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 selfidentical 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 meaningpreserving.