It's a simple exercise, using mathematical induction, that Peirce's Law
is is independent under axioms (1) and (2) with the Rule of Detachment,
but not under (1) and (3):
(1) A --> (B --> A)
(2) A --> (B --> C) --> ((A --> B) --> (A --> C))
(3) (~A --> ~B) --> (B --> A)
Not certain how "non-trivial", but this is a good illustration of how
selection of one's axioms can be crucial, or perhaps "non-trivial".
----- Message from klkevel...@hotmail.com ---------
Date: Thu, 21 Jul 2011 23:43:51 -0400
From: Keith Kevelson <klkevel...@hotmail.com>
Reply-To: Keith Kevelson <klkevel...@hotmail.com>
Subject: [peirce-l] Peirce's law ((P>Q)>P)>P
To: PEIRCE-L@LISTSERV.IUPUI.EDU
Dear list,
I was wondering if anyone has come up with some good, non-trivial
examples of Peirce's law holding when Q is false. I've come up with
some examples, but they all imply the truth of Q. How can you have a
false logical relationship still imply the truth of its initial
proposition?
Thanks,Keith
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Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info
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