Dear Irving, Is it fair to say that a calculus of Logic looks at the relates of
operators as values of a 2-element set, 'true' and 'false.' (at least
classically) The universe of discourse is about the true and the false, and
thus it is restricted to those two values and is not about any objects
whatsoever. So, rather than sets of objects having to satisfy a truth
relation, the objects calculated upon are simply the truth values. I am trying
to understand what is meant by restricted. For instance, when Mitchell (1883)
talks about restricting the universe of discourse, he seems to mean the
universe of possibility. But that is a different meaning of restriction.
Likewise, when Aristotle restricts the universe of discourse to logical
subjects, that is also a different meaning of restriction. Thanks for all
your pre print links, notices and information. Jim Willgoose
Date: Tue, 8 Nov 2011 19:50:10 -0500
From: ianel...@iupui.edu
Subject: Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic
To: PEIRCE-L@LISTSERV.IUPUI.EDU
Dear Steven,
There is a growing body of scholarship among philosophers of
mathematics, including Douglas Jesseph and Mick Detlefsen, that
identifies Hilbert as influenced by, if not an actual disciple of,
Berkeley, and who at the same time argue that Berkeley was a formalist
and in that sense a predecessor of Hilbert and Hilbert's formalism. One
very significant difference, of course, between Berkeley and Hilbert,
however, is that Berkeley rejected the absolute infinite, whereas
Hilbert profoundly embraced it, as a student and follower of
Weierstrass and a colleague and defender of Cantor. I don't know
off-hand whether Hilbert directly read Berkeley's The Analyst or On
Infinities, let alone his more philosophical writings, but he most
assuredly encountered Berkeley's views at least through his reading of
Kant as well as in Cantor's major historico-philosophical excursuses in
his set theory papers, and probably also in his discussions with
Husserl at Göttingen.
Best regards,
Irving
- Message from ste...@semeiosis.org -
Date: Tue, 8 Nov 2011 15:40:20 -0800
From: Steven Ericsson-Zenith ste...@semeiosis.org
Reply-To: Steven Ericsson-Zenith ste...@semeiosis.org
Subject: Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic
To: Irving ianel...@iupui.edu
Dear Irving,
Thank you for the correction regarding the source of Hilbert's
remarks. I believe I read it in Unger's translation of The
Foundations of Geometry, perhaps in the foreword or annotations, but
I still have to check this. I assume that Hilbert is making a remark
that appeals to Berkeley's similar comments in stating the case of
idealism. Suggesting he was familiar with Berkeley.
It isn't clear to me how you can/must infer that there is or is not
experiential inference in the distinction between must and can.
Must and will appear to me to speak to the over confidence of
1900. But, again, I appreciate both the point and the correction.
With respect,
Steven
On Nov 8, 2011, at 7:43 AM, Irving wrote:
In response to posts and queries from Steven, Jon, and Jerry,
(1) Regarding Steven's initial post: My initial discomfort stemmed from
associating Hilbert's remark with the Peircean idea of logic as an
experiential or positive science, since Hilbert as a strict formalist
did not regard mathematics (or logic) as in any sense an empirical
endeavor. I suggest that the quote from Kant with which Hilbert began
his _Grundlagen der Geometrie_ had the dual purpose of paying homage to
his fellow Königsberger and, more significantly, to suggest that,
although geometry begins with spatial intuition, it is, as a
discipline, twice removed from intuition by a series of abstractions.
Whether he held space to be a priori or a posteriori, I cannot say for
certain, but my strong inclination is to hold that he conceived
geometry to be a symbolic science, with points as the most basic of the
primitives, in the same sense that he held the natural numbers to be,
not mental constructs, but symbols.
(Incidentally, the precise formulation of the quote from Hilbert is:
Wir müssen wissen. Wir werden wissen. Which should be translated as:
We must know. We will know. There is no can in this quote; so no
experiential inference would seem to be indicated.)
(2) Hilbert did not himself include the comment on tables, chairs, and
beer mugs in G.d.G. It was reported by Blumenthal in his 1935 obituary
of Hilbert, recorded as a part of a conversation. If it does appear in
G.d.G., it does so in an edition that includes a reprint of Otto
Blumenthal's obit of Hilbert.
(3) Regarding the points made by Jon Awbrey and Jerry Chandler: In
attempting to sort out the various notions of formal, whether it
applies to Peirce and to Hilbert, to logical positivism,