[FOM] mathematics as formal
steven at semeiosis.org
Sat Mar 29 18:34:01 EDT 2008
On Mar 25, 2008, at 1:27 PM, rgheck wrote:
> I thought logic was the study of such things as validity. It's no
> convention that, if it's true that p and also true that q, then it's
> true that p and q. It may be due to convention that the word "if"
> if, etc. (Then again, it may not be.) But that's an entirely different
> matter, and it is of no concern to logic.
In my view the notion of validity applies only to convention. That is,
the subject of validity is convention, and the question of whether the
convention is absolute, true and complete is of interest but it is a
The discussion by Hilbert and Ackermann of the Decision Problem
[Mathematical Logic, P112] and Church's result (referenced by Hilbert)
that denies universal validity serves, I suggest, as an adequate
illustration that validity is a matter of conventions in logic as we
understand it. It tells us something about those conventions. That is,
it is presumptuous to assume, and it is not clearly shown, that our
logical conventions are absolute, true and complete. Or rather I take
the position that in the absence of universal validity we have yet to
identify a logic that is not merely a pragmatic convention.
This is not a question without controversy, and Quine did take
exception to it, wrongly in my view.
However, I will finally appeal to Rudolf Carnap's principle of
tolerance: "It is not our business to set up prohibitions, but to
arrive at conventions." [Logical Syntax, P51]. For without this open
mindedness in foundational matters we can never make new discoveries.
Dr. Steven Ericsson-Zenith
Institute for Advanced Science & Engineering
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