I think this is basically right, though I would put it a little differently and in a way that displays the logical connection of the theses, since the theses are not logically independent. The crucial point is (C). So it belongs first in order:
1. One who advocates a 'thin' theory of existence views existence, both general and singular, as fully capturable by the apparatus of quantification plus (absolute) identity. If so, then it follows that
2. A thin theorist views the question 'What is it for an individual to exist?' as a question that does not have a deep philosophical or metaphysical answer. And from (1) it also follows that
3. Thin theorists reject any distinction in reality between an individual and its existence.
This is an excellent start, but much more needs to be said. (1) and (3) both require commentary. I'll leave (3) for later.
With respect to (1), we can and must ask: quantification how interpreted? There are two main styles of interpretation, the objectual (referential) and the substitutional. (C. J. F. Williams also speaks of a third style, the 'Prioresque' which is a modification of the substitutional interpretation. But we leave this for later.) The following provides a rough illustration of the difference:
Obj. '(Ex)(Fx)' is true iff 'F' is true of some individual
Subs. '(Ex)Fx' is true iff some substituend for 'x' in 'Fx' yields a true sentence.
To appreciate the difference you must appreciate the difference between a substituend of a variable and a value of a variable. An example of a substituend for the individual variable 'x' would be the proper name 'Socrates.' An example of a value of 'x' would be Socrates. In the equation 'x + y = y + x' substituends are numerals, not numbers, and values are numbers, not numerals. Note that if we substitute 'Socrates' for 'x' in the open sentence 'x is wise' the result is 'Socrates is wise' not '"Socrates" is wise.' That is to say: a substituend of an individual variable is a proper name functioning as a proper name, thus used, not mentioned.
All right, but what is the practical difference between the two readings? One difference emerges when we note that there are individuals that lack names. Consider the true existentially quantified sentence, 'There are cacti behind my house that bear no name.' Read objectually, the sentence is true iff 'cactus behind my house that bears no name' is true of some individual — which is certainly the case. Read substitutionally, however, the sentence does not come out true. For on the substitutional interpretation, 'There are cacti behind my house that bear no name' is true iff some proper name substituted for 'x' in 'x is a cactus behind my house that bears no name' yields a true sentence. But there is no such name.
The cacti behind my house are unnamed, but nameable. But there are also in principle unnameable objects among the real numbers. If there are nameless and unnameable objects, then (Obj.) and (Subs.) come apart. And it may also be the case that they come apart if there are objectless names. Consider the false existentially quantified sentence 'There are winged horses.' On an objectual reading, this comes out false, as it should. But on a substitutional reading it comes out true. For on the latter reading, 'There are winged horses' is true iff some substituend for 'x' in 'x is a winged horse' yields a true sentence. Now 'Pegasus' is such a substituend. Plugging this name in for 'x' yields the true sentence, 'Pegasus is a winged horse.'
With this rough understanding of the difference between objectual and substitutional interpretation of quantifiers under our belts, let us now formulate two versions of (1) above:
1A. On a thin theory, existence is fully capturable by the apparatus of quantification objectually interpreted.
1B. On a thin theory, existence is fully capturable by the apparatus of quantification substitutionally interpreted.
Now I am pretty sure that Peter Lupu intends (1A) since his version of the thin theory is close to Quine's and Quine, we know, takes his quantifiers objectually. For Quine, names are eliminable and reference is routed though bound variables. (1B), however, caters better to what the thin theorist aims at, namely, the total elimination of existence as an extralogical, metaphysical topic.
Let me now try to argue that a theory of existence as what objectually interpreted existential quantification expresses is not a truly thin theory of existence. First of all, let us be clear that a truly thin theory of existence eliminates any vestige of existence as a first-level property. Thus on a truly thin theory, 'Cats exist' gets rendered as
4. For some x, x is a cat (Something is a cat)
and not as
5. There exists an x such that x is a cat.
(5) implies that the values of 'x' that make (5) true exist. But those values are individuals. So (5) implies that existence is a first-level property — which contradicts the thrust of thin theories. One can also see this by reflecting on Quine's slogan, "To be is to be the value of a [bound] variable." Since Mungo is a cat, Mungo is a value of the bound variable in (5). Given that to be is to be the value of a bound variable, we may infer that Mungo is or exists. But Mungo is an individual, and first-level properties are properties of individuals. Therefore, existence for Quine is a first-level property — which contradicts the whole thrust of thin theories, which is to remove existence from individuals.
What I am saying, then, is that (1A) cannot be one of the planks in a truly thin platform. So if Peter interprets quantification objectually, then he is not a thin theorist strictly speaking.
The nearest you come to it is when you make the slide from ‘exist’ being a first-level predicate to ‘exist’ being a first-level property. A presuppositionist thin would not disagree that ‘exist’ is a first-level predicate, since ‘for some x, x is Socrates’ is well-formed, thus ‘for some x, x is ---’ is a genuine predicate. But it doesn’t follow that existence is a property, i.e. something that an individual may coherently lack. For ‘for some x, x is not Socrates’ is incoherent, ill-formed. It is tantamount to ‘Socrates’ not meaning anything at all, and so any sentence that contains the name not having any meaning either.
You say(my boldening)True, but a strange way of wording that suggests to me that you allow that there might be values of 'x' that make (5) true that don't exist. But I asked about this earlier and you denied that this was the issue at stake. So I remain confused.
Ockham says that your argument is problematic for only the presuppositionist logician. But I'm not sure about this either. Your interpretation of (5) appears to beBut for the presuppositionist Exists(x) is True for all x so (5) is justThe presuppositionist has no need for an explicit Exists() predicate.
I don't follow. Surely it's true in any domain containing an object other than Socrates?
>>Ockham, 'for some x, x is not Socrates’ is incoherent, ill-formed. [???]
Thanks for spotting that. Should have been ‘NOT for some x, x is Socrates’. Sorry – in a hurry as usual.
comes out False if the domain contains Socrates, and True otherwise. I don't see the incoherence.
Thanks for the kind words. I try to be clear, though at the end of the post I am not sure I achieved the goal. Clarity is an intellectual virtue, I suppose, though not clarity for its own sake. But it is probably better to have the moral virtues than the intellectual ones.
You say
5. There exists an x such that x is a cat.
(5) implies that the values of 'x' that make (5) true exist.
(my boldening)True, but a strange way of wording that suggests to me that you allow that there might be values of 'x' that make (5) true that don't exist. But I asked about this earlier and you denied that this was the issue at stake. So I remain confused.
What I want to say is that 'There exists an x such that Fx' attributes existence to x and that this contradicts the whole thrust of a thin or deflationary theory of existence, which is to eliminate existence as an attribute of individuals. The deflationism of Frege and latter-day Fregeans such as C J F Williams consists in the thesis that existence can never be attributed to what Frege calls objects but only to what Frege calls concepts. Now if this is right, then there is no contrast at the level of objects between existence and nonexistence. That contrast is situated at the level of concepts as the contrast intsnatiated/not instantiated.
The point of my saying that the values of 'x' exist is that this makes existence an attribute of objects as opposed to an attribute of concepts. The point is not that the values of 'x' exist as opposed to not existing.
You say there are three varieties of thin theory. It would help if you explicitly define each of these.
You write, " ‘for some x, x is Socrates’ is well-formed, thus ‘for some x, x is ---’ is a genuine predicate." True, but it doesn't follow that '___exists' is a first-level predicate.
>>You say there are three varieties of thin theory. It would help if you explicitly define each of these.
Well I did so on the 7 May and at least once before, but I can’t find the link. Of the third (‘assertionist’) variety there are two sub-versions. The Russellian, where the name is a telescoped description. And my version, where the name stands for a singular concept, and not for any other property (other than being that individual named), or complex group of properties.
David Brightly:
>>Ockham, not for some x, x is Socrates comes out False if the domain contains Socrates, and True otherwise. I don't see the incoherence.
If the domain does not contain anything that the word ‘Socrates’ refers to, then ‘Socrates’ is not a name, but a meaningless mark. Ergo the expression ‘Ex x = Socrates’ is not well formed, for it must contain a name where the meaningless mark ‘Socrates’ occurs.
This is on a presuppositionist theory, of course, where it is presupposed, not asserted, that the expression ‘Socrates’ has a referent. On an assertionist theory (the third of those linked to above) the existence of a referent for the name is asserted, and the name can be allowed to be meaningful even when it does not have a reference.
Bill
>>You write, " ‘for some x, x is Socrates’ is well-formed, thus ‘for some x, x is ---’ is a genuine predicate." True, but it doesn't follow that '___exists' is a first-level predicate.
It depends whether what fills the gap in ‘--- exists’ is a logically proper name or not. If logically proper, then the predicate must be first-level, surely.
What he confusingly called the 'Ockhamist' thesis is not in fact Ockhamist. Ockham's theory is much closer to my own, since he holds that (some) singular sentences contain the assertion of existence, and are thus two propositions rolled up in one. Sainsbury does not subscribe to this.
---------------- Sainsbury's theory
1 There are singular referring expressions (like many proper names) and plural ones (like compound names: “Plato and Aristotle”);
2 There are simple referring expressions (like many proper names) and complex ones (like compound names and various species of definite description);
3 Some intelligible referring expressions have no referents;
4 A referring expression without a referent may occur in a truth (e.g. “Vulcan does not exist”);
5 Semantic theory is governed by negative free logic (NFL) rather than by classical logic;
6 Reference is an absolute relation, and is not world-relative;
7 Referring expressions are rigid designators and constitute a uniform semantic category;
8 A singular referring expression meets the condition: it if refers to x and to y, then x=y.
9 In semantic theory, referring expressions are associated with reference-conditions rather than referents. An example:
for all x (“Hesperus” refers to x iff x = Hesperus);
10 Semantic theorems are often (and ideally) homophonic;
11 Coreferring expressions may be assigned distinct reference-conditions;
12 Subject–predicate sentences are associated with Ockhamist rather than Strawsonian truth conditions. (Ockhamist: S–P is true iff S has a unique referent which satisfies P and is false otherwise. Strawsonian: S–P is true iff S has a unique referent which satisfies P and is false iff S has a unique referent which fails to satisfy P.)
>>ockham - There are some clear attractions to the assertionist view, at least for me. But I'm still a bit hazy concerning the question of how quantification relates to existence claims on this view. Could you direct me to a good exposition of this matter?
The classic manifesto of assertionism is of course Russell's Theory of Descriptions. This describes exactly how quantification relates to existence claims.
An earlier version of the same theory was given by the original William of Ockham. See my translation here. Ockham argues that 'the chimaera is a chimaera' is false, because it is an 'exponibile' proposition, i.e. a compound proposition that unpacks into the two simple propositions 'the chimaera is something', which assertions existence, i.e. somethingness, and 'it is a chimaera' which predicates the same thing of itself, a predication which is true of anything, i.e. anything that is 'something', i.e. anything. But the chimaera is not anything, so 'the chimaera is a chimaera' is false.
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