[FOM] The denial of '~p'

Richard Heck rgheck at brown.edu
Thu Aug 26 16:41:43 EDT 2010

On 8/26/10 9:53 AM, Alex Blum wrote:
> One anomaly in thinking of 'p' as the denial of '~p' is that while it is
> immediately clear that it must be the case that one of the two is true. It
> is not immediately clear that this disallows them from being jointly true.
> However, it is immediately clear that this disallows, the denial of each,
> i.e.,'~p' and '~~p', from being jointly true.
I'm confused. How can it be any less clear that `p' and `~p' cannot both 
be true than it is that `~p' and `~~p' cannot both be true? Surely what 
makes it clear that the latter cannot both be true (in so far, with a 
nod to dialetheists, it is) is the fact that one is the negation 
(denial, if you wish) of the other. But that is true in the other case, 
too: whether `p' is the denial of `~p' or not, surely `~p' is the denial 
of `p', and so they cannot both be true.

I would have thought, moreover, that if anything isn't clear here, it is 
that one of `p' and `~p' must be true. There are plenty of relatively 
sane views on which that need not hold, independently even of whether `p 
v ~p' must be true.

Richard Heck

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