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. 

Related articles

The Function-Argument Schema in the Analysis of Propositions

Comments

[The London Ostrich]

>> What is particularly interesting here is the claim that Russell’s theory of proper names is a nod to to the scholastic theory.

Russell probably wasn’t aware, but this actually was Ockham’s theory. He says that some propositions (Summa Logicae chapters 11-20) are ‘exponible’ i.e. can be analysed into a conjunction of two different propositions p & q, whose negation therefore involves a disjunction. Thus (chapter 12) excluded middle only applies if the subject is not empty, i.e. if ‘a chimaera is something’ is true, then either ‘the chimaera is a man’ or ‘the chimaera is a not a man’ is true. But both are false if nothing corresponds to ‘the chimera’. See also chapter 14.

For ‘a chimera is a non-being’ is literally false, and so is anything similar, because anything of that sort has the exponents ‘a chimera is something’ and ‘that thing is a non-entity’, of which the first is false.

But this depends on the distinction between propositional and predicate negation, which collapses if proper names are logically proper in Russell’s sense. Either Fa or not Fa, tertium non detur. We owe to Kripke the thesis that the meaning of a proper name is not descriptive, and we owe to others the thesis that Devitt has called Semantic Presupposition, namely that the meaning of a singular term is either descriptive or else it is the term’s referent, and there are no other possible candidates for a singular term’s meaning. One other possible candidate is ‘singular description’ or haecceity, but as you have pointed out, there are difficulties with this.

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.

I agree. But let me suggest yet another candidate. Let us define the term ‘XXX’ as follows. Let the token ‘N’ be the most recent occurrence of the proper name ‘N’ in the text or in the discourse. Then by definition if that token of ‘N’ has a referent, ‘XXX’ has the same referent. Then the following syllogism is valid:

Frodo is a hobbit, XXX lives in a hole, so some hobbit lives in a hole.

For if the major is true, there is some individual corresponding to ‘Frodo’, and that individual is a hobbit. But ‘XXX’ picks out the individual who is a hobbit, because ‘is a hobbit’ is predicated of the most recent occurrence of a proper name, so if the minor is true, that hobbit lives in a hole. So the conclusion is true, i.e. cannot be false. So the syllogism is valid.

Now it is a separate argument as to whether ordinary proper names function somewhat like this. The relevant point is that ‘XXX’ is not descriptive, since unlike a pronoun it connotes no gender or personhood or animalhood etc. Its meaning is purely intralinguistic. So it is not descriptive. But neither is its meaning a referent. It is perfectly meaningful in the ‘Frodo’ case, even though nothing corresponds to ‘Frodo’. So we have a perfect example of a term which defies Semantic Presupposition. Its meaning is neither descriptive nor is it the terms’s referent.

[BV]

>>the meaning of a singular term is either descriptive or else it is the term’s referent, and there are no other possible candidates for a singular term’s meaning.<<

This presupposes that there are genuinely (irreducibly) singular terms. That is not obvious. Perhaps there are none, and that, despite appearances, all reference, both linguistic and mental, is general.

One view might be reductive: There is extralinguistic singular reference all right, but it is really general.

Is your view eliminativist?: There is no extralinguistic singular reference.

Isn't is absurd to say that the meaning of a proper name is exhausted by its referent? What makes a thing ITS referent?

[BV]

Let me see if I understand your main point.

'XXX' is a meaningful singular term but its meaning is not descriptive (nor is there any concept that 'XXX' expresses) and its meaning is not its extralinguistic referent: it lacks one.

So here we have a singular term that escapes between the horns of Devitt's Dilemma (although Devitt, I presume, would not consider it a dilemma).

One obvious objection to this is that the extralinguistic referent of 'XXX' is the extralinguistic referent of its antecedent. Compare: 'Stacey is a smoker; he/she/it can't quit.' The antecedent of 'he/she/it' is 'Stacey.' 'Stacey' has an extralinguistic referent and 'he/she/it/it' has the same extralinguistic referent.

Note that in 'Peter smokes and he drinks' 'he'does not refer to 'Peter' but to Peter! The antecedent of the pronoun is a name, but the referent of the pronoun is the name's referent.

I could claim you are confusing antecedency with reference. I could also claim that 'back' in ''back reference' is an alienans adjective and that back reference is not reference any more than a decoy duck is a duck, 'decoy' being an alienans adjective.

[The London Ostrich]

I so knew you would say that. More later, off to chop some kindling with my axe. (In an literal, not a metaphorical sense - October is upon us).

[Richard Hennessey]

An important topic and great discussion. May I suggest that one way out of the impasse in which you have found yourself would be to deny the Aristotelian and Thomistic thesis that individuum ineffabile est and affirm that the individual is in fact intelligible and so conceivable and effable. Aquinas himself was able to affirm something like this in his commentary on Aristotle’s Metaphysics when, in Book I, Lesson 1, Comments 15 and 16, he affirms that there is a “cogitative power” or “particular reason” (ratio particularis) in addition to a “universal reason” (ratio universalis).

15. Now, as is stated below (18), in men the next thing above memory is experience, which some animals have only to a small degree. For an experience arises from the association of many singular [intentions] received in memory. And this kind of association is proper to man, and pertains to the cogitative power (also called particular reason), which associates particular intentions just as universal reason associates universal ones. Now since animals are accustomed to pursue or avoid certain things as a result of many sensations and memory, for this reason they seem to share something of experience, even though it be slight. But above experience, which belongs to particular reason, men have as their chief power a universal reason by means of which they live.

16. And just as experience is related to particular reason [in men], and customary activity to memory in animals, in a similar way art is related to universal reason. Therefore, just as the life of animals is ruled in a perfect way by memory together with activity that has become habitual through training, or in any other way whatsoever, in a similar way man is ruled perfectly by reason perfected by art. Some men, however, are ruled by reason without art; but this rule is imperfect.

[BV]

Must be getting nice and crisp in old London towne. In these parts it's still summer.

You "so knew"? Cute, but not in keeping with your station and its duties.

Would you accept the following characterization of your view? It is a version of linguistic idealism in which the existence of (extralinguistic) reference is denied and all so-called reference is in reality intralinguistic back reference.

[The London Ostrich]

>>Would you accept the following characterization of your view? ..

Not really but more later. Bedtime for ostriches, wood has been chopped.

Internet says temperature in Phoenix is 33C. I wish.

[BV]

Thank you for the comment, Richard.

While the distinction between ratio particularis and ratio universalis is relevant to our problem, I found Aquinas' discussion too murky to be helpful. On the other hand, what Royce says (quoted here: https://thomism.wordpress.com/2015/03/24/knowing-individuals/) is along the lines of my own thinking.

[The London Ostrich]

The Thomism URL is actually this https://thomism.wordpress.com/2015/03/24/knowing-individuals/

(You included a bracket by mistake, easily done).

[The London Ostrich]

>>Would you accept the following characterization of your view? It is a version of linguistic idealism in which the existence of (extralinguistic) reference is denied and all so-called reference is in reality intralinguistic back reference.
‘Extralinguistic reference’, in the sense of some semantic relation between singular terms and reality, I deny, yes, although I don’t deny that reality exists and that we can say things that are true, and so on. Here is my problem with the extralinguistic hypothesis.

There was a man called 'Moses'. Moses lived in Egypt.

I think we agree that the first sentence is not referential but general. It says there was a man, that he was called 'Moses', but without telling us which particular man this was. There could have been many men called 'Moses', indeed there have been (e.g. Moses Mendelssohn, Moses Maimonides). Moreover *man called 'N'* is a concept, which may or may not be satisfied, whereas if the sentence were referential, it must identify some actually existing man in order to assert of him that he is called ‘Moses’ etc.

I think we agree here. But what about the second sentence? (1) it seems to refer back to the first sentence, to say of the man called ‘Moses’ that he lived in Egypt. This can’t be back reference in the extralinguistic sense because the first sentence doesn’t refer to anything. So it must be back reference in the intralinguistic sense only. The two sentences do not differ in meaning from

There was a man called 'Moses'. He lived in Egypt.

Or even

There was a man called 'Moses', who lived in Egypt.

Both sentences together have a general, not a singular meaning. The singular term in the second sentence serves merely to tie the predicate of the second, to the subject of the first.

>> One view might be reductive: There is extralinguistic singular reference all right, but it is really general.
Right. I don’t see any other way to explain how a singular proposition/sentence can refer back to a proposition that is perfectly general in meaning, except by the intralinguistic connection. Or perhaps you could try?

[BV]

>>There was a man called 'Moses'. Moses lived in Egypt.<<

The first sentence is clearly general for the reasons you give. It follows that it is not singular. Does it follow that the first sentence is not referential? Not straightaway. You need an auxiliary assumption, something like: All reference is singular. (Quine would demur.) I grant that it is very plausible that all reference is singular.

On the other hand, it sounds strange to say that the first sentence does not refer to anything. After all, the first sentence is (contingently) true. So there has to have been some man called 'Moses.' The existence of some man or other named 'Moses' is what makes the first sentence true. So it is also plausible to say that there is general reference to some man or other.

You could say that the first sentence is about something but does not refer to anything (since reference is singular only). The first sentence is surely about something in the way that 'There was a man named "Kryptosscheissfresser von Bummelstadt"' is not about anything. This yields two different extralingustic relations: reference and aboutness.

>> This can’t be back reference in the extralinguistic sense because the first sentence doesn’t refer to anything. So it must be back reference in the intralinguistic sense only.<<

Suppose there was only one man called 'Moses.' The first sentence would still be general. But it would be made true by that one man named 'Moses.' The sentence featuring 'he' would be about that same man. I conclude that the function of 'he' cannot be wholly intralinguistic inasmuch as it is about an extralinguistic individual.

[The London Ostrich]

>>Does it follow that the first sentence is not referential?
Depends on our working definition of ‘referential’. I say, with Mill and others: a term refers iff it tells us which individual the predicate applies to. Thus ‘Some man is standing’ is true if Mark is standing, but ‘Mark is standing’ only if Mark is standing. I.e. ‘some man is standing’ does not tell us which man is standing, only that some man is. ‘Mark is standing’ is true iff Mark is standing. Also, suppose ‘some man’ refers, say to Mark. Then ‘it is not the case some man is standing’ is true if Mark is not standing, and Matthew is. But clearly it is false in that situation (assuming Matthew is a man). I am borrowing these points from Geach.

So we have a puzzle:

There was a man called ‘Moses’. Moses lived in Egypt.

The first sentence is not referential. It does not tell us which man was called ‘Moses’ (Maimonides? Mendelssohn? The Prophet?). But the second sentence does tell us, namely it is whoever the first sentence says was called ‘Moses’. And the two sentences together are not referential: they don’t tell us which man called ‘Moses’ lived in Egypt. The contention of the intralinguistic theory is that we could construct a whole narrative like this, which as a whole does not refer to anything in the sense that there might have been two individuals or parallel worlds of which the narrative was true. Bu the proper names and other singular terms back-refer within the narrative, to identify the different characters within it.

Obviously you will object. You want there to be some semantic connection between language and reality such that the narrative can be true only of a certain individual or set of individuals. The problem is the second sentence of the example above. If ‘Moses’ in the second sentence has some semantic power linking the sentence to reality, then the two sentences together must give us more information than just ‘There was a man called ‘Moses’ who lived in Egypt’. But what is that information?

[The London Ostrich]

Btw "Kryptosscheissfresser von Bummelstadt" is funny.

[BV]

One of my slogans, adapted from Butchvarov, is that there is more to a true sentence than the sentence that is true. Do you agree that if 'Someone is standing' is true, then there is at least one extralinguistic item involved in making it true?

That is obvious to me. Of course, it needn't be Mark. It could be Matthew, Luke, John, or Shlomo . . . .

[The London Ostrich]

>>Do you agree that if 'Someone is standing' is true, then there is at least one extralinguistic item involved in making it true?

Obviously. That is different from my thesis that the semantics telling us which individual verifies the predicate is intralinguistic.

But you haven't answered the question. If ‘Moses’ in the second sentence of

There was a man called ‘Moses’. Moses lived in Egypt

has some semantic power linking the sentence to some definite individual in reality, then the two sentences together must give us more information than just

There was a man called ‘Moses’ who lived in Egypt

But what is that information?

[BV]

Does 'The greatest philosopher who published nothing was Greek' refer to anything?

[The London Ostrich]

>>Does 'The greatest philosopher who published nothing was Greek' refer to anything?

It depends on the context. In the following narrative, it would clearly not refer to Socrates:

There was a philosopher who was a greater philosopher than any other. He was Greek. The philosopher published nothing. This Greek was a friend of Socrates. Socrates was therefore not the greatest philosopher who published nothing.

My thesis is that singular reference can only take place within a narrative. We can rapidly shift between narratives. For example, if we are talking about early 20th century philosophy, the term ‘Russell’ will have a clearly understood meaning within the narrative corresponding to that tradition. If we are talking about the origins of fox terriers, its meaning will be that of ‘the Reverend John Russell’.

You will object that ‘‘Bertrand Russell’ refers to Bertrand Russell’ expresses a word-world relation. But this is precisely what I dispute. The use of second token, the one that is apparently used, involves a covert mention, similar to ‘Gorgione was so-called’. If you reply that ‘Russell’ clearly refers to Russell, this is not an objection. Clearly we agree that ‘‘Russell’ refers to Russell’ is true. We disagree on the analysis. I say it is true when both terms, the one that is mentioned and the one that is ‘used’ belong to the same anaphoric chain, i.e. a chain where every singular term refers back to a previous term, and where the genesis of the chain is some indefinite antecedent that doesn’t back refer at all. For example, the chain above: ‘a philosopher .. he .. the philosopher .. This Greek etc’.

[BV]

So you admit that in some contexts one can refer using a definite description? But then not all reference is via singular terms. Def. desceriptions are not singular. Isn't part of what you are maintaining that all reference is via irreducibly singular terms?

[The London Ostrich]

Definite descriptions for me are irreducibly singular terms. Consider:

A man and a boy were standing by a fountain. The man had a drink.

The definite description ‘the man’, in that context, is irreducibly singular, i.e. aptus natus praedicari de uno solo. Note, not just true of only one thing, but naturally or essentially referring to it, in the specific context.

[BV]

Do you mean definite descriptions used attributively or referentially? (K. Donellan's distinction)