Jon A., Edwina, Kirsti, Jon A.S., list,
The issues about universals and essences have been with us for a
couple of millennia, and nobody has a proposed useful definition that
everyone can accept. Peirce developed his semiotic as a foundation
that *avoids* those terms.
JA
I find it more useful to focus on the pragmatics of language use
relative to the context of interpretation, frame of reference,
sign relational space, or universe of discourse at hand than to
go chasing after ontological absolutes.
ET
I think the search for 'this' and 'only this' meaning of a term
slips into that essentialism of 'ontological absolutes'.
Yes. Peirce's principle that "symbols grow" is incompatible with
any theory that depends on monadic predicates with a fixed definition.
It's more compatible with Wittgenstein's language games (which may
have been inspired by LW's discussions with Frank Ramsey).
K
In separating any point within the continuum in question, continuity
gets violated. But this violation may and can be mended. The point,
thus separated, must be re-positioned into the continuity
Ketner & Putnam discussed this issue in their intro to RLT.
In Aristotle's ontology, which Euclid adopted, the parts of a line
are not points, but line segments. A point is just a marker with
an indexical (a Greek letter) to support references in a proof.
JAS
A true singularity--determinate in every conceivable respect--would
be a discontinuity, and hence is only an ideal.
Yes, but the word 'ideal' is just as problematic as any other term.
In mathematics, there are many ways to handle limiting cases and to
reason about them effectively. I would consider any or all of them
Wittgensteinian language games. If you find them useful, use them.
If not, don't. But don't pretend that any one of them is fundamental.
I'd also like to mention the article, Signs and Reality, which I
published in the _Applied Ontology Journal_ in 2015:
http://www.jfsowa.com/pubs/signs.pdf
Since most of the readers of that journal know little or nothing
about Peirce's semiotic, I began with some quotations from the book
_Universals: An Opinionated Introduction_ by David Armstrong.
DA
So let me begin by saying what the problem is. It may turn out that
it is really a pseudo-problem. That was the opinion of Wittgenstein
and his followers, for instance. Quine is not far from thinking the
same. But whether it is a real problem or not should not be decided
in advance.
In the final chapter, DA says
Metaphysicians should not expect any certainties in their inquiries...
Of all the results that have been argued for here, the most secure,
I believe, is the real existence of properties and relations. Whether
they be universals or particulars is a more delicate matter, and just
what properties and relations are required is obscure, and in any case
not for the philosopher to determine.
From page 2 of signs.pdf:
To illustrate the issues, Armstrong cited a “distinction that
practically all contemporary philosophers accept... It is the
distinction between token and type” by Charles Sanders Peirce.
As an example, he noted that the phrase /the same/ in the sentence
/Two ladies wore the same dress/ means the same type of dress, not
the same token. In general, tokens are particulars, and types are
universals. But Armstrong cited many more examples that show the
complexities and ambiguities in any attempt to define precise
identity conditions.
Those quotations by a philosopher who is firmly in the analytic
tradition gave me "a thin opening wedge" for inserting Peirce's
semiotic and using it to rip apart the foundation.
But I also admit that any *applied* ontology that is implemented
on a digital computer must have precise, formal definitions for
its predicates. But I would treat those predicates as the symbols
in a "language game" that is useful for that particular application.
To be scientific, any ontology must be considered just as fallible
as any scientific theory.
John
