McGinn Logical Properties ch 1, Identity
Each object is identical with itself and nothing else, and is essentially self-identical. This is numerical identity.
McGinn: Qualitative identity is analyzable in terms of x and y being numerically distinct but having numerically identical properties.
McGinn rejects relative identity (x can be the same F as y, but not the same G as y) for reasons of Leibniz's Law (if x=y, then x has a property F iff y has F). So if x is the same F as y but not the same G as y, x has a property y doesn't have and thus x is distinct from y. David Wiggins thinks that all identity claims are made under a sortal (some sort F, so x is the same statue as y or x is the same clay as y, rather than x is identical with y, full stop. McGinn thinks that this is unmotivated once one gives up relative identity.
All this is pretty commonly accepted. But now, can identity be analyzed in simpler terms? Perhaps, can it be analyzed via Leibniz's Law + identity of indiscernables (x=y iff (x has F iff y has F)) ? [Note that McGinn calls this "Leibniz's Law", but usually Leibniz's Law is taken only to be half of this biconditional: if x=y, then for any property F, x has F iff y has F. The converse, if for any property F, x has F iff y has F, then x=y is the identity of indiscernables and is controversial. Leibniz's Law, as we will use the term, is the claim that if x=y, then any property x has, y has; and any property y has x has. This is of course a different view from the view that if x has a property iff y has a property, x=y.
Now, if we include haecceities (properties like being Socrates or being this chair) then it will be true if x and y share all the same properties, x=y; for then x will have being y and y will have being x. If you don't include haecceities, then x and y having all the same properties doesn't seem to be sufficient for x being identical with y.
Also, this assumes property identity. Consider again the reduction of identity: x=y iff (x has F iff y has F). We're assuming that the F x has is identical with the F y has. And this can't be defined via another reduction of identity via properties of properties on pain of regress.
McGinn: It is odd that a simple claim "a is identical with b" should be analyzed in terms of a universal biconditional claim about properties ('for any property p x has p iff y has p'). It's not clear to me how strange this is, though reducing identity to anything might strike one as a bit odd.
So identity is primitive and can't be reduced to anything simpler. Indeed, nothing is more basic. Everything is essentially self-identical. McGinn claims it is more basic than existence, because even nonexistent objects are self-identical and (essentially so). It should be noted that most philosophers don't think that there are such objects, and, if they think Sherlock Holmes has reality, he has it as a mind-dependent abstract object. The view that there are no nonexistenct objects is actualism. (See the Plantinga papers in the course reader for more.) Now, one might think this: There is no Sherlock Holmes, but he still has the property actually of being self-identical. One might think this if one thinks that objects can have properties in possible worlds even if they don't exist in that world. The view that objects have properties only in worlds where they exist is serious actualism.
Ch 2 Existence
The grammatical form of
(1) Bill Clinton exists.
and
(2) Bill Clinton runs.
Are the same. The latter involves ascription of a property to Bill Clinton. So then, it would seem, should the former—it involves an ascription of existence.
But then what about
(3) Vulcan does not exist.
To what is nonexistence ascribed?
Many people say that existence (and nonexistence) are not properties. Some people say this because everything would have it, and properties have to be possibly not possessed. (But everything has the property of being such that it isn't red all over and green all over and everything has the property being self-identical.)
The (later)Russellian/Fregean view of existence statements: When you say Bill Clinton exists, you aren't saying some object (BC) has a property (existence). Rather, you are saying some property or set of properties (e.g. being Bill Clinton) is exemplified. So on this view, existence is a second-order property.
The Fregean formulation of this is that existence is a function from first-order concepts (the such-and-such) to truth values. So the logical form of "The car in the driveway exists" is "There is an x such that x is a car and x is in the driveway." This sentence can be thought of as a function from an individual concept (the x such that x is a car and x is in the driveway) to a truth value. [Don't worry too much about this. The important thing to understand is that on the Frege-Russell view of existence sentences of the form "X exists" where "X" is a proper name have as a logical form something like "The individual concept of X is exemplified" or "There is an instance of the individual concept of X." So, "Russell exists" has the logical form of (something like): "The individual concept of Russell is exemplified" (or "being Russell is exemplified" or "The G is exemplified", where "G" is some conjunction of properties that uniquely picks out Russell. Existence on this view is a property of properties, not something had by objects (like, say, being bent).
McGinn objections to the "orthodox view" of Russell and Frege.
1) Paraphrasing "X exists" by "the concept of X is exemplified" does not analyze away existence on the first-order level, because the concept of X must be exemplified by something that exists. And a regress looms if this second existence claim is also paraphrased away.
What if one says not that there needs to be something which exemplifies The concept of X, but that this sentence must be true "The concept of X is exemplified." This is the substitutional interpretation. But substitutional quantification problematic. What makes the sentence true—it looks like an (existing) instance/exemplification of the concept of X.
2) More serious: What about the concept of X. It exists, right? Then we have a the concept of the concept of X (e.g.), and it exists, right? So there is a regress of explanation. We can't explain away the apparent first-order nature of existence (it looks to be a property of objects like being tall is) by having it function as a second-order property.
3) The third objection: Suppose you claim that "exists" sometimes expresses a first-order property and other times expresses a second-order property. Suppose you want to in say "Bill Clinton exists", "exists" expresses a first-order property, but in "a man exists" it expresses a second order property. Then how will you account for the fact that the first entails the second? How will a first-order exemplification entail the second-order exemplification here? So, the argument from one to the other is like this: BC has the property of existence. BC has the property being a man. Therefore there is an instance of being a man? This isn't valid. (NB: This strikes me as an unconvincing objection.)
Also, what will "something exists" be analyzed as in a second-order manner? (NB: This is a serious problem.) One might try to analyze it as "The property of being self-identical is exemplified", but this doesn't seem to be what "something exists" really says. Then again, it's not a huge stretch over a second-order interpretation of "Bill Clinton exists"—if one can swallow that that says "the concept of BC is exemplified", then perhaps one can accept this rendering of "something exists." There also is the problem of getting "something exists" to follow from, e.g. "Bill Clinton exists" if the former has this strange reading.
4) It's not clear that "x exists and has no properties" is impossible (says McGinn). But this isn't sayable on the orthodox/Russell-Frege view. It would be equivalent to: "The concept of x is exemplified and x exemplifies no properties." Furthermore, it's not clear that the concept of existence should commit us to thinking that there are individual concepts or haecceities or other sorts of individually essential properties. [NB: But if you already believe in them anyway, you might make use of this analysis of existence.
P30: Returning to the first-order view (the property view—existence is a property of objects like being tall is).
Why would someone think that existence isn't a first-order property? Perhaps it's because it's too universal? But some properties are such that everything has them—being a thing, being such that it isn't red all over and green all over at the same time, being such that it is self-identical, etc.
Taking existence to be a second-order property helps in negative existential claims, like, "Vulcan does not exist." If nonexistence is a property of things, there is a problem—there's no Vulcan for it to be a property of.
There are two places where existence as a first-order property has been thought to be problematic: semantics the existential quantifier and claims of nonexistence.
1)
McGinn's proposal for the existential quantifier: "ExFx" is to be translated as "For some x, x is F and x exists." Usually "something is F" would be rendered as "Ex Fx." But here "some" (and similar words) aren't taken to have existential import. McGinn says that this allows "some" to function as "all" does—it tells us how many of something we're talking about. "All" doesn't have existential import: "All Fs are Gs" doesn't commit one to the existence of Fs.
Sometimes by Gricean conversational implicature, "Some" will acquire existential force. But strictly it just indicates number. So we can make sense of sentences like "some things you're looking for don't exist" if "some" doesn’t carry existential import.
2) McGinn's proposal for dealing with nonexistence: (NB: I think this section is seriously misguided.) Nonexistent objects like unicorns and Sherlock Holmes are essentially nonexistent. They are mind-dependent objects. (NB: If they don't exist, they aren't the objects of our mental activity and don't exemplify properties, or so Plantinga would argue. At any rate, it's not clear to me what he might mean by saying that nonexistent objects are intentional objects—if they don't exist, they're not objects of any sort, unless one wants to go Meinongian). Possible objects exist but don't actually exist (NB: I haven't a clue what this means.)
"Vulcan does not exist" predicates existence of a non-existent, mind-dependent object. So this is a sort of Meinongianism, though Meinong thought that nonexistent objects may have being without being dependent on a mind
Impossible objects exist, but don't possibly have actuality. (NB: It's not clear what this means, either.)
It's worth noting that people like Saul Kripke (in unpublished lectures) and Peter Van Inwagen think that Sherlock Holmes exists as an abstract object, created by A.C. Doyle. Plantinga and David Lewis think that something like the following is correct: A sentence like "Sherlock Holmes is a detective" is false because Sherlock Holmes doesn't exist. But the sentence "In the Sherlock Holmes stories, Sherlock Holmes is a detective" is true. So the fictional sentences come out true with truth-in-fiction sentential operators.
Overall: It's not clear to me that McGinn has a plausible way of dealing with negative existentials, and it is tempting to go with the orthodox view of existence with them. So it's tempting to go with it for ordinary existence statements, too, for reasons of uniformity. What does one say to his objections, then? To his first objection, one simply is giving truth conditions for "x exists" and it's not an objection to note that the thing exemplifying the concept of x exists. To his second objection, there is an infinite hierarchy of concepts (and concepts of concepts, etc.). One isn't really analyzing away existence here, rather, one is giving truth conditions for a sentence like "Bill Cinton exists." This doesn't require that one have in mind propositions about individual concepts of individual concepts of…Bill Clinton. To his third objection—the entailment objection, there isn't any structural account of why "BC exists" entails "a man" exists. But so what? To his fourth objection, "Something exists" has as truth conditions "Something is self-identical"; the truth conditions here don't need to be meaning-preserving.