition is not the same as an assertion.

The Ostrich tells us, "But having the same content is not the same as expressing the same proposition." I don't understand that. A content in this context just is a proposition.

Is Assertion Closed Under Entailment? Assertion and Presupposition

Suppose a person asserts that p. Suppose also that p entails q. Does it follow that the person asserting that p thereby asserts that q? If so, and if p and q are any propositions you like, then assertion is closed under entailment. If assertion is not closed under entailment, then there will be examples in which a person asserts that p, p entails q, but the person does not assert that q.

By 'entailment' I understand a relation between propositions. P entails q iff it is impossible for p to be true, and q false. By 'assertion' I mean a speech act, an act of asserting, a concrete, datable, linguistic performance, not a proposition. By 'the content of an assertion' I mean the proposition expressed when a person makes an assertion. A proposition is not the same as a sentence. 'The war has come to an end' is a sentence in English. 'Der Krieg hat zu Ende gekommen' is a sentence in German. The sentences are different, both at the type level and at the token level. And yet they can both be used to express one and the same thought. That same thought is the proposition. By 'thought' here I do not mean an occurrent episode of thinking, but the accusative (direct object) of such an act of thinking. You could also call it a 'content' although that term is ambiguous for reasons I won't go into now.

Preliminaries aside, back to our question.

That James no longer works for Amazon has among its entailments that James worked for Amazon, that someone named 'James' worked for Amazon, and that someone no longer works for Amazon.

Now suppose I assert that James no longer works for Amazon. Do I thereby assert that James worked for Amazon? I say No.

Here is a more striking example. Sophomore Sam asserts that there are no truths. The content of his act of assertion, namely, the proposition that there are no truths, entails that the content of his assertion is not true. But surely the latter is no part of what Sam asserts.

So assertion is not closed under entailment.

Suppose that Tom asserts that he is glad that Trump beat Hillary. The content of the assertion entails that Trump beat Hillary. But that Trump beat Hillary is not what Tom asserts. We can say that Tom's act of assertion presupposes that Trump beat Hillary. But neither Tom nor his act of assertion is a proposition. So if Tom's act of assertion presupposes that Trump beat Hillary, then presupposition is not a relation between propositions, but a relation between a non-proposition (a person or his speech act) and a proposition.

On the other hand, that Tom is glad that Trump beat Hillary entails that Trump beat Hillary. This is a relation between propositions and it makes some sense to say that the first presupposes the second.

This raises a question. Is presupposition primarily something that people do, or is it primarily a relation between propositions?

The Problem of the Unity of the Proposition

Jacques writes,

I'm thinking about this problem and getting increasingly frustrated by the way in which it's discussed in philosophy. I wonder if you have any ideas. Let me explain what bothers me . . .

Typically, philosophers begin with the idea that 'the proposition' needs to be explained or characterized in some special way that will solve the alleged problem. So Frege had his unsaturated concepts, Russell worried about the relating relation, etc. And nowadays there is this vast literature about structured or unstructured propositions, acts of predication, etc.

I don't understand how anything of this kind could possibly help. To explain, I take it that the most basic and intuitive problem here is really the problem of the nature of thought. At least that is the most natural and paradigm case: I think that a is F, and now we ask what is going on in my mental life that makes that happen. How is it even possible? But when we posit these mysterious entities, propositions, as the objects or contents of thoughts we're just pushing the question back.

I agree that introducing propositions only pushes the problem back. But what exactly is the problem? The problem is to provide a satisfying answer to the following question: In virtue of what do some strings of words attract a truth-value? A truth-valued declarative sentence is more than a list of its constituent words, and (obviously) more than each item on the list. A list of words is neither true nor false. But an assertively uttered declarative sentence is either true or false. For example,

Tom is tired

when assertively uttered or otherwise appropriately tokened is either true or false. But the list

Tom, is, tired

is not either true or false. And yet we have the same words in the sentence and in the list in the same order. There is more to the sentence than its words whether these are taken distributively or collectively. How shall we account for this 'more'?

Some will say that the sentence is true or false in virtue of expressing a proposition that is true or false. On this account, the primary truth-bearer is not the (tokened) sentence, but the proposition it expresses. Accordingly, the sentence is truth-valued because the proposition is truth-valued.

But a similar problem arise with the proposition. It too is a complex, not of words, but of senses (on a roughly Fregean theory of propositions). If there was a problem about the unity of a sentence, then there will also be a problem about the unity of the proposition the sentence expresses on a given occasion of its use. What makes a proposition a truth-valued entity as opposed to a mere collection (set, mereological sum, whatever) of its constituents?

So here is one way the introduction of propositions "pushes the problem back." So far, then I am in agreement with Jacques.

If some proposition p just inherently means that a is F, or is inherently true if a is F, regardless of any beliefs or concepts or mental activities of mine, then surely I could operate with proposition p while taking it to mean or represent some other situation–that a is not F, or that b is G, or whatever.

This is not clear. Someone who introduces Fregean or quasi-Fregean propositions as the contents of such propositional attitudes as belief and desire will say that believing that whales are mammals involves no judgmental synthesis, no mental activity on the part of the believer, since this synthesis is already accomplished in the proposition. (How this synthesis is accomplished is a very difficult question, an insoluble one in my opinion.) So I could not take the proposition Whales are mammals to mean Grass is green. The Fregean proposition is part of the mechanism whereby I mean that whales are mammals.

The brute fact that it represents, if that even makes sense, seems to have no implications for my representational use of the proposition or relation to it (or whatever it is that I'm supposed to be doing with propositions).

But you are not using the proposition to represent the fact. Your intending the fact is routed through the proposition which is the sense of the corresponding declarative sentence. (Frege of course has no truck with truth-making facts; he holds the bizarre view that the referent, Bedeutung, of the sentence is THE TRUE. I am sketching here, but not endorsing, a quasi-Fregean theory of propositions.)

Even if we could explain how it is unified, that would still seem to leave the basic problem of how I am able to think a unified thought by means of that entity. (If I'm thinking that proposition p is true, or represents the world accurately, what is it about my activity or state of mind that somehow unifies the representational content p with the further property of being true or being-an-accurate-representation?)

I think you are missing the point that the proposition is a semantic and epistemic intermediary; it is not the direct object of a mental act. You are not thinking that Snow is white is true; you are thinking that snow is white via the propositional content Snow is white.

On the other hand, if p is such that, necessarily, in having p before my mind I entertain or grasp the thought that a is F, the basic mystery is just being described or reiterated. What on earth am I doing when I somehow manage to think that a is F? Postulating this thing that is supposed to enable me to think so doesn't seem like any kind of explanation. What kind of thing is this, meaningful or representational in itself, yet also necessarily dictating my representational grasp of it? Why not just say that I think that a is F, with no hint of any analysis or explanation of that fact about me?

Are you proposing a Wittgensteinian eschewal of theory and philosophical explanation?

Tom believes that Cicero is a Roman; Cicero is Tully. But Tom does not believe that Tully is a Roman. Is there not a genuine puzzle here the solution to which will involve a theory of propositions?

One view is that the ultimate truth-bearers are token acts of predication. For example, the thing that is true is my act of predicating property F of object a, according to rules somehow determined by property F. But this too seems hopeless as an explanation or analysis. Phrases like 'predicating a property of an object' don't mean anything more than 'thinking that something is a certain way'. No doubt, once I do that, I'm doing something that we might call 'correct' or 'true' depending on what the world is like. But is there any real difference between predicating F to a, on the one hand, and just thinking that a is an F? I have no idea what these people are talking about, or how they think this is explanatory. Every theory seems ultimately to depend on the unexplained notion of someone having a propositional thought–that a certain proposition is true, that some possible world is actual, that a property is instantiated, or whatever. And yet that seems to be the very notion that we want to understand here–the notion of propositional thought, thinking that something is the case. Alternatively, they're positing these non-propositional events or activities–just the brute fact that someone 'predicates' or someone 'grasps' a proposition, without these things being taken to depend on thinking that things are thus-and-so. But in that case, the theories are all obviously false; they just deny the phenomenon we want to explain.

Do you have a reference in the literature for me?

Suppose I say of Elliot that he is sober. That is a token act of predication: I apply the predicate 'sober' to Elliot. But Karl can say the same thing by applying the predicate 'nuechtern' to Elliot. So I don't see how token acts of predication could be the ultimate truth-bearers. These acts are different. But the content expressed is the same. Besides, how can an act be true or false?

I get the impression that you are driving in a Wittgensteinian direction, We say things like 'Hillary is a liar' and we think the corresponding thoughts. Apparently, you want to leave it at that and not seek any philosophical explanation on the ground that these explanations don't really explain anything.

Would you go so far as to say that the problem of the unity of the sentence, the problem of what makes a sentence different from a list of words, is a pseudo-problem?

Well, I don't know if that makes sense, but I'd appreciate any thoughts you might have. I feel this is an absolutely fundamental set of problems, with important implications, but the philosophical literature just seems to confuse me . . .

It makes plenty of sense . . .

Propositions About Socrates Before He Came to Exist

This continues the discussion with James Anderson. See the comments to the related article below. Here is Professor Anderson's latest comment with my replies.

So are you saying that prior to the time Socrates comes into existence the proposition It is possible that Socrates come into existence doesn't exist at all?

Yes, if either Socrates himself, or an haecceity property that deputizes for him, is a constituent of the proposition in question. For it is surely obvious that before Socrates came to exist, he did not exist, and so was not available to be a constituent of a proposition, a state of affairs, or anything at all. As for the putative property identity-with-Socrates, I have already shown to my satisfaction that there cannot be any such property if properties are necessarily existent abstract objects.

No, if we think of 'Socrates' along Russellian lines as a definite description in disguise replaceable by something like 'the most famous of the Greek philosophers, a master dialectician who published nothing but whose thoughts were presented in dialogues written by his star pupil and who was executed by his city-state on the charge of being a corrupter of youth.' I have no objection to saying that, prior to the time Socrates comes into existence, the following proposition exists: It is possible that some man having the properties of being famous, Greek, etc, come into existence.

Are you thereby committed to the contingent existence of propositions?

Not across the board.

Or would you favor full-blown nominalism about propositions?

Not at all. Here is an argument for propositions that impresses me.

Here's my reasoning laid out step by step. Perhaps you can tell me where you would want to jump out of the cab.

1) Socrates came into existence at t.

2) It is possible that Socrates come into existence at t. [actuality entails possibility]

It is a modal axiom that everything actual is possible. So of course actuality entails possibility. But it doesn't follow that before Socrates came into existence, that he, that very individual, was possible. For it might be that he, that very individual, becomes possible only at the instant he becomes actual. If a thing is actual, then it is possible; but that says nothing about when it is possible.

3) The proposition It is possible that Socrates come into existence at t is true. Call this proposition P. (P is a tenseless proposition, although it makes reference to a particular time.)

You are moving too fast. Yes, the proposition P is true. But that P is tenseless is a further premise of your argument and should be listed as such and not introduced parenthetically. Can you prove that P is tenseless? It is not obvious or a non-negotiable datum.

I grant that there are tenseless propositions. Whales are mammals. Numbers are abstract objects. 7 plus 5 is 12. The same goes for their negations. But one cannot assume that every proposition is tenseless. (I grant that every Fregean proposition is tenseless, but that is a technical use of 'proposition.') It might be that P is true only at t and at times later than t.

4) P is necessarily true. [by S5]

Not if P is true only at t and at times later than t. Does this violate S5? Not obviously. On S5, Poss p –> Nec Poss p. Can it be shown that 'p' here includes within its range propositions of de re possibility such as P?

5) P is true at all times. [because necessary truths cannot fail to be true]

6) P is true prior to t (i.e., before Socrates comes into existence).

7) Prior to t, it is possible that Socrates come into existence (at t).

I have given reasons to deny each of these propositions.

At the very least, we have a stand-off here. Professor Anderson has not proven his point. Perhaps I cannot prove my point either. Then we would have an aporia.

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.

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.

Logical Form, Equivocation, and Propositions

Ed Buckner wants to re-fight old battles. I'm game. The following post of his, reproduced verbatim, just appeared at Dale Tuggy's site:

The concept of logical form is essential to any discussion of identity, and hence to any discussion of the Trinity. Here is a puzzle I have been discussing with the famous Bill Vallicella for many years.

(Argument 1) ‘Cicero is a Roman, therefore Cicero is a Roman’

(Argument 2) ‘Cicero is a Roman, therefore Tully is a Roman’

My puzzle [is] that the first argument is clearly not valid if the first ‘Cicero’ means the Roman, the second the American town, yet the argument seems to instantiate a valid form. Bill objects that if there is equivocation, then the argument really has the form ‘a is F, therefore b is F’, which fails to instantiate a valid form.

I then ask what is the form of. Clearly not of the sentences, since the sentences do not include the meaning or the proposition. Is it the form of the proposition expressed by the sentences? But then we have the problem of the second argument, where both ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid. But I think no one would agree that the second argument is valid.

So logical form does not belong to the sentences, nor to the propositions expressed by them. So what is it the form of?

My answer is that the logical form of the argument is the form of the Fregean propositions expressed by the sentences that make up the argument. Let me explain.

An Aristotelian proposition is an assertively uttered meaningful sentence in the indicative mood that expresses a complete thought. What makes such a proposition 'Aristotelian' as opposed to 'Platonic' is that the meaning of the sentence is not something that can subsist on its own apart from the assertive tokening of the sentence. The meaning of the sentence depends on its being expressed, whether in overt speech or in thought, by someone. If there were no minds there would be no Aristotelian propositions. And if there were no languages there would be no Aristotelian propositions. In this sense, Aristotelian propositions are linguistic entities.

A Fregean proposition is a nonlinguistic entity that subsists independently of minds and language. It is the sense (Sinn) of a declarative sentence from which indexical elements have been extruded. For example, 'I am blogging' does not express a Fregean proposition because of the indexical 'I' and because of the present tense of the verb phrase. But 'BV blogs at 10:50 AM PST on 4 September 2017' expresses a Fregean proposition.

A Russellian proposition is a blurry, hybrid entity that combines some of the features of a Fregean truth-bearer and some of the features of a truth-maker. A Russellian proposition does not reside at the level of sense (Sinn) but at the level of reference (Bedeutung). It is out there in the (natural) world. It is what some of us call a fact or 'concrete fact' (as in my existence book) and others a state of affairs.

We needn't consider why so many distinguished philosophers have opted for this (monstrous) view. But this is the view that seems to have Ed in its grip and that powers his puzzle above.

If we take the relatively saner (but nonetheless problematic) view that propositions are Fregean in nature, then the puzzle is easily solved.

. . . ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid.

The puzzlement disappears if we reject the Russsellian theory of propositions. A man cannot be contained in a proposition. and so it cannot be the same man in both propositions.

On the Logical Independence of Person and Proposition

If the Father of Lies speaks a truth per accidens, it is still a truth. And if the Father of Lights speaks a falsehood per impossibile, it is still a falsehood.