Re: An argument against modus ponens

On Sep 19, 8:32 pm, John Jones <jonescard...@xxxxxxx> wrote:
OK. But I need you to make a distinction between rules of inference and
axioms.

Bitch, please.
We have always been making this distinction.
If you are only just NOW noticing that it is important,
well, at least you FINALLY learned something.
But the whole question of what to call an axiom (or call something
else) is a red herring. You can GET BY in MANY DIFFERENT ways.
You MAY CHOOSE to call NOTHING an axiom and still work in any
axiomatic
system you like (you would just have to systematically prepend
relevant
axioms as hypotheses of conditionals). The fact that members of the
same subclass
of strings kept appearing in your hypotheses would cause those strings
to be
"acting as" axioms DESPITE your refusal to CALL them that.
You can also call EVERY theorem an axiom and just blithely note that
some of the axioms are provable from some of the others, but you don't
have to get systematic about which is shorter or which comes first, at
least
not overtly (though in fact anybody working with the theorems will
eventually
start to NOTICE that some of them can cause shorter proofs by coming
first).



.

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