[FOM] Logical Correctness

Antonino Drago drago at unina.it
Thu Nov 22 16:19:11 EST 2012

  Wednesday, November 21, 2012 11:57 PM Lotfi A. Zadeh wrote: 
      In dealing with a problem in nonmonotonic reasoning, the following question arose. Informally, consider the sentence 
  if it is impossible that p, then it is possible that p, 
  where p is a factual proposition. The sentence is counterintuitive. Could it be logically correct, considering various interpretations of impossible, implication, possibility and p? 

  My answer is that "impossiblity" is a modal word. 
  Being modal logic equivalent via S4 model to intuitionist logic (also intutively, "impossiblity" is equivalent to "it is not the case it is not", i.e. a doubly negated sentence which is not equivalent to the corresponding affirmative sentence "it is the case"; hence, the former sentence belongs to intuitionist logic and so), the inference at issue is not only counterintuitive, but also wrong, because it applies the double negated law of classical logic to an intuitionist sentence.
  For an instance, it is wrong to derive from "the impossibility of the perpetual motion" the sentence "the perpetual motion exists".
  Best wishes for great discoveries in exploring the world of the doubly negated sentences.
  Antonino Drago
My answwer is that Lotfi A. Zadeh 
Professor Emeritus
Director, Berkeley Initiative in Soft Computing (BISC) 

729 Soda Hall #1776
Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California 
Berkeley, CA 94720-1776 
zadeh at eecs.berkeley.edu 
Tel.(office): (510) 642-4959 
Fax (office): (510) 642-1712 
Tel.(home): (510) 526-2569 
Fax (home): (510) 526-2433 
URL: http://www.cs.berkeley.edu/~zadeh/

BISC Homepage URLs
URL: http://zadeh.cs.berkeley.edu/


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