Re: Axioms or 'Taxioms'?


Hatto von Aquitanien wrote:
Virgil wrote:

I would say that a system of propositions is a collection of related
positive assertions.


What you would say does not govern what mathematicians would say.

"I should like to divide up the totality of *mathematical* *propositions*
into definitions and all the remaining propositions (axioms, fundamental
laws, theorems)." - Frege

?There is, a class of *propositions* which, under the name of maxims or
axioms, pass as the principles of the sciences.... The scholastic
philosophers said that these propositions were self-evident ex terminis,
that is, as soon as the terms in them are understood? - Leibnitz

--
Nil conscire sibi

Are you really so stupid to expect that Leibnitz, who was around 300
years ago, would mean the same thing by all words as mathematicians do
now? Languages evolve. Stop disrespecting dead men by quoting them as
though they back up your tedious arguments about linguistics.

So mathematicians don't always use the same language. So what? It
doesn't *matter* whether you call these things axioms or propositions
or assertions. All that matters is that the person you are
communicating with understands your meaning. That *you* have a pedantic
disagreement with the way modern mathematicians use the word 'axiom' is
of no importance to anyone.

--
mike.

.

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