[FOM] Negation as a non-primitive logical constant
Irving
ianellis at iupui.edu
Thu Apr 15 13:35:33 EDT 2010
On Thu, 8 Apr 2010, Joao Marcos wrote:
>> I was wondering which are the earliest references to be found in the
>> literature to the "intuitionistic" definition of negation of A in
>> terms of A implying bottom
I am not entirely certain that I completely understand what the
question may be. If what is at issue is the answer to the historical
question of the first identifiable definition of negation in
intuitionistic logic by an intuitionist logician, then it would be
worth starting by examining Brouwer's paper "De onbetrouwbaarheid der
logische principes" (Tijdschrift voor Wijsbegeerte 2 (1908), 152-158),
in which he explicitly presents the new -- intuitionistic -- meaning of
negation for the first time in his new interpretation of the law of
excluded middle.
There is an historical aacount in Miriam Franchella, "Brouwer and Griss
on Intuitionistic Negation", Modern Logic Volume 4, Number 3 (1994),
256-265. For an exposition, looking at Heyting's formalization of
Brouwer's intuitionism for starters, one might begin by examining W.
Russell Belding, "Intuitionistic Negation", Notre Dame Journal Formal
Logic Volume 12, Number 2 (1971), 183-187.
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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