[FOM] Intuitionists and excluded middle

Keith Brian Johnson joyfuloctopus at yahoo.com
Tue Oct 18 20:51:37 EDT 2005

Taking "having a truth-value" to mean "having a constructible proof"
or, alternatively, taking it to mean "having been constructibly
proven," I can't see the meaning of denying either (a) or (b), at least
not while holding time and claimant fixed.  Surely every sentence
either has a constructible proof or it hasn't for any particular time
and any particular claimant; surely every sentence either has been
constructibly proven or it hasn't for any particular time and any
particular claimant.  If "having a truth-value" is taken as "having
been constructibly proven," then it is perfectly possible that a
sentence's truth-value will *change* rather than remaining fixed for
all time; was that the sort of denial being expressed?  I don't think
the sentences were being relativized to individual claimants, were
they?  I'm puzzled as to the meaning of the denials quoted below.

Keith Brian Johnson

--- Hendrik Boom <hendrik at pooq.com> wrote:

> On Mon, Oct 17, 2005 at 08:32:19PM -0700, Keith Brian Johnson wrote:
> > 
> > Do intuitionists deny [...] (a) that every sentence either has a
> > truth-value (possibly more than one) or does not;
> Yes.
> > > 
> > Do intuitionists deny [...] the stronger
> > (b)that every sentence either has exactly one truth-value or has
> none? 
> Yes.
> But I think they would agree that every sentence has at most one
> truth value.
> -- hendrik
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