## Wednesday, May 09, 2012

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Dear Dr. Vallicella,

Could the reader's suggestion possibly be emended by quantifying over predicates? Thus, we could write it as (∀F)~(∃x)(Fx), where "x" ranges over individuals. Does this solve the problem, or do you think this emended version still runs into difficulties?

Not sure If I understood this statement:
"Surely, 'Some individual exists' could be true even if there are are no individuals that are either Fs or Gs. "
On the premiss that the smallest unit of *reality* is a state of affairs
and a state of affairs is by definition a compound of *logically* distinct objects, it follows that in *reality* no single object of our system can be given outside a certain combination.
What gives us the impression that objects can exist isolatedly
is a confusion between *logic* articulation and *real* articulation.
On this view, independent existence would hold between 2 atomic states of affairs not between their logical constituents.
The important epistemic consequence of this is that:
The statement "a, b, c, etc. exist" is equivalent to a metalinguistic list of *nouns* (i.e. linguistic units with their syntactic function)
but in order to get a, b, c, etc. as *logically* distinct units (i.e. corresponding to nouns with their syntactic function) I must get
ab, ac, bc, etc. (i.e. I must be shown how a, b, c, etc. synctactically operates in propositional-like contexts) beforehand, not vice versa.

I guess this takes me outside of 'Fresselian logic', but surely 'something exists' can be expressed in a second-order logic by saying that some property is instantiated by some individual?

∃P ∃x P(x)

And surely we need to be able to ask other questions relating to propositions that can only be expressed in a second-order logic, like 'why are most professors over 50 years old?'

Bill,

How about the following in classical logic:

1. Something exists: (Ex) (x=a), for an arbitrary a;
2. Everything exists; (x)(Ey)(x=y);
3. Nothing exists: (x)~(x=x);
4. Something does not exists; (Ex)~(x=x).

As for Free logic, there is an existence predicate which would carry the translations.

Leo,

What your formula says is that no property is instantiated. But if 'Nothing exists' is true, then there are no properties.

Matt,

Your formula entails that something exists. But 'Something exists' does not entail your formula. For all logic can tell us, there could be individuals but no properties, or individuals and second-level properties, but no first-level properties. Your 'P' is a first-level property variable.

Aresh says, "On the premiss that the smallest unit of *reality* is a state of affairs . . . ."

Where does this premise come from? The smallest units of reality in Frege-Russell logic are the individuals that satisfy first-level predicates.

The monadic state of affairs *a's being F* decomposes into the individual a and the property F-ness, which are 'smaller' units of reality than the state of affairs.

Hi Peter,

How goes it?

>>1. Something exists: (Ex) (x=a), for an arbitrary a;<<

That doesn't say that something exists; it says that a exists. 'a' here is not a variable but a placeholder for a name such as 'Socrates.' If a exists, then something exists, but if something exists it doesn't follow that a exists.

>>2. Everything exists; (x)(Ey)(x=y);<<

Your formula does not say that everything exists; it says that everything is identical to something or other.

>> 3. Nothing exists: (x)~(x=x);
4. Something does not exists; (Ex)~(x=x).<<

The first does not say that nothing exists; it says that nothing is self-identical. The possibility -- if it is a possibility -- that nothing exists is not the possibility that everything is self-diverse.

The second does not say that something does not exist; it says that something is self-diverse.

Vulcan does not exist; ergo, something does not exist; but that is not to say that something, namely Vulcan, is self-diverse.

Existence and self-identity are not the same property.

You are right but I was still trying to understand the way you are using the Frege-Russell logic to interpret Wittgenstein's stand, and to me what W. has in mind corresponds more to what I reported in my previous comment
"On the premiss that the smallest unit of *reality* is a state of affairs . . . ."
is how I interpret what you recalled in a previous post: "the world is the totality of facts (Tatsachen) not of things (Dinge)"

Bill,

"Existence and self-identity are not the same property."

Well, this assumes that existence is a property and more specifically a property of individuals (first-order property). But setting that aside, the suggestion I have made above (following Hintikka) is that identity can be used to express existence. So if something is identical to a, then something exists (and so on for the rest).

"...but if something exists it doesn't follow that a exists."

Here you use 'a' as a name for a particular object. In this sense, you are right. But (as you say) a here is used more like a place holder. Hence, it is neither a name nor a variable. Since I have not used 'a' as a name, the above objection does not apply to the suggestion I made.

The central issue as I see it is whether individual-existence can be fully expressed only in terms that appeal to the individual whose existence is asserted and nothing else or not. If the later, then individual-existence, if it can be expressed at all, must be expressed by appealing to something beyond the individual. Hence, Fresselians think of existence as a second-order concept.

Bill, my suggestion is that we call the concept at the root of the Porphyrean tree 'Object'. Then I think we can translate 'Something exists' into ∃x.Object(x), ie, there is at least one object. More here.

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