FOM: Re: Field on LEM and determinate truth value
neilt at mercutio.cohums.ohio-state.edu
Fri Mar 6 15:42:35 EST 1998
Hartry Field wrote:
> in reasoning in languages
> with vague or otherwise indeterminate predicates, we ought to apply
> classical logic and classical truth theory; so e.g. either 'George is bald'
> or 'George is not bald' will be true, even when George is a borderline case.
> But if George is borderline it won't be determinate which is true--neither
> will be determinately true.
He then went on to say:
> many formally undecidable sentences (eg about the value of
> the continuum) will be not only formally undecidable but objectively
> indeterminate. They are still either true or false, by classical logic plus
> classical truth theory, but not determinately true or determinately false.
Let P be such a sentence: formally undecidable; objectively indeterminate
(presumably, in truth value, not in meaning?); either true or false; but
not determinately true or determinately false. [Please note that if there
is any redundancy in this specification, it is from Hartry's description
Hartry, can you suggest what kind of *justification* one might have for
using, say, the classical law of excluded middle on P? I had thought that
the only justification ever offered for the use of excluded middle was
the principle of bivalence---that is, the belief/insistence that every
declarative sentence enjoyed a *determinate truth value* (true or false),
independently of our knowledge of that truth value, and independently
of our means of coming to know what that truth value is.
But, if I understand you correctly, you are suggesting that one would
be justified in applying excluded middle to sentences *that do not have
determinate truth values*.
First question: Have I understood your position correctly?
Second question: If so, how do you justify such uses of excluded middle?
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