Thanks again Irving. Do you know if L. Couterat was at the 1900 Paris
conference? My historical curiosity lies with both his contribution to the 1901
Baldwin entry "symbolic logic, algebra of logic," which Peirce supervised, but
also the intoductory textbook which he wrote a few years after that Baldwin
entry. He seems to have the concept of an open function, symbolizing "Px" or
"Sx" for the purpose of defining binary functions for Product and Aggregate. He
replaces the variable "x" in "Px" with the disjunction of individual classes
thereby suggesting existential quantification. But what is missing are the
individual argument places! The effect appears to be to distribute functions
across the binary functions. There are no "zero-place" individuals.
> Date: Wed, 7 Dec 2011 08:19:57 -0500
> From: ianel...@iupui.edu
> Subject: Re: [peirce-l] SLOW READ: On the Paradigm of Experience Appropriate
> for Semiotic
> To: PEIRCE-L@LISTSERV.IUPUI.EDU
>
> Once again, there is a complex of related dichotomies that van
> Heijenoort applied to distinguish the Aristotelian-Boolean stream (of
> which Peirce was a part, according to Van) from the Fregean, including
> logic as calculus/logic as language,model-theoretic (or
> intensional)/set-theoretic,
> (or extensional, so as to include both Russell's use of set theory and
> Frege's course-of-values semantic), syntactic/semantic, and, finally,
> relativism/absolutism.
>
> I think that what Ben intends by his neologism "unic-universalist" is
> essentially what Ben has in mind for Van's use of absolutism, namely,
> (a) a universal universe of discourse (Frege's Universum); (b) a fixed
> universe, that includes all objects and functions; and (c) a single
> logic. These properties, and the entire interrelated complex of
> properties, together make, for Van, Frege's Begriffsschrift (and
> Whitehead & Russell's Principia Mathematica), both logic as language
> AND logic as calculus, and preeminently -- first and foremost -- a
> language, whereas, with the intensional or class-theoretic semantic
> tied to a subject-predicate or merely relational syntax, together with
> a restricted, pre-defined, universe of discourse, makes the logical
> systems of Boole, De Morgan, Jevons, Peirce, Schröder, et al., mere
> calculi.
>
> Beyond that, it was the failure to distinguish between sets and classes
> or, more properly, subsets and proper subsets (or for Frege, between
> functions and higher-order functions, where a lower-order function
> could serve as the indeterminate argument for a higher-order function)
> -- i.e. the very universality, that caused the introduction of the
> Russell paradox. The idea of universality disabling the possibility for
> Frege or Russell to step out of their logical systems to ask
> metalogical questions about the model-theoretic or proof-theoretical
> properties of their system was dealt with by Van in "Système et
> métasystème chez Russell".
>
> The only point in my book on van Heijenoort where I essentially
> disagreed with Philippe de Rouilhan was on the question of whether Van
> came down on the side of relativism or on the side of absolutism.
> (Incidentally, de Rouilhan has agreed to provide a revised and extended
> discussion and translation into English of his article "De
> l'universalité de la logique" for the issue of Logica Universalis that
> I am guest-editing to celebrate the centenary of Van's birth. That
> issue of L.U. is scheduled for publication precisely on Van's 100th
> birthday, 23 July 2012.)
>
> In his unpublished research notes on the nature of logic, Van made
> multiple efforts to sort out whether there is *one* logic (absolutism,
> -- or "unic-universalism"?) or several logics(relativism). (The idea of
> the medieval terminology logica magna -- not logica docens -- and
> logicae utenses has to be understood, when dealing with van Heijenoort,
> in the sense of one logic, a logic tout court (he calls it in his
> notes), versus several logics. And in doing this, he attempted to
> understand the connection of logic and [ordinary] language. He never
> really decided; what we end up with is the question of whether
> [ordinary] language can be applied to study the nature or properties of
> logic, or whether we can even conceive of alternative logics, because
> we require a "basic logic of language" to do so. Without making it
> explicit, he appears to be on the verge of stepping here into a
> Carnapian metalinguistic regress. And here his notes "Logic, nature of"
> end.
>
> I tie all this together, and give a full exposition, in "Jean van
> Heijenoort's Conception of Modern Logic, in Historical Perspective", my
> main paper for the L.U. centenary issue.
>
> One unrelated word regarding Wikipedia, which was indirectly raised as
> an issue in connection with the model-theoretic/semantic... discussion.
> Many of you already know that I do not hold it in high regard. Whatever
> the virtues of a community of inquiry, and although I have heard that
> they have recently tightened the promiscuity with which the contents of
> Wikipedia articles may be tampered, I continue to distrust the
> authenticity of those contents. I suggest that a community of inquiry
> has value only to the extent that the contributors have a verifiable
> level of expertise in their field and that their contributions have
> been refereed by bona fide experts. The problem with Wikipedia, as I
> see it, is that there are no serious controls on contributors or
> contributions. The worst offense, which led me to abandon Wikipedia
> several years ago, was that someone, or several someones, kept playing
> with Bertrand Russell's birth year, about every few days. The other
> incident occurred as recently as two years ago, when a student went to
> Wikipedia to get "instructions" on how to multiply an n X m matrix,
> instead of looking at a mathematics textbook or a legitimate math web
> site -- and naturally got the worked examples totally wrong by
> following the instructions on Wikipedia. And that's my anti-Wikipedia
> rant. Suffice it to say:, with apologies to Ben: Wikipedia is NOT the
> Stanford Encyclopedia of Philosophy or the Internet Encyclopedia of
> Philosophy.
>
>
> Irving
>
> ----- Message from bud...@nyc.rr.com ---------
> Date: Tue, 6 Dec 2011 17:19:01 -0500
> From: Benjamin Udell <bud...@nyc.rr.com>
> Reply-To: Benjamin Udell <bud...@nyc.rr.com>
> Subject: Re: [peirce-l] SLOW READ: On the Paradigm of Experience
> Appropriate for Semiotic
> To: PEIRCE-L@LISTSERV.IUPUI.EDU
>
>
> > Jim, list,
> >
> > Yes, I was just reading an article that said that Van Heijenoort said
> > that Frege's logic has just one universe of discourse, whereas others
> > allowed variations. Frege as "unic-universalist" (my word) rather
> > than merely universalist.
> > Van Heijenoort lists two further consequences of the lingua-calculus
> > distinction and the universality of Fregean logic. Whereas Boole's
> > universal class or De Morgan's universe of discourse can be changed
> > at will, Frege's quantifiers binding individual variables range over
> > all objects. There is no change of universes: 'Frege's universe
> > consists of all that there is, and it is fixed' (ibid. ["Logic as
> > Calculus and Logic as Language"], 325). Furthermore, Frege's system
> > is closed, nothing can be outside the system. There are no
> > metalogical questions and no separate semantics. - Volker Peckhaus,
> > "Calculus Ratiocinator vs. Characteristica Universalis? The Two
> > Traditions in Logic, Revisited" (16.5.2003), page 4,
> > http://kw.uni-paderborn.de/fileadmin/kw/institute/Philosophie/Personal/Peckhaus/Texte_zum_Download/twotraditions.pdf
> > I particularly need to read/re-read an article or two by Irving.
> > (Meanwhile my days will be increasingly busy through Friday).
> >
> > An insistence on limiting logic to a single monolithic universe of
> > discourse has long seemed strange to me. Makes me think of Russell's
> > worry (during some period) that mathematics deals with numbers larger
> > than the number of particles in the (physical) universe. Anyway that
> > insistence weakens the affinity between the idea of a total
> > population and the idea of a universe of discourse, though I guess
> > one doesn't need to admit various universes of discourse in order to
> > admit various total populations. Of course there are other reasons
> > that one might like not to be limited to a grand and single universe
> > of discourse.
> >
> > Anyway, the Wiki sentence as written is a statement about the
> > supposed opinions of van Heijenoort, Hintikka, and Brady. Irving has
> > indicated that it is mistaken as to van Heijenoort's view of the
> > dichotomy. So even if we start to see how the stated opinion makes
> > partial sense in a way that suggests how to salvage it, then there's
> > still the problem of attribution. So I've ratched down my personal
> > sense of urgency about it by removing it from the article for the
> > time being. I'd like to get it repaired and put it back in since it
> > does broach important issues in the development of logic and Peirce's
> > role in it.
> > Jean Van Heijenoort (1967),[85] Jaakko Hintikka (1997),[86] and
> > Geraldine Brady (2000)[79] divide those who study formal (and
> > natural) languages into two camps: the model-theorists /
> > semanticists, and the proof theorists / universalists. Hintikka and
> > Brady view Peirce as a pioneer model theorist.
> >
> > 79. a b Brady, Geraldine (2000), From Peirce to Skolem: A Neglected
> > Chapter in the History of Logic, North-Holland/Elsevier Science BV,
> > Amsterdam, Netherlands.
> >
> > 85. ^ van Heijenoort (1967), "Logic as Language and Logic as
> > Calculus" in Synthese 17: 324-30.
> >
> > 86. ^ Hintikka (1997), "The Place of C. S. Peirce in the History of
> > Logical Theory" in Brunning and Forster (1997), The Rule of Reason:
> > The Philosophy of C. S. Peirce, U. of Toronto.
> > Best, Ben
> >
> >
> > ----- Original Message -----
> > From: Jim Willgoose
> > To: bud...@nyc.rr.com ; peirce-l@listserv.iupui.edu
> > Sent: Tuesday, December 06, 2011 3:47 PM
> > Subject: RE: [peirce-l] SLOW READ: On the Paradigm of Experience
> > Appropriate for Semiotic
> >
> >
> > Ben,
> >
> > One quick further thought. If the pretension to a "universal
> > language" is so great that one does not consider a comparison of
> > models, then it becomes easier to see the pairing of
> > "proof-theoretic/universalist." So, maybe Frege would historically be
> > seen this way. (absolute model) On the other hand, if Lowenheim
> > finishes something he sees philosophically in Peirce/Schroder, then
> > you might get the pairing "model theorist/particularist."
> >
> > jim W ----- Original Message -----
> > From: Jim Willgoose
> > To: PEIRCE-L@LISTSERV.IUPUI.EDU
> > Sent: Tuesday, December 06, 2011 3:21 PM
> > Subject: Re: [peirce-l] SLOW READ: On the Paradigm of Experience
> > Appropriate for Semiotic
> >
> >
> > Ben,
> >
> > Thanks for all the work on Wiki. Here is a quick distillation
> > of the idea. A signature such as { ~, &, NEG, POS} might be adequate
> > for modeling the Boolean functions of propositional logic. (In fact,
> > G. Hunter in "Metalogic, 1970 U. Cal. Press attributes the discovery
> > that {~,&} is the smallest signature adequate for modeling the
> > Boolean functions to Peirce). Now, if every tautology is satisfied
> > in the model you are half way to having a logic! In so far as it is
> > formal, it can apply to any material propositions. Thus, it is
> > "universal" in that sense. But it is hardly universal with repect to
> > Truth writ large.
> >
> > It lacks universality in so far as the full predicate logic
> > generates truths that cannot be written with that signature. So, if
> > you compare the expressiveness of the two models, you begin to see
> > that the semantic power of a model is relative to another.
> > (particularist)
> >
> > So, it is questionable just what is being claimed by a
> > "universal language."
> >
> > Jim W
> >
> >
> > Date: Tue, 6 Dec 2011 13:57:46 -0500
> > From: bud...@nyc.rr.com
> > Subject: Re: [peirce-l] SLOW READ: On the Paradigm of Experience
> > Appropriate for Semiotic
> > To: PEIRCE-L@LISTSERV.IUPUI.EDU
> >
> >
> > Jim, Irving, John, Peter, list,
> >
> > Thank you for the added comment, Jim. I've been stealing time to try
> > to rummage through online sources but this subject is very abstract
> > for me. I'll just have to remove the problematic sentence pending
> > clarification.
> >
> > Best, Ben
> >
> > ----- Original Message -----
> > From: Jim Willgoose
> > To: PEIRCE-L@LISTSERV.IUPUI.EDU
> > Sent: Sunday, December 04, 2011 3:47 PM
> > Subject: Re: [peirce-l] SLOW READ: On the Paradigm of Experience
> > Appropriate for Semiotic
> >
> >
> > Ben, Irving, John, Peter et. al.
> >
> > I do not grasp the pairing of model theorist/semanticist or proof
> > theorist/universalist either. It seems that a "universal grammar" ( a
> > term adopted once by Peirce) need not be understood in only one of
> > the following ways. First, it need not be understood as strong
> > enough to represent or express any domain of knowledge. But secondly,
> > it need not be understood solely as relating to proof. Thus, if a
> > formal grammar is presupposed by both logic and methodology, it seems
> > an open choice whether one wants to write a proof in it for a limited
> > domain of knowledge, or use a fragment of it to "model" other domains
> > of knowledge. Putnam seems to suggest that Peirce was in the vanguard
> > of treating model theory as particularist. ( I will look for the
> > paper) Experience teaches us what the limitations are. But I will
> > say (following Putnam) that model theory as a body of knowledge
> > appears a posteriori.
> >
> > Jim W.
> >
> >
> >
> > --------------------------------------------------------------------------------
> > Date: Sun, 4 Dec 2011 13:52:56 -0500
> > From: bud...@nyc.rr.com
> > Subject: Re: [peirce-l] SLOW READ: On the Paradigm of Experience
> > Appropriate for Semiotic
> > To: PEIRCE-L@LISTSERV.IUPUI.EDU
> >
> >
> > Irving, list,
> >
> > ---------------------------------------------------------------------------------
> > You are receiving this message because you are subscribed to the
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> > PEIRCE-L@LISTSERV.IUPUI.EDU
>
>
> ----- End message from bud...@nyc.rr.com -----
>
>
>
> Irving H. Anellis
> Visiting Research Associate
> Peirce Edition, Institute for American Thought
> 902 W. New York St.
> Indiana University-Purdue University at Indianapolis
> Indianapolis, IN 46202-5159
> USA
> URL: http://www.irvinganellis.info
>
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