Re: [peirce-l] “On the Paradigm of Experience Appropriate for Semiotic”

2011-11-09 Thread Jon Awbrey

* Comments on the Peirce List slow reading of Joseph Ransdell,
  On the Paradigm of Experience Appropriate for Semiotic,
  http://www.cspeirce.com/menu/library/aboutcsp/ransdell/paradigm.htm

Peirce List,

Here is the reply I made to John Sowa's earlier remarks on the CG List:

I am not saying that Peirce didn't use the word formal in
the same sense as *some* 20th century logicians. But not all
subsequent philosophers of logic and mathematics used the word
formal in the same sense as that, or even all the time, and it
often becomes necessary in certain discussions to point that out.

It is clear that one of the connotations of formal for Peirce
is non-psychological, but that is precisely to differentiate
the normative science of logic from the descriptive science
of psychology.

It is also necessary to distinguish Peirce's use of formal semiotics,
referring to the forms of sign relations that connect objects with signs
and their interpretant signs, from any use of formal to suggest wholly
detached from all connection to meanings or objects or purposes outside the
sheer game of manipulating meaningless tokens according to arbitrary rules,
because there have arisen now and again tendencies to use formal that way.

Jon

---

JA = Jon Awbrey
JS = John Sowa

JA: Those remarks were tailored to the ears of a particular body of readers
who are accustomed to hearing the word formal used as something akin
to a pejorative term, as in mere formalism or merely formalistic.

JS: But note the date of 1869 -- that was a year before Peirce's famous
paper on relatives.  It was also ten years before Frege's famous
Begriffsschrift, which everybody cites as the first complete version
of FOL with the first complete *formal* rules of inference.

CSP (1869):
All that the formal logician has to say is, that if facts capable
of expression in such and such forms of words are true, another
fact whose expression is related in a certain way to the expression
of these others is also true The proposition ‘If A, then B’ may
conveniently be regarded as equivalent to ‘Every case of the truth
of A is a case of the truth of B.’”

JS: See http://www.peirce.org/writings/p41.html for the full article.

JS: He used the word 'formal' several times in that article, and in
each case, he used it in the same sense as the 20th century logicians.
He also contrasted that use with psychological discussions of 'thought'.

JA: But Peirce also used the word formal in another, more specialized sense,
in which it became the practical equivalent of normative. In that sense,
his definition of logic as formal semiotic places logic within the sphere
of the normative sciences, where it normally belongs.

JS: Peirce was very precise in his choice of worlds.  He often referred to
logic as normative.  Since he frequently used both words, one should not
assume that he might sometimes use one of them to mean the same as the
other.  In the following statement, he would have written 'normative'
if that had been the point he was trying to make:

CSP: Logic will here be defined as formal semiotic. A definition of a sign will 
be
 given which no more refers to human thought than does the definition of a 
line
 as the place which a particle occupies, part by part, during a lapse of 
time.

JS: Here he is using the word 'formal' in contrast with a psychological 
interpretation.
He makes a similar contrast in his earlier article of 1869.  Since he is 
trying to
make a similar point both articles, the most reasonable interpretation is 
that he
is using the word 'formal' in the same sense.

---

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Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic

2011-11-09 Thread Jim Willgoose

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,