I would argue that a proposition (a) of the form "It is possible that X" is logically equivalent to "X or not X". Note that a proposition (b) of the form "It is not possible that X" is logically equivalent to "not X". Propositions (a) and (b) are not contradictory or paradoxical.
I would further argue that when in normal speech a proposition of the form "It possible that X" is used, the intent is to imply that an attempt was made to infer the truth value of X, but that a proof was not found, although one could exist. Thus in usual speech this is not a trivial proposition, as "X or not X" would be, in the sense that the proposition conveys information about the attempt to prove or disprove X.
Jorge Moraleda, Ph.D.
Chief Scientific Officer
PathWork Informatics
2 North First Street, Second Floor
San Jose, CA 95113
office 408.279.9010 x7505
cell 650.283.9282
www.pathworkinfo.com
At 08:54 AM 7/13/2005, [EMAIL PROTECTED] wrote:
Consider the following line of reasoning. Let p be the proposition "Ronald was born in New York." From p, we can infer q: Ronald was born in the United States. From q, we can infer r: It is possible that Ronald was born in New Jersey. On the other hand, from p we can infer s: It is not possible that Ronald was born in New Jersey. We have arrived at a contradiction. What is wrong? Note: To answer the question, familiarity with modal logic is not needed.
--
Lotfi A. Zadeh
Professor in the Graduate School, Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720 -1776
Director, Berkeley Initiative in Soft Computing (BISC)
Tel.(office): (510) 642-4959
_______________________________________________
uai mailing list
uai@ENGR.ORST.EDU
https://secure.engr.oregonstate.edu/mailman/listinfo/uai
_______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
