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Re: Nothing is colder than itself: a truth of logic?

X1 is more Y than X2 implies X1 is Y1 and X2 is Y2.
If X1 = X2 = X, say
and IFF Y1 and Y2 are incompatible, i.e. if Y1 then not Y2 and vice verrsa,
then X is Y1 and Y2 is impossible,
i.e. X is more Y than itself is impossible.
There is nothing more to say or that need be said.
Present this to your teacher with my compliments.
His formula (x)(~Cxx) where c='1 is colder than 2' is not where it is at.
The problem is not just "colder than" - it is "more Y than".
The solution is as I have said. I will not contribute further to this.

Something about you (optional) logician-philosopher

Re: Nothing is colder than itself: a truth of logic?

I know you said you won't contribute further to this, but here is a paraphrase of my professor's response in case anyone is interested:

"Logic must be defined as strictly as possible so as to prevent people from making metaphysical assumptions and calling them, and all that they imply, truths of logic. The best way to do that is to say simply that logic is the first-order predicate calculus with identity. I grant that X is more Y than itself is impossible, but it is not a truth of logic– it is a truth of the logic of quantitative relations, which is only an extension of logic proper.

In order to teach the above lesson to my students I give them arbitrary word problems to symbolize where they have to make the immediate inference that something is colder than itself. It is a kind of shock therapy."