[FOM] The denial of '~p'

Alex Blum blumal at mail.biu.ac.il
Sat Aug 28 14:12:32 EDT 2010

Richard Heck objects to my:
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.

He writes:

| 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.

But in one case we are assuming that a statement and its denial cannot both 
be true and in the other we are not.

| I would have thought, moreover, that if anything isn't clear here, it is
| that one of `p' and `~p' must be true.

That's not me. I wrote: "it must be the case that one of the two is true".
Surely there is a difference.


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