Steven D'Aprano wrote:
> On Sun, 01 Nov 2009 21:32:15 +0100, Mick Krippendorf wrote:
>>
>> (Ax)(x is a fire-breathing animal <-> x is a real number equal to
>> sqrt(-1)).
>>
>> And since there are neither such things, it follows that s1 = s2.
>
> That assumes that all({}) is defined as true. That is a common definition
> (Python uses it), it is what classical logic uses, and it often leads to
> the "obvious" behaviour you want, but there is no a priori reason to
> accept that all({}) is true, and indeed it leads to some difficulties:
>
> All invisible men are alive.
> All invisible men are dead.
>
> are both true. Consequently, not all logic systems accept vacuous truths.
>
> http://en.wikipedia.org/wiki/Vacuous_truth
You're right, of course, but I'm an oldfashioned quinean guy :-) Also,
in relevance logic and similar systems my beloved proof that there are
no facts (Davidson's Slingshot) goes down the drain. So I think I'll
stay with classical logic FTTB.
Regards,
Mick.
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