SUO: Re: Mapping : Frying Pan -> Fire
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John F. Sowa wrote:
>
> Jon,
>
> Mathematics has always been an embarrassment for
> professed nominalists because mathematicians truly
> believe in the existence of all kinds of abstract forms,
> which were Plato's original inspiration for his heaven.
>
> > ... that divinest of abstractions,
> > just to name names, a set.
>
> I regard geometry and arithmetic as far more divine
> than set theory. And I regard the project of trying
> to reduce all other mathematical forms to sets as
> a misguided plot on the part of closet nominalists.
John,
They way things are at present, with the mess that so-called analytic philosophers
have made of intellectual history and logical literacy alike, it will take all the
resources of our GoBack and WayBack utilities just to recover the good sense that
words like abstraction, comprehension, concept, connotation, denotation, extension,
intension, normative, predicate, proposition, rational, real, reification, relation,
sign, symbol, subject, the list goes on and on, once had in former and formative times.
But we cannot reconstruct the solid sense of these concepts by continuing
to operate on the 2-dimensional board that these Flatlanders have set up.
Right at the moment, I am trying to focus on the salvation or the salvaging
of the original idea of "intension", by any other word, just a property.
The error of nominal thinking is not in the admission of extensions to the kingdoms
of the intellect, it is in the denial of election to intensions, in their own right.
Peirce's work, early and late, is steeped in a recognition of the integral relationship
between extensions and intensions, and he, like Leibniz, was quite capable of thinking
in both extensions and intensions on one and the same day, despite the need that some
people seem to have to classify solid thinkers in one or another 2-listic pigeonhole.
The way that it is now, when somebody newspeaks about a "relation", I have very little way
of telling from the evidence of what they say afterwards whether they are talking about
a particular piece of syntax, or a single k-tuple instance of the relation in question,
but I rarely get the sense that they are talking about real relations, no matter if
one seeks information about them in their extensional or their intensional facets.
This has nothing to do with whether one favors analytic or synthetic geometry.
Both sorts of geometers will tell you that you can't learn much about geometry
by constantly staring at the same chalk figure of the same damn triangle, and
less so if you view it literally and not generically as one example among many.
It has rather to do with two particular fallacies that are rampant these days:
the syntactic fallacy that confounds the properties of signs with the properties
of their objects, and the generalization fallacy that fails to grasp the fact that
a relation, no matter whether you take it in extension or intension, is quite another
thing from a single instance under that relation. The compounding of these fallacies
is like epoxy glue in the brain.
> They tried to tame the wild and wooly Platonic forms
> by replacing all of them with just one well behaved
> house pet called a set. Quine is one of the worst
> offenders.
Again, those who know their ways will tell you that sets are as wild and wooly
as anything can be. But that is not really the point. Talk about sets ranks
among the inescapable competencies of any ontology that would dream to approach
the status of an upper level technical ontology, much less a research-oriented
scientific ontology. Yet again, to the extent that Quine fesses geunuine sets,
he might yet be saved -- it's no longer up to us -- but the diehard nominalizer
does not even admit these, going for a "no class" theory, so aptly denominated.
> > Why do people with some reputed training in the 20th century excuse for logic
> > have so much trouble grasping a simple fact of simple mathematics? Inasmuch
> > as they seem to be otherwise healthy intellects, I have no choice but to put
> > it down to the deleterious effects of the particular logical tools they use.
>
> No. They were corrupted by the same person who drove Ludwig Boltzmann
> to suicide: Ernst Mach -- that darling of the Vienna Circlers, who
> married Peirce's logic to Mach's positivism.
Well, that's an interesting line, but I hardly think that it can be
stretched far enough to cover the widespread disability that we see.
Something more pervasive must be sought, it seems to me.
Jon Awbrey
> Bottom line: The greatest evil in logical positivism
> lies in the noun, not the adjective.
>
> John
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