# [FOM] Logical Correctness

Charlie silver_1 at mindspring.com
Thu Nov 22 15:25:55 EST 2012

```	  Take Zadeh's assertion below that "p is a factual proposition".  On what seems a standard reading, p could be true or false, depending on facts.  Thus, p is (factually) possible.

Then, the antecedent of "If it is impossible that p, then it is possible that p" is false, making the material conditional true.

I'm aware Zadeh probably interprets these things non-standardly, but I don't know what sorts of interpretations he has in this case.  A start would be to explain "factual statements" in some way so they could be impossible.   Otherwise, as mentioned, the conditional is trivially true.

Basing my guess on his well-known, fuzzy analysis of "tall," I'd assume he may want to apply the same sort of evaluation on "impossible," such that there's no single impossibility, but grades of impossibilities.   Maybe something could be fuzzily "impossible," meaning something like: more impossible than possible.  --->  But I'm just guessing.  I'd be interested in his telling us his ideas about this.

Charlie Silver

On Nov 21, 2012, at 2:57 PM, Lotfi A. Zadeh <zadeh at eecs.berkeley.edu> wrote:

> Dear all,
>
>     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? There are some related basic questions. Could the sentence be logically correct if possibility is allowed to take values in the unit interval? How can one deal with the question under discussion when p is a proposition such as Robert is rich, where rich is a multivalued (fuzzy) predicate? If it is possible that Robert is rich, what is the possibility that Robert is not rich? What is the possibility that Robert is poor? A less simple example of p: Most Swedes are tall. Can fuzzy modal logic deal with such questions?
>
>     With warm regards
>
>     Sincerely,
>
>
> --
> 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
>
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