[hist-analytic] Aune's objections to Jones on the analytic (1)
Roger Bishop Jones
rbj at rbjones.com
Sat Apr 11 02:35:56 EDT 2009
On Friday 10 April 2009 22:25:44 Bruce Aune wrote:
>3. But--and here is the difficulty with Roger’s claim that the
>standard criticism of Kant’s definition is untenable because any
>judgment can be put into subject-predicate form—the predicate of the
>transformed judgment is not contained in the concept of its
>subject. The subject of the transformed example is “=x,” and the
>predicate is "x = x & if the relation of every member of a series to
>its successor is one- or many-one, and if m and y follow in that
>series after x, then either y comes in that series before m, or it
>coincides with m, or it follows after m.’ I take it as obvious that
>this last predicate is NOT contained in the concept of the subject,
>‘= x’.
This is not correct.
The subject of the transformed example is the concept P
which I have defined as self identity, i.e. as the trivial
concept which is true of everything.
The predicate of the transformed example is the concept Q.
If S is analytic then Q will also be the trivial concept
i.e. it will be the same concept as P and the required
containment will hold.
>4. If you think, Roger, that the predicate here is contained in the
>concept of the subject, PROVE IT. That is all you have to do.
QED
However, there is a flaw in my argument.
The assumption that analyticity is preserved by equivalence
is too strong, for we are here talking of material equivalence
and such an equivalence may be contingent.
It therefore does not suffice to show that:
|- (S) (EP)(EQ) (S <=> (x)(P x => Q x))
It is necessary to show (using |= for "is analytic")
|- (S) (EP)(EQ) (|= (S <=> (x)(P x => Q x)))
which is more difficult because it is metatheoretic.
I shall have to come back later on this.
Roger Jones
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