[FOM] Regarding Terminology
Harvey Friedman
hmflogic at gmail.com
Sat Dec 1 19:26:04 EST 2012
I use "negated tautology" for a proposition formula false under all
assignments. Of course
A and not A
is not, strictly speaking, a negated tautology But it is
propositionally equivalent to such, and presumably for many practical
situations, "negated tautology" will work just fine.
Harvey Friedman
On Thu, Nov 29, 2012 at 1:12 PM, <T.Forster at dpmms.cam.ac.uk> wrote:
> I've also heard `self-contradiction'..
>
>
>
> On Nov 29 2012, Aatu Koskensilta wrote:
>
>> Quoting Alasdair Urquhart <urquhart at cs.toronto.edu>:
>>
>>> In Section 15 of his Introduction to Mathematical
>>> Logic, Alonzo Church uses the word "contradiction"
>>> for a propositional formula that is false under
>>> all assignments to its variables. This terminology
>>> seems perfectly satisfactory to me.
>>
>>
>> In a wider context this terminology is not completely happy,
>> unfortunately. By a tautology is usually meant a sentence that is true by
>> virtue of its truth-functional structure, a substitution instance of a
>> validity in propositional logic. But there are contradictions e.g. in
>> first-order logic -- (x)(Ey)P(x,y) & (Ex)(y)~P(x,y) for instance -- that
>> are not (substitution instances of) logical falsehoods in propositional
>> logic, that are not false by virtue of their truth-functional structure.
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