Re: Axioms or 'Taxioms'?

In article <q-adndgc1btufAjZnZ2dnUVZ_omdnZ2d@xxxxxxxxxxxxx>, Hatto von
Aquitanien <abbot@xxxxxxxxxxxxxx> wrote:

Virgil wrote:

In article <I9OdnWiggqK34w_ZnZ2dnUVZ_q-dnZ2d@xxxxxxxxxxxxx>,
Hatto von Aquitanien <abbot@xxxxxxxxxxxxxx> 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

Frege, 1848-1925, is long since gone.

?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

Leibniz, 1646-1716, is even longer gone.

It is what mathematicians would say NOW that is relevant.

I will have to grant that I was not able to find a single example of an
English mathematician who uses the term "proposition" in the sense used by
American and continental European mathematicians. But the English language
is no longer defined by what usage is current in England. Furthermore,
since I have also demonstrated that my preferred use is support by an
authoritative English philosophical reference, I proclaim vindication.

I find it hard to believe that you actually believe what you are
saying. You have hosts of mathematicians telling you what the common
usage of various words are, and you simply refuse to believe them.
.

Relevant Pages

  • Re: Axioms or Taxioms?
    ... positive assertions. ... What you would say does not govern what mathematicians would say. ... into definitions and all the remaining propositions (axioms, ... axioms, pass as the principles of the sciences.... ...
    (sci.math)
  • Re: Axioms or Taxioms?
    ... What you would say does not govern what mathematicians would say. ... into definitions and all the remaining propositions (axioms, ... English mathematician who uses the term "proposition" in the sense used by ...
    (sci.math)
  • Re: Axioms or Taxioms?
    ... positive assertions. ... What you would say does not govern what mathematicians would say. ... into definitions and all the remaining propositions (axioms, ... axioms, pass as the principles of the sciences.... ...
    (sci.math)
  • Re: Axioms or Taxioms?
    ... positive assertions. ... What you would say does not govern what mathematicians would say. ... into definitions and all the remaining propositions (axioms, ... axioms, pass as the principles of the sciences.... ...
    (sci.math)
  • Re: Axioms or Taxioms?
    ... What you would say does not govern what mathematicians would say. ... into definitions and all the remaining propositions (axioms, ... axioms, pass as the principles of the sciences.... ...
    (sci.math)
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