On 9/27/2018 10:54 PM, Jerry LR Chandler wrote:
Pure mathematics has infinitely many theories.
If you only want a restricted version, it has that also.
Fine. If you wish to hypothesize that pure mathematics can
generate large categories of theories, I will grant you that
that is readily conceivable.
Good. That's what Peirce and many other mathematicians have said.
And that is the only point I was trying to make.
Meaningless theories, no matter how many, are all of the same type,
that is, meaningless. Applied mathematics must necessarily be a
correspondence relationship between meaningful symbols and
meaningless symbols.
We agree on the fact that they aren't applied to anything that
exists. But the words meaning(ful/less) make a value judgment.
Such statements are in the branch of philosophy called normative
science.
Since pure mathematics is prior to philosophy, Peirce did not
call those theories meaningless. He said that there are three
"universes": possibilities, actualities, and the necessitated.
The domain of discourse of that infinite set of consistent theories
is the universe of possibilities. The theorems of those theories
are the universe of necessities. And what exists in our universe
are the actualities.
Applied mathematics must necessarily be a correspondence relationship
between meaningful symbols and meaningless symbols. I published this
argument more than twenty years ago.
Yes. Peirce and many others would agree with you.
John
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