SUO: Plea for Relements
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John,
I agree with this, and, in its cognitive application, for much
the same reason that I am skeptical of the way that some folks
do neural modeling -- it's too much to expect the human brain
to have the neural equivalent of exact real number computation
just in order to compute, say, either-or.
Still, as I have suggested on numinous occasions, there is a good idea
lurking behind fussy sets, which are after all just triadic relations,
f : P x Q -> R, where P is a domain of elements, Q is a domain of sets,
and R is the real domain, and f(p, q) is the "degree of membership" of
the element p in the ordinary set q.
Instead of the nuanced membership relation p in_r q, where f(p, q) = r,
we can see that a logically more fundamental notion is the relativized
membership relation p in^j q, where we say that p in^j q if the judge j
judges the element p to fall in the set q (or to fall under the sign q).
This notion of "interpretive membership" or "relative elementhood"
is a useful way to talk about epistemic and ontological relativity.
Jon Awbrey
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John F. Sowa wrote:
>
> Tom,
>
> I agree:
>
> > Haack's "Philosophy of Logic" is an excellent book on the relationship
> > between formal logic and patterns of reasoning in natural language.
>
> I cited her comments about fuzzy logic in my KR book:
>
> The philosopher Susan Haack (1978, 1996) was one of the early critics of
> fuzzy logic, and she has continued to sharpen her arguments against the
> claims that natural language justifies or even requires "degrees of truth".
> Her most serious criticism is not that fuzzy logic is vague, but that it is
> too precise: instead of modeling the way people talk and think about vagueness,
> fuzzy logic forces an unwarranted quantification of vagueness.
>
> John
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