The Aporetics of Singular Sentences

I should issue a partial retraction.  I wrote earlier,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL."  ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' )

The animadversions of Edward the Nominalist have made me see that my assertion is by no means obvious, and may in the end be just a dogma of analytic philosophy which has prevailed because endlessly repeated and rarely questioned.  Consider again this obviously valid argument:

1. Pittacus is a good man
2. Pittacus is a wise man
-----
3. Some wise man is a good man.

The traditional syllogistic renders the argument as follows: 

Every Pittacus is a wise man
Some Pittacus is a good man
-----
Some wise man is a good man.

This has the form:

Every P is a W
Some P is a G
-----
Some W is a G.

This form is easily shown to be valid by the application of the syllogistic rules. 

In my earlier post I then repeated a stock objection which I got from Peter Geach:

But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.

The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory) of 'Every Pittacus is wise'; it is its contrary. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different.

My objection, in nuce, was that 'Pittacus is wise' and 'Pittacus is not wise' are contradictories, not contraries, while 'Every Pittacus is wise' and 'Every Pittacus is not wise' ('No Pittacus is wise') are contraries.  Therefore, TFL does not capture or render perspicuous the logical form of 'Pittacus is wise.'

To this, Edward plausibly objected:

As I have argued here before, ‘Pittacus is wise’ and ‘Pittacus is not wise’ are in fact contraries. For the first implies that someone (Pittacus) is wise. The second implies that someone (Pittacus again) is not wise. Both imply the existence of Pittacus (or at least – to silence impudent quibblers - that someone is Pittacus). Thus they are contraries. Both are false when no one is Pittacus.

I now concede that this is a very good point.  A little later Edward writes,

The thing is, you really have a problem otherwise. If 'Socrates is wise' and 'Socrates is not wise' are contradictories, and if 'Socrates is not wise' implies 'someone (Socrates) is not wise', as standard MPC holds, you are committed to the thesis that the sentence is not meaningful when Socrates ceases to exist (or if he never existed because Plato made him up). Which (on my definition) is Direct Reference.

So you have this horrible choice:  Direct reference or Traditional Logic.

But must we choose?  Consider 'Vulcan is uninhabited.'  Why can't I, without jettisoning any of the characteristic tenets of MPL, just say that this sentence, though it appears singular is really general because 'Vulcan' is not a logically proper name but a definite description in disguise?  Accordingly, what the sentence says is that a certain concept -- the concept planet between Mercury and the Sun -- has as a Fregean mark (Merkmal) the concept uninhabited.

Now consider the pair 'Socrates is dead' - 'Socrates is not dead.'  Are these contraries or contradictories?  If contraries, then they can both be false.  Arguably, they are both false since Socrates does not exist, given that presentism is true. Since both are false, both are meaningful.  But then 'Socrates ' has meaning despite its not referring to anything.  So 'Socrates' has something like a Fregean sense.  But what on earth could this be, given that 'Socrates' unlike 'Vulcan'  names an individual that existed, and so has a nonqualitative thisnsess incommunicable to any other individual?

If, on the other hand, the meaning of 'Socrates' is its referent, then, given that presentism is  true and Socrates does not exist, there is no referent in which case both sentences are meaningless.

So once again we are in deep aporetic trouble.  The proper name of a past individual cannot have a reference-determining sense.  This is because any such sense would have to be a Plantingian haecceity-property, and I have already shown that these cannot exist.  But if we say that 'Socrates' does not have a reference-determining sense but refers directly in such a way as to require Socrates to exist if 'Socrates' is to have meaning, then, given presentism,  'Socrates' and the sentence of which it is a part is meaningless. 

Comments

[Account Deleted]

It seems that according to TFL-ers

(1) Pitacus is wise;

is analyzed as the apparently general statement:

(2) Every Pitacus is wise.

I asked previously: What is the logical form of (2)? It is ambiguous at least between:

(a) (x)(If Pitacus = x, then Pitacus is wise);
or
(b) (x)(If x Pitacusizes, then x is wise).

Clearly, (a) and (b) assign a different logical form to (1). Call the former the ‘(a)-model’ and the later the ‘(b)-model’. So I ask again: Do the TFL-ers opt for the (a)-model or the (b)-model as an analysis of (1) that shows the alleged *universal* element in the use of names? Or perhaps they have a totally different model, one not yet exhibited here? No one responded with a clear answer to this question. Yet, clearly, an answer to this question is mandatory for without it one cannot determine any of the issues Bill is discussing in the present post.

I have also pointed out that the (a)-model cannot be an adequate account of (2), and therefore of (1), because the term 'Pitacus' is used in (2) as a singular term. The (b)-model, on the other hand, does not have this inadequacy. Moreover, if ‘Pitacus’ fails to refer, then (a) would be just as “meaningless” (I am granting this here) as would be a construal of (1) as a singular proposition a-la modern logic. So the supposedly great advantage of the TFL-er’s in cases of empty names would be wiped out.

But now consider what happens if TFL-ers opt for the (b)-model as an analysis of (2) and, therefore, of (1). Consider (1) and (1*):

(1*) Picatus is not wise.

What is the logical form of (1*), if we take the (b)-model as our model of analyzing (1)? The answer is that (1*) is ambiguous between:

(a*) (x)(If x Pitacusizes, then it is not the case that x is wise);
And
(b*) It is not the case that (x)(If x Pitacusizes, then x is wise).

Accordingly, (b) and (b*) are contradictories and (b) and (a*) are contraries. The question is this: When someone asserts (1*), which one they mean (a*) or (b*)? And how do we decide these questions?

Notice, however, that none of this requires resorting to an alternative to modern logic. Everything I have stated above is couched in terms of the resources of modern logic. The alleged *universal* element embedded in singular terms that the TFL-ers insist upon is captured by the (b)-model by simply using a convention that converts every name into a predicate. Whether this is how ordinary names are used remains a separate matter. But the logical resources that go into the analysis according to the (b)-model are all part of modern logic.

[Bill Vallicella]

Peter,

It's the scholastics vs. the Fregeans, and I think you are simply begging the question against the scholastics. This is shown by the way you disambiguate (2). For one thing, there is no identity relation in TFL, as Sommers makes very clear.

You told me you have Sommers, The Logic of Nat'l Language. On p. 17 he lists four points on which the scholastic and Fregean doctrines differ. I suggest you study that very carefully.

You ask about the logical form of (2). But that question makes no sense from the TFL perspective. (2) gives the logical form of (1) 'Pittacus is wise.' You beg the question if you go on to ask about the log. form of (2) and expect an answer in Fregean terms.

The logical form of affirmative singular sentences is '*a is P' where '*a' is a singular subject with wild quantity. See Sommers, p. 123. There are no atomic propositions in TFL and if you assume that there are then you assume what they deny.

In other news, vol. I of Kripke's phil papers is scheduled for release in October. Title is *Philosophgucal Troubles.*

[Account Deleted]

Bill,

1) "...,and I think you are simply begging the question against the scholastics."

That depends on which question am I begging and whether the question so begged has a reasonable justification.

2) "there is no identity relation in TFL, as Sommers makes very clear."

Yes! And that should already be one count against the scholastics. However, a brief reading of Sommers' account on p.123 in which he offers an account of identity in scholastic terms reveals some questions. Problems that I see immediately: what are the symbols 'x' in his "every x is an x"? What is the symbol '*a'? Sommers says that "'*a' is a singular subject with wild quantity." But what does this phrase mean? What does the term 'wild' here have anything to do with quantity? Obviously, it is used metaphorically. But what is it a metaphor for?

Second, what is a 'singular subject'? What does it contrast with? These are all questions that arise from a brief reading of two pages in Sommers. They leave huge questions unanswered, questions I do not have the time to explore in detail in Sommers (for reasons to be outlined below).

Take the (Obviously false) pair of sentences: "John is identical to everyone" and "Everyone is identical to everyone". Since the term 'John' is represented as 'Every John' which simply means everyone, the two sentences mentioned are given the same reading even though they are clearly distinct. And if it is claimed they do have a different reading in scholastic terms, what would these two readings be?

3) "(2) gives the logical form of (1) 'Pittacus is wise.' You beg the question if you go on to ask about the log. form of (2) and expect an answer in Fregean terms."

(2) is a mere paraphrase of (1). I can drop the term 'logical form' and simply ask some questions about the relationship between (1) and (2). For instance:

(a) What is the relationship between (1) and (2) (and we cannot use the term 'logical form' here in its non-scholastic connotation)?

(b) How do we know that (2) is related to (1) in a manner that reveals something about (1), whereas (E3) or (E4) and the other potential alternatives below are not?

(E3) Some Pitacus is wise;
(E4) Not Every Pitacus is wise;
(E5) Pitacus is every wiseman;
(E6) Pitacus plus wise;
(E7) Every Pitacus is not every wiseman.

etc.

4) "The logical form of affirmative singular sentences is '*a is P' where '*a' is a singular subject with wild quantity."

What is the logical function of 'wild quantity'? Surely the term 'wild' is used as a metaphor here. What is it a metaphor for? What is the term 'singular subject' contrasted with?

On a more general note: Every hypothesis, regardless of how wild it may be, can be saved if only one is willing to deny enough presuppositions. I suppose one may even propose to replace our current modern astronomy with Ptolemy's. If one is willing to put the effort into inventing significantly more epicycles, some perhaps permanently invisible; view all the myriad of galaxies as mere glow created by of the movements of the planets on their epicycles and so forth.

But I ask: What is the point? What are we trying to accomplish? What are the benefits of a provably impoverished system of logic over one which proved itself by advancing formal studies beyond anything imaginable merely one hundred years ago? None of these questions (nor any of my other questions) have been addressed by either you or Ed (or anyone else for that matter). Until I see some effort to answer these question in a serious way I think the above enterprise is just so many epicycles all over again.

As for Sommers' book and project: while we may always keep an open mind to the possibility that ideas ignored at a given time are ahead of their time and that accounts for their being ignored, in some cases being ignored is justified. In this case, Sommers' project is not a head of its time but it is instead behind the time by over one hundred years. This has been the impression I get from the reception of the book in the philosophical community. And since one must make a judgment on a case by case basis, I judge Sommers' project, Ed's proposals regarding singular propositions etc., and the scholastic logic in general as being justifiably surpassed by modern logic. However, as I said earlier, I am willing to keep an open mind if given a good reason to do so. So far, no one offered such a reason.

I heard about Kripke's new book; I find the title somewhat puzzling.

[Account Deleted]

Addendum,

What does the paraphrase 'Every Pitacus' that is supposed to unveil the hidden generality in the use of the name 'Pitacus' means?

Can it mean:

(a) Everything called 'Pitacus';

No! Because this reintroduces the name as a singular term and the generality involved in 'every' is merely attached by fiat without any purpose.

Can it mean:

(b) Every object that is Pitacus;

First, what is the role of the copula 'is' here? It cannot be identity because the scholastic logic rejects identity. So what is its role? Second, (b) involves the term 'Pitacus' essentially; what is its use in the paraphrase? Is it used as a singular term or as ....what? Third, clearly, nothing other than the individual object Pitacus is Pitacus. So why have the 'every' there? What purpose does it serve? Why not have instead 'some', 'none', etc?

I can't think of any other interpretations of 'every Pitacus' that makes any sense, even remotely. Can you?

[arash]

Bill, you wrote: "If, on the other hand, the meaning of 'Socrates' is its referent, then, given that presentism is not true and Socrates does not exist, there is no referent in which case both sentences are meaningless."
But, as far as I've understood, you meant: "given that presentism is true"

[Bill Vallicella]

Arash,

Thanks for catching that mistake. Yes, that is what I meant.

Peter,

Make a thorough study of Sommers' book, as Edward and I have, and then we can discuss it.

[Account Deleted]

Bill,

Good advise generally, not practically feasible for me presently.

[Leo Carton Mollica]

Peter,

Sommers says that "'*a' is a singular subject with wild quantity." But what does this phrase mean? What does the term 'wild' here have anything to do with quantity? Obviously, it is used metaphorically. But what is it a metaphor for?

I am not nearly so familiar with Sommer's logic as is our host, but it is my understanding that "wild quantity" is to be understood roughly thus: in TFL, quantity is represented by either a "-" (which stands for "all" and functions just as a minus-sign does in arithmetic) or a "+" (which stands for "some" and functions just as a plus-sign does in arithmetic) and modifies a term (so "-P" would mean "all P" and "+P" "some P"). To assign a "wild quantity" (±) to a term is to say that it is a matter of indifference whether the term be taken as modified by a "-" or a "+". Dr. Vallicella can, of course, correct me if I am wrong.

(Incidentally, Brandon Watson of Siris has a nice series of introductory posts on Sommers' TFL, which series I found very useful and would certainly recommend. Dr. Watson also gives some reasons to prefer TFL over MPL.)

By the by, I am sorry for never responding to you on the presentism thread. In response to your last question, I provisionally take duration of an individual throughout time to be established by its enduring through change.

[Bill Vallicella]

Leo,

That's right. 'Wild' is from card-playing, e.g., the Joker is wild.

Thanks for the reference to Watson. So he finished his doctorate? Did he get a regular job? Last I checked he was a grad student.

[Bill Vallicella]

I looked quickly at Watson's series of posts but did not see any discussion of what interests me primarily, the points of difference between the scholastic and Fregean approaches.

[Account Deleted]

Leo,

Thanks for explaining Sommers' account. I am not sure I thoroughly understand it or see any use for it, even if I understood it, in light of what modern logic offers in comparison.

As for presentism: no problem! We respond when we can. As for the content of your response, I have this question: Change presupposes time. What notion of time is involved in the sort of change your version of presentism requires?

[Leo Carton Mollica]

Dr. Vallicella,

Yes, he received his doctorate in philosophy from the University of Toronto. His dissertation, I believe, concerned Malebranche on the external world. He's teaching at a community college in Austin, last time I checked.

This post covers a few of the differences, albeit not in all that much depth.

Peter,

Dr. Watson gives a couple of reasons for choosing TFL over MPL in the post linked to above (which is part of a different series than the one I linked to in my last comment, which is a point I had forgotten).

Two responses as far as time goes: a.) I deny that change derives from, is dependent upon, or otherwise presupposes time; to the contrary, I take time to be logically and ontologically dependent upon change. b.) I don't have an entirely satisfactory answer to your question, but I would again say that time is a measure of what is before and what is after as far as change is concerned, and that the present we can maybe define negatively as what is neither past nor future. But let me think about it.

[Account Deleted]

Leo,

Incidentally, thanks for the references to Watson's explanation of TFL. I hope I have the time to carefully study it. However, my honest opinion is that despite the fact that an able mathematician such as Englebretsen immersed himself into it, I still find TFL and all its very complex notation Ptolemy's counterpart in logic. I do not see how whatever merit this system may have it can outweigh the enormous usefulness and provable richness that modern logic offered and still offers. I take it that the majority of logicians who studies the system came to this very conclusion. And some might have even seen how TFL is isomorphic to some sub-system of modern logic.

As for presentism, I cannot really understand the notion of change or the notion of before/after w/o presupposing the flow of time. I am particularly unclear about the following statement:

"I take time to be logically and ontologically dependent upon change."

Suppose you have two states of some object or system e and e*. Now, in order to say that e and e* represent a change in the object or system you must say that e precedes e*. O/w I cannot see how you can describe what change is. Now, so far as I can see the same holds regarding the pair before/after. These are inherently temporal terms and so far as I can see cannot be decoupled from assuming a temporal reality and the fixing of some point of reference from which one can then talk about before that point/after that point.

[Leo Carton Mollica]

Peter,

Suppose you have two states of some object or system e and e*. Now, in order to say that e and e* represent a change in the object or system you must say that e precedes e*. O/w I cannot see how you can describe what change is.

What's to prevent us giving change an Aristotelean interpretation in terms of act and potency?

As for "before" and "after", both are relation terms, which designate relations. But relations are logically and ontologically posterior to their relata. So, even if "before" and "after" are intrinsically temporal, if they relate changes, then they are posterior to those changes. Does that make sense?

[David Brightly]

Ed Ockham writes

If 'Socrates is wise' and 'Socrates is not wise' are contradictories, and if 'Socrates is not wise' implies 'someone (Socrates) is not wise', as standard MPL holds, you are committed to the thesis that the sentence is not meaningful when Socrates ceases to exist (or if he never existed because Plato made him up). Which (on my definition) is Direct Reference.

But I'm not sure this can be right. For consider a typical non-existence proof such as that of a rational square root of 2. We usually begin by saying Suppose such a rational number exists. Call it 'r'. Then r=p/q for some integers p and q with highest common factor 1, and r*r=2. We go on to deduce a contradiction and then conclude that our assumption was false. But the bolded sentence is perfectly meaningful even though it uses the name of a non-existent rational. Similarly, suppose there is a planet between Mercury and the Sun that explains the peculiarities of Mercury's orbit. Call it 'Vulcan'. A planet within Mercury's orbit large enough to account for Mercury's orbital peculiarity is large enough to be observed. Therefore Vulcan is observable. But Vulcan is not observed. Contradiction. Ergo, etc. These examples suggest to me that the device of existence assumption gives standard MPL the resources to offer a third way between DR and TFL. They also raise interesting questions about the functioning of proper names.

[Account Deleted]

David,

You are absolutely right. The quoted claim against which you argue betrays a deep misunderstanding of the distinction between meaning and reference and the resources available to direct reference (or non-Fregean) theories that maintain that names have no meaning (in the Fregean sense). Moreover, it also fails to appreciate that modern logic features many different systems, some of which can easily handle vacuous terms (e.g., Free Logic).

[Bill Vallicella]

Hi David,

Thanks for the comment. Your countryman Edward seems to have gone AWOL (or else he is busy making money). I'd like to see his response to your comment.

[Edward the nominalist]

I am a bit late to this, for holiday reasons. A handful of points.

1. Attacking the translation of 'Pittacus is wise' as 'every Pittacus is wise' is a straw man. I don't know if Sommers does it. Aristotle denies we can do this. Ockham is quite clear that a singular term like 'Pittacus' behaves like a universally quantified noun, so the universal sign is already embedded in there. Saying 'every Pittacus' is like saying 'every every man'.

2. Peter Lupu and others ask 'why bother', given that we have wonderful modern logic. One reason is given by Sommers: we want something that explains the logical form of natural logic (hint: the title of his book), which MPL was never designed to do. MPL was designed to resolve problems in mathematics. TFL by contrast was developed to resolve philosophical and theological problems. It is questionable whether MPL is useful here. Another reason is the well-known failure of MPL to handle the difficulties of empty names and identity statements.

Peter claims that free logic can address these difficulties. (a) exactly how? and (b) this opens a big can of worms. There are 'many different systems' of modern logic. Which is the correct one? If we are interested in using logic to resolve philosophical problems, then we are by definition interested in which one is the 'right' logic.

3. To David Brightly's objection. How is this an objection? If a singular term fails to refer then 'Fa' is false, because it implies that something - namely a - is F. But if 'Fa' is false, then 'not Fa' is true, but this implies that something - namely a - is non-F. So neither is true. But that is impossible. Therefore 'a' cannot signify anything. How then can we suppose that it does signify?

4. Peter objects that we can evade this by the distinction between meaning and reference. But in that case, he has acknowledged that reference is not a semantic relation between a singular term and whatever it refers to. And there are strong arguments (if you believe in MPL) that it is a semantic relation. I discuss this here http://ocham.blogspot.com/2011/05/roots-of-direct-reference-argument-4.html .

[Edward the nominalist]

On the ' deep misunderstanding of the distinction between meaning and reference', I suggest Peter should read Frege first. For Frege says (On sense and reference, Geach and Black p. 69) "If anything is asserted there is always an obvious presupposition that the simple or compound proper names used have meaning. If therefore one asserts 'Kepler died in misery' there is a presupposition that the name 'Kepler' designates something; but it does not follow that the sense of the sentence 'Kepler died in misery' contains the thought that the name 'Kepler' designates something [my emphasis]. If this were the case the negation would have to run not 'Kepler did not die in misery' but 'Kepler did not die in misery, or the name 'Kepler' has no reference'. That the name 'Kepler' designates something is just as much a presupposition for the assertion 'Kepler died in misery' as for the contrary assertion.