[hist-analytic] Frrom AUNE: Analytic and A Priori
Roger Bishop Jones
rbj at rbjones.com
Wed Mar 18 16:06:56 EDT 2009
Bruce mentions again a point which I have already answered
so I will give another answer.
On Wednesday 18 March 2009 11:12:36 Bruce Aune wrote
> But as I said several times in response
> to Roger, a useful notion of analyticity should provide an a priori means
> of deciding on the truth-value of sentences, and this is something a mere
> appeal to necessity cannot do.
I have responded to this, and I don't recall an answer.
My response was that in this respect my proposal is no
better nor worse than the more usual definition,
(true in virtue of meaning) and this claim is supported
by an argument which I presented to the effect that my
definition in terms of necessity is consistent with
the definition as "true in virtue of meaning"
(to which also I recall no response).
However, I might as well stop pulling my punches and
tell you what I really feel, which is that your requirement
can and should be rejected.
It is clear that to establish "truth" of a sentence must
be in general no more difficult than establishing "analyticity",
since every analytic sentence is true.
It is also clear that even when the semantics of a language
as a whole is as clear as it possibly could be, for example
the semantics of first order arithmetic (which is as clear
as any language of similar expressive power, and clearer
than most) this does not mean that there is any reliable
way of deciding whether sentences in the language are true.
The sentences of arithmetic vary enormously in their
difficulty from "1+0=1" to Fermat's last theorem (which took
hundreds of years to prove), and Goldbach's conjecture (which
remains unproven), and of course there are many conjectures
of which the truth remains unknown (consistency of NF)
or which are known to be neither provable nor refutable in ZFC.
Mathematicians have precise criteria for when a concept
is well-defined, this is essential to the rigour of mathematical
proofs, for faulty definitions lead to contradictions.
But there is absolutely no connection between whether a concept
is well defined, and whether or not we are able to determine
its truth in all cases or any case.
I was very pleased to see you willing to countenance the
possibility that analyticity and necessity are coextensive.
Of course, a primary merit of my proposed definition is that
it makes this a trivial result.
However I think it worth giving an alternative description
of why this definition defeats Kripke that makes it seem
perhaps a little less like begging the question.
Both analyticity and necessity are semantic notions.
Necessity will be a semantic notion for anyone who accepts
1. necessity is a property of propositions
2. propositions are the meanings of sentences
since necessity is then an operator on meanings.
By defining analyticity in terms of necessity, I ensure
that the "meaning" relative to which analyticity is measured
is the same as the meaning relative to which necessity is
judged. In fact the operator in question is exactly the
same in both cases, the operator which is true iff the
truth conditions of the proposition show that the proposition
is true under all conditions (in all possible worlds).
Kripke obtains different results because he judges
analyticity against a notion of "meaning" which is
less complete than that against which he judges necessity.
He does this by introducing rigid designators which
designate the same thing in every possible world but
which do not mean the thing they designate.
This is effectively a hypothesis that the meaning
of the language provides an incomplete account of its
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