SUO: Re: Plea for Relements
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Tom,
You know I try to see the good in everybody,
and this little exorcise was just my try at
trying to see something good in fuzzy sets,
which I would otherwise think are otiose
given a due understanding of information
theory. My rehabilitation of them was
prisioned in the context of Peirce's
theory of signs, that permits me to
spy some spirit lurking behind all
the fuzz that has hopes of being
reformable as a sign relation.
I took your remark as charging either psychologism or relativism,
which are the usual suspects in this case, so I guess reflexively
defended myself against those two charges. Just to extenuate my
circumstances a bit further, I will explain that Peirce's theory
of signs merely requires you to add another column, labeled with
the heading Interpretant, to the table labeled Word and Object.
It does not discharge the latter columns in favor of the former.
For Peirce, logic is "formal semiotic". Aside from referring to
the forms of relations, the word "formal" has for him the force
of "normative". In its normative objective, logic is distinct
from psychology, a descriptive science, even if all the given
subject material happens to form exactly the same dataset.
So a sign relation L c Objects x Signs x Interpretants
can be studied abstractly, with regard to its form,
and apart from the Interpretive Branch, its Agent.
Jon Awbrey
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Tom Johnston wrote:
>
> John:
>
> sorry for being so cryptic. I did not mean "solipsism" in the full
> philosophical sense. Instead, my question was aimed at this remark:
>
> >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).
>
> I think that a passage of Quine's was in the back of my mind (surprise!).
> Here it is:
>
> "The uniformity that unites us in communication and belief is a uniformity
> of resultant patterns overlying a chaotic subjective diversity of
> connections between words and experiences. Uniformity comes where it matters
> socially; hence rather in point of intersubjectively conspicuous
> circumstances of utterance than in point of privately conspicuous ones......
>
> Different persons growing up in the same language are like different bushes
> trimmed and trained to take the shape of identical elephants. The anatomical
> details of twigs and branches will fulfill the elephantine form differently
> from bush to bush, but the overall outward results are alike". (Word and
> Object, p.8, Chapter 1, section 2).
>
> So this logically fundamental notion describes the twigs and branches.
> Somehow we develop "a uniformity of resultant patterns" that enables us to
> communicate well enough to have greater survival value socially than we do
> individually. I wonder how (as do psycholinguists, cognitive scientists and
> all of us). That's all my question alluded to. As such, it probably wasn't
> very relevant.
>
> Tom
>
> -----Original Message-----
> From: John F. Sowa [mailto:sowa@bestweb.net]
> Sent: Wednesday, August 27, 2003 9:17 PM
> To: Tom Johnston
> Cc: Jon Awbrey; SUO; port-l@listserv.iupui.edu
> Subject: Re: SUO: RE: Plea for Relements
>
> Tom,
>
> The following discussion addresses a technical point
> about the model-theoretic foundations of conventional
> logics and fuzzy logics.
>
> It is by no means a complete theory of ontology and
> epistemology, which solipsism purports to be.
>
> Tom Johnston wrote:
> > And this does not collapse into solipsism because.....?
>
> Most people who take Peirce seriously, including Jon and
> me, assume the existence of a physical universe populated
> with people and other sentient beings, who have minds
> that operate along principles roughly analogous to our own.
>
> Peirce was very explicit about debunking Descartes's
> error of doubting things in his philosophy that he would
> never doubt in practice. That point was never in question
> in the following exchange.
>
> John
>
> > -----Original Message-----
> > From: Jon Awbrey [mailto:jawbrey@att.net]
> > Sent: Tuesday, August 26, 2003 3:01 PM
> > To: sowa@bestweb.net
> > Cc: Tom Johnston; SUO; port-l@listserv.iupui.edu
> > Subject: Plea for Relements
> >
> > 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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