Metaphysical circularity

Following my post on my return from sunny Greece, the Maverick now has finally conceded that the 'thin' definition of 'exists'

(1) A-B exists =df A is B

cannot be circular, at least in the strict and ordinary sense of circular. However, he insists that the following equivalence (note the omitted 'df') is still circular.

(1a) A-B exists = existing A is B

He adds: "One response I anticipate Ed making is to say that there is no difference between 'x' and 'existing x': whatever is a value of the one is a value of the other, and vice versa. If so, then perhaps (1a) collapses into (1) and there is no circularity in the sense in which the examples above are circular." That's roughly right, but let's see why I am saying that. It follows from definition (1) that "A man who is white" is equivalent to "an existing white man", and it clearly follows from this that "existing white man" is equivalent to "white man". Thus (1a) above is a mere logical consequence of the original definition.

But Maverick goes on to claim that I am confusing semantic with metaphysical circularity. He says (I modify his wording to accommodate my example):

A presupposition of (1)'s truth is that the domain of quantification -- the domain over which the variable 'A' ranges -- is a domain of existents. Therefore, if I want to know what it is for A to exist, you have not given me any insight by telling me that for A to exist is for A to be identical to something that exists. For of course the A is identical to something that exists, namely the A! Suppose we distinguish between semantic and metaphysical circularity. I am willing to concede that (1) is not semantically circular. But I do maintain that (1) is metaphysically circular: its truth presupposes that the domain of quantification is a domain of existing items.

I reply: the fact that the "domain of quantification", i.e. all the items which satisfy 'A is B' is not a presupposition of the definition, but rather a consequence of it, for essentially the same reason I gave above. Let's first define 'satisfy':

(2) 'A is B' is satisfied by any A that is B

And then make the following assumption:

(3) 'A man is white' is satisfied by that man over there.

Then the following statements logically follow:

(4) That man is white (2, 3)

(5) That white man exists (1, 4)

(6) 'A man is white' is satisfied by an existing white man (3, 5)

So of course the items in the domain of quantification have to be existing items, but the sense in which they 'have to be' existing is a matter of logical consequence alone. They 'have' to exist in the same sense that a bachelor 'has' to be unmarried.

He adds that his claim that the thin conception is 'ontologically' or 'metaphysically' circular is something I fail to understand. This I agree with, of course, for the reason that 'metaphysical circularity' is incoherent.

Existence and the enlargement principle

In my earlier post I argued that the 'thin conception' of existence does not involve any obvious circularity.  We define the verb 'exists' in terms of the following equivalence

"An American philosopher exists" is(def) equivalent to "some philosopher is American"

The verb 'exists' only appears on the left hand side of the definition, and so the definition is not circular, by the definition of circularity.  To the objection that the right hand side has an elided adjective 'existing', i.e. that the definition should really be

"An American philosopher exists" is(def) equivalent to "some existing philosopher is American"

I appealed to what I will call the 'enlargement principle'.  This is the principle that any adjective or qualifying term must, if it is to be meaningful, enlarge the conception signified by the term that it contracts. Thus 'blue' enlarges the concept signified by 'buttercup' when we attach the terms to form the composite 'blue buttercup'. Thus it is meaningful.  But 'existing' does not enlarge the concept signified by 'American philosopher', for the sentence 'some philosopher is American' already states that an American philosopher is existing.

Against.  Consider the concept signified by 'character in War and Peace'. There are hundreds of such characters.  Some of these, such as Napoleon and the Czar of Russia, and the Russian general whose name I have forgotten, are or were historical characters.  So they are existent in some sense (i.e. they used to exist, or exist in the afterlife).  Others, such as Prince Bolkonsky or Natasha, never existed at all.  So the contracting term 'existing' or 'historical' does enlarge the conception signified by the term it is attached to.  And it does diminish the extension of the contracted term.   The total number of characters in the book is large, but decreases significantly when we consider only the real historical ones.  Thus the term 'existing' or 'historical' or 'real' is meaningful, and a real predicate. Thus the thin conception of existence does involve circularity.

Is any man's parent male?

Nice to know these medieval problems are still a difficulty. Anthony argues that 'every man's parent is male' is false because (if I am understanding him) every man has two parents. OK, then if Aristotelian theory is correct, and if that sentence really does have the logical form 'every A is B', it follows that its contradictory 'some man's parent is not male' is true. But what makes that true? Well, take any man you like, say John. Jean is a parent of his, and she is not male, so 'some man's parent is not male' is true because of John and Jean. But John was any man you like. It therefore follows that 'every man's parent is not male' is true.

But that causes a problem. Assuming that every parent is either male or female, 'every man's parent is not male' implies 'every man's parent is female'. But the whole argument began with the assumption that 'every man's parent is male' is false because every man has two parents. Why, by equal reasoning, isn't 'every man's parent is female' false also?

Does a Common Term Suppositing with a Present Tense Verb Supposit Only for Presently Existing Things?

Sorry for the strange title but it is a literal translation of one of the questions (Latin: Utrum terminus communus supponens verbo de praesenti supponat tantum pro praesentibus) in Scotus’ Questions on the Perihermenias, and I am struck by the increasing resemblance between the discussion going on here, and the discussions on the same subject going on in the late 13th century in Oxford and Paris. In my last post, I discussed the slightly paradoxical syllogism

(1) No y is identical with Caesar
(2) Some x was identical with Caesar
(3) Some x is not identical with any y

to which David Brightly objected that

For (1) to be true it's clear that the range of the quantified expression 'no y' cannot be all men who ever were. Rather the present tense 'is' modifies the quantifier 'no man' restricting the ys in (1) to the presently existing men. Similarly in (2) the past tensed 'was' modifies the quantifier 'some x', restricting the xs to the men who ever were, ie, no restriction at all.

Well that’s true, and that’s one solution proposed by some of the scholastics, who thought that the present tense of the main verb of the sentence restricts (Latin: restringit) a common term like ‘man’ to suppositing (i.e. ranging over) presently existing men (praesentibus).

What’s wrong with that solution is the present tense that we have to use when we say what things are in the domain or range of quantification. David says that using a verb in the past tense allows the quantifier it to range over all the man that ever were. The problem is the implied present tense of the ‘ranging’. How is it that the quantifier ‘ranges’ – present tense – over past men, men who longer exist? Surely it can’t. Nor can the domain now ‘contain’ all such men. It used to contain them, but now it doesn’t. So the second premiss (2) cannot be true. There cannot be any x that was identical with Caesar, because however wide the domain or range of quantification, the domain exists in the present. It has to exist in the present because we say that it is the range of our quantification, and to say that we must use the present tense.

Anthony is closer when he says that the real problem is presentism, but there are problems with presentism also, which I will talk about later.

Clarification

David Brightly has rightly questioned whether my argument is valid:

Caesar was a man
Caesar is not (any longer) a man
Some man is not a man

It's not, unless our domain of quantification consists only of men.  But I can easily restate the argument

No y is identical with Caesar
Some x was identical with Caesar
Some x is not identical with any y

I don't see any way round that.  Of course, some x was identical with some y (for y = Caesar, where the verb "=" has past tense).  And perhaps we could read the existential quantifer as tensed - there was an x such that x is not identical with any y.  But there's no way we could make any sense of it in standard predicate logic.  Moreover, the standard way of understanding quantification as a kind of relation between variables or open sentences or predicates on the one side, and objects on the other, makes no sense either.  For example, logicians say that the predicate "- was an emperor" is satisfied.  Is satisfied?  Or was satisfied?

Quantifying over

In an earlier post I asked whether some men are not men. Intuitively all men are men, and so ‘some men are not men’ is false. Yet if the term ‘man’, occurring in the subject position of a sentence, means something like ‘someone who is, was or will be a man’, and given that Caesar was once a man, but is no longer a man, i.e. not now a man, it seems to follow that some men (e.g. Caesar) are not men, i.e. were men but aren’t now. Thus, counterintuitively, some men are not men. From this we derived the even more puzzling ‘some present events are not present events’. Caesar’s crossing the Rubicon was once a present event. And if ‘present event’ means ‘event which is, or was once, or will be present’, and since Caesar’s crossing the Rubicon is not present, it apparently follows that at least one present event (crossing the Rubicon) is not a present event.

David Brightly, taking the approach of a contemporary logician, helpfully suggests that “we just stipulate in advance which men we propose to quantify over and this bounds what 'some man' may refer to. It could be men alive, dead or alive, living in Midsomer, ever been married, whatever is appropriate, as long as we make it explicit and make appropriate adjustments elsewhere.”

I object that it is a problem either way. If the English word ‘man’ in fact only means presently existing man, it immediately follows that we can’t quantify over men in the 13th century, for there are none to quantify over. Nor were there any. ‘Some man lived in the 13th century’ is false, unless there is a 700 year old man still alive. The question is what the word ‘man’ ranges over. If only presently existing entities, then there were no men alive 10 years except for those alive now, thus very few men who were alive 90 years ago. Census records are all false. There were not 7 million people living in London in the 1920s. More like a few thousand (namely all present Londoners who are old enough to have lived here 90 years ago).

If by contrast we accept that there were 7 million Londoners in the 1920s, we have to accept that most of these, namely the ones who have died, are no longer Londoners. Thus, some Londoners are not Londoners. You can’t escape the problem by specifying ‘domains of quantification’.

Meinongians who aren’t Meinongians

To explain the apparent paradox of the title, there are at least two senses of the term ‘Meinongian’. In the first sense, a Meinongian affirms the reality of fictional characters (by saying for example that there is such a person as Sherlock Holmes, or Sherlock Holmes exist). In the second sense, a Meinongian denies Brentano’s thesis and thus drives a wedge between ‘thing’ and ‘existing thing’: some things are fictional characters, but those things do not exist.

Peter van Inwagen is an example of the first kind of Meinongian, but not the second. He argues* (p. 237 ff) that the correct way, and the only way, to understand the use of variables and quantifiers is to show how they can be translated into expressions of ordinary English that we already understand. He gives a few examples to show how it is clear that the formal predicate calculus is simply a regimentation of the ‘all’ and ‘there are’ of ordinary English. He concludes (p.239) “The existental quantifier therefore expresses the sense of ‘there is’ in ordinary English. (As an opponent of any form of Meinongianism, I would say that the existential quantifier is appopriately named – for the reason that, in expressing the sense of ‘there is’ in English, it thereby expresses the sense of ‘exists’ in English).” To the objection (p.242) that this account of the meaning of a sentence containing quantifiers does not tell us the conditions under which it would be true, he neatly replies that “the conditions under which a sentence would be true, are not the first thing about the meaning of a sentence. The first thing about the meaning of a sentence is what the sentence means” – which is just what his account tells us about sentences containing quantifiers, he says.

This has an important consequence for fictional discourse (meaning not the discourse you find in works of fiction, but rather what is spoken or written about works of fiction, such as found in literary criticism). Such discourse can potentially include complex quantification. Inwagen’s example is

(1) There is a fictional character who, for every novel, either appears in that novel or is a model for a character who does.

This involves apparent existential quantification and a complex quantificational structure, as well as the ability to generate all the inferences licensed by quantifier logic. For example, we can deduce

(2) If no character appears in every novel, then some character is modelled on another character.

If the quantification is real, and given Inwagen’s rejection of the second kind of Meinongianism (i.e. the kind that accepts existential quantification but not existential commitment) then we must accept the reality, indeed the real existence, of fictional characters. If the quantification is not real, we must explain (p.244) how to paraphrase the two sentences above, show whether the second sentence follows from the first, and if not, why it does not. In summary:

*The existential quantifier expresses the sense of ‘there is’ and ‘there exists’ in English.

* ‘For some x, x is a fictional character’ is true.

* There are fictional characters, i.e. fictional characters exist.

Thus Inwagen is a Meinongian in the first sense. He affirms the reality of fictional characters in the most direct way, claiming that they exist. But he is not a Meinongian in the second sense. For he upholds the Brentano thesis - ‘For some x, x is a fictional character’ = ‘There are fictional characters’ = ‘Fictional characters exist’.

Van Inwagen recognises he must explain the apparent truth of sentences like ‘Sherlock Holmes does not exist’. I will discuss his explanation tomorrow.

* "Quantification in fictional discourse", in Empty Names, Fiction and the Puzzles of Non-existence, Stanford 2000, pp. 235-247.

Quinean and non-Quinean quantification

In a short paper published in 2000, Thomas Hofweber discusses an attempt to defend Meinong by distinguishing what he calls Quinean and non-Quinean quantifiers. A Quinean quantifier (or a Quinean occurrence of a quantifier) is where we can modify it with 'who/which exists' without change of truth conditions of the proposition in which it occurs. Thus in

(a) Something is eating my cheese, probably a mouse.

the occurrence of the quantifier 'something' is Quinean. Clearly 'something which exists' is intended. By contrast, the occurrence of the same quantifier in

(b) Something is keeping me awake at night, namely the monster I dream about.

is non-Quinean. Monsters don't exist, so nothing which exists is keeping me awake at night. Therefore modifying 'something' with 'which exists' would change the truth conditions of the second sentence, therefore the occurrence of the quantifier is non-Quinean.

This is pretty close to the thesis of Peter Lupu's that I was moaning about earlier. The idea is that we can explain the consistency of the conjunction 'Tom is thinking of a mermaid, but nothing is a mermaid' by interpreting the 'nothing' as a Quinean quantifier. That is, the conjunction really means Tom is thinking of a mermaid, but nothing which exists is a mermaid. However, the 'something' in the claim 'there is something Tom is thinking of' is non-Quinean, since it is false that there is something which exists which Tom is thinking of.

I have given enough objections to this sort of thing for now. Enough to say that it can be true that Tom is thinking of a mermaid even if absolutely nothing whatever is a mermaid, i.e. where non-Quinean quantification for 'absolutely nothing' is intended. I have another fundamental objection to this idea, namely the use that Meinongians put it to.

Even if we buy the distinction between Quinean and non-Quinean quantifiers, a further problem is the way Meinongians persistently make inferences from contexts that involve non-Quinean quantification, to contexts that unambiguously require Quinean quantification. I already gave an example here of a move such as this:

Tom is thinking of something, therefore Tom's thinking is directed towards something.

This is illegitimate because (in my terminology) 'is thinking of' is a logically intransitive verb, whereas 'is directed towards' is logically transitive. In Hofweber-speak, even if the first 'something' is non-Quinean, the second is unambiguously Quinean. Nothing can be 'directed towards' something unless it is something which exists. The Meinongian makes these illegitimate moves all the time. Example: he argues (p. 255, my emphasis) that Quinean quantifiers are restricted to things that exist, and so

since non-Quinean quantifiers don't have such a restriction this shows that the domain of quantification really is what the non-Quinean quantifiers range over. Quinean quantifiers range over a subdomain of this domain, namely over all or some of the things in the domain that exist. Thus the true domain of discourse contains non-existent objects ...

Note the verb 'contains'. This verb is unambiguously logically transitive, i.e. 'a contains an F' is always inconsistent with 'nothing is an F'. Thus the quantifier 'an F', as it occurs as the accusative of 'contains', is Quinean. Even if we buy the distinction between Quinean and non-Quinean, the quantifier 'everything' in 'everything that the true domain of discourse contains' is Quinean. Thus everything the Meinongian wants to talk about, he cannot talk about. Therefore he should remain silent. Another example of language on holiday tomorrow.

* "Quantification and non-existent objects", in *Empty Names, Fiction and the Puzzles of Non-existence*, Stanford 2000, pp 249-273.