Re: [peirce-l] What Peirce Preserves
Jon Awbrey wrote: "I would tend to sort Frege more in a class with Boole, De Morgan, Peirce, and Schröder, since I have the sense when I read them that they are all talking like mathematicians, not like people who are alien to mathematics." I would thoroughly concur. Although Peirce had, perforce, deliberately identified himself as a "logician" in _Who's Who_, and part 2 of his 1885 AJM paper, after being accepted by Sylvester, was refused publication by Simon Newcomb (who succeeded Sylvester as AJM editor) because Peirce insisted that the paper was "logic" rather than "mathematics", each of these people worked in mathematics as mathematicians (Boole, De Morgan Peirce, Schröder primarily in algebra, but also contributing to differential and integral calculus and function theory; Frege primarily in function theory, but also working in algebra; and all to some extent in geometry as well). My points were -- to put them as simplistically and succinctly as possible -- that: (a) _Studies in Logic_ did not get laid aside because of the diffusion of its contents (Epicurean logic; probability, along with algebraic logic) but because (i) philosophers either mathophobic or innumerate were unprepared or unable to tackle the algebraic logic; while (ii) the mathematician who were capable of handling it did not ignore _Studies..._ in the "pre-Principia" day (witness Dodgson's being inspired to devise falsifiability trees by Ladd-Franklin's treatment of the antilogism and Marquand's contribution on logic machines; witness the praise for _Studies..._ by Venn, Schröder, and even Bertrand Russell's recommendation to Couturat that he read _Studies..._); (b) once the "Fregean revolution" began taking effect, in the "post-Principia" era, not only _Studies in Logic_ slid off the radar even for those capable of handling the mathematics, but so did most of the work in algebraic logic from Boole and De Morgan through Peirce and Schröder to even the "pre-Principia" Whitehead, in favor of logistic, that is in favor of the function-theoretic approach rather than the older algebraic approach to logic, and THAT was why, in 1941, Tarski expressed surprise and chagrin that the work of Peirce and Schröder hadn't been followed through and that, in 1941, algebraic logic languished in the same state in which it had existed forty-five years earlier. Incidentally, Gilbert Ryle attributed the interest of philosophers in logistic preeminently to the advertisements in favor of it by Bertrand Russell, convincing philosophers that the "new" mathematical logic could help them resolve or eliminate philosophical puzzles regarding language and epistemology (at the same time, we might add, that Carnap was arguing for the use of he logical analysis of language in eliminating metaphysics). (I do not believe that in my previous posts I said anything to the contrary or said anything that could be construed to the contrary.) - Message from jawb...@att.net - Date: Mon, 07 May 2012 09:25:22 -0400 From: Jon Awbrey Reply-To: Jon Awbrey Subject: Re: What Peirce Preserves To: Jack Rooney Re: Irving H. Anellis, et al. At: http://thread.gmane.org/gmane.science.philosophy.peirce/8116 Peircers, Looking back from this moment, I think I see things a little differently. The critical question is whether our theoretical description of inquiry gives us a picture that is true to life, preserving the life of inquiry and serving to guide it on its way, or whether it "murders to dissect", leaving us with nothing but a Humpty Dumpty hodge-podge of false idols and torn and twisted bits of maps that mislead the quest at every turn. There is a natural semantics that informs mathematical inquiry. It permeates the actual practice even of those who declare for some variety of nominal faith in their idle off-hours. Peirce is unique in his ability to articulate the full dimensionality of mathematical meaning, but echoes of his soundings keep this core sense reverberating, however muted, throughout pragmatism. If I sift the traditions of theoretical reflection on mathematics according to how well their theoretical images manage to preserve this natural stance on mathematical meaning, I would tend to sort Frege more in a class with Boole, De Morgan, Peirce, and Schröder, since I have the sense when I read them that they are all talking like mathematicians, not like people who are alien to mathematics. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey word press blog 1: http://jonawbrey.wordpress.com/ word press blog 2: http://inquiryintoinquiry.com/ - End message from jawb...@att.net - Irving H. Anellis Visiting Research
Re: [peirce-l] Poles RE: [peirce-l] Not Preserving Peirce
It is also of course worth mentioning, especially in connection with algebraic logic in Poland, Henry Hiz's article "Peirce's Influence on Logic in Poland" in Houser, Roberts, & Van Evra's collection _Studies in the Logic of Charles Sanders Peirce_. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Not Preserving Peirce
I trust that it is understood that I neither explicitly asserted, nor even implied, that Tarski was the only Polish logician, or the only Pole to write about logic. I merely mentioned Tarski's as one of a given genre of textbooks of the early "post-Principia". My chief point regarding Tarski was that he was among the few in the post-Principia era who advocated on behalf of a continuation of the Boole-Peirce-Schroder algebraic style of logic, and that for four decades he was what we might call the fountainhead of a school of specialists in the subfield of algebraic logic emanating out of U Cal-Berkeley. I did refer to his teacher Lukasiewicz, in particular as being one of the Warsaw logicians who interested Tarski in the work of Peirce and Schroder. Neither was my reference to Tarski's textbook intended to suggest that it was the only textbook in Polish of the early "post-Principia" era that treated "mathematical" or "symbolic logic", any more than that Carnap's _Abriss_ or _Einfuhrung_ were the sole such books in German, only that it was an example of such books that began appearing in the early "post-Principia" era that did not shy away from a mathematical outlook. I suppose I should also have mentioned Lukasiewicz's _Elementy logiki matematicznej_ (1929), which belonged to that slightly earlier genre of textbooks in mathematical logic of the "post-Principia" era that, like Cooley's, were based upon lecture notes, in the case of Lukasiewicz's, prepared by Mojiesz Presburger as the editor. Incidentally, Jan Sleszynski, known in Russian as Ivan Sleshinskii, produced a Russian translation of Louis Coututrat's _L'algèbra de la logique_ (in and respectively), and Stanislaw Piatkowski (1849-?) was, apparently, the first to write in Polish about algebraic logic, in his doctoral thesis Algebra w logice (1888), but was critical of it., He nevertheless established a reputation as a "pioneer" of mathematical logic in Poland, as Tadeusz Batog called him, and Batog and Roman Murawski account him as central to the beginnings of mathematical logic in Poland. None of this, so far as I am aware, alters or otherwise affects the main point of my previous post, which was in response to a specific question, first and foremost regarding the status of the relevance of _Studies in Logic_ vis-à-vis (a) the difusion of topics in _Studies..._ and (b) the rise of logistic as supplanting the older Boole-Peirce-Schröder tradition. - Message from johnphilipda...@hotmail.com - Date: Sat, 5 May 2012 15:42:07 -0400 From: Jack Rooney Reply-To: Jack Rooney Subject: RE: [peirce-l] Not Preserving Peirce To: "Irving H. Anellis" , peirce-l@LISTSERV.IUPUI.EDU An addendum: Many Poles besides Tarski wrote about logic. A book or three have been written on the subject of Polish studies of logic between the WW. - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from johnphilipda...@hotmail.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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Not Preserving Peirce
My response to that part
of the issue would be that, in the post-Principia era, logicians who
had mathematical background gradually gravitated towards the
Frege-Russell approach, towards logistic, or function-theoeric, as
opposed to the algebraic Boole-Peirce-Schröder approach. That, too, is
one of the principal issues that "From Algebraic Logic to Logistic..."
attempts to explain.
It is worth noting:
(1) that _Studies..._ was well appreciated by logicians with strong
mathematical qualifications during Peirce's lifetime; here, we may
point to De Morgan, Venn, Schröder, MacColl, and Charles Lutwidge
Dodgson (a.k.a Lewis Carroll). Thus, for example, as Francine Abeles
demonstrated, it was reading Marquand's contributions to _Studies_ on
logic achines together with Ladd-Franklin's contribution, focusing on
the antilogism, that led Dodgson, in the unpublished-in-his-lifetime to
combine these to develop his version of the falsifiability tree method
for polysyllogisms. Beyond that, even while Bertrand Russell was
pointedly denying that he was familiar with any of Peirce's work in
logic, he was privately writing to Louis Couturat in 1899 recommending
that Couturat read _Studies..._.
(2) As usual, accuracy, exactitude, precision -- "picky, picky, picky"
-- is more complicated than we would sometimes wish. "Und in dem 'Wie',
da liegt der Unterschied." No one would, so far as I am aware, not even
I, claim that algebraic logic vanished altogether from the scene with
the arrival of logistic. It became, along with model theory, recursion
theory, proof theory, set theory, one of the specialized branches of
mathematical logic, beyond general logic (which, incidentally, also
encompasses, in the AMS subject classification scheme, besides prop
calc, FOL, higher-order calculi, non-classical logics, probability
logic -- thus continuing in some repects to justify the "mix" of topics
in intro logic texts for philosophers), and that primarily thanks to
Jan Lukasiewicz, who referred to Peirce's work in his claases at Warsaw
and especially his foremost student, Alfred Tarski. But listen to
Tarski decrying, in 1941, in "The Calculus of Relations" (p. 47) the
lack of attention to algebraic logic during the early post-Principia
period, noting that, "given the wealth of unsolved problems and
suggestions for further research to be found in Schröders _Algebra der
Logik_ [1890-1895]", it is "amazing that Peirce and Schröder did not
have many followers." Tarskis analysis of this situation and the
reasons for it appear to rest on the assumption that the absorption of
algebraic logic into Whitehead and Russells logical system was at the
cost of ignoring the mathematical content of the algebraic theory.
Tarski then wrote [1941, 74] that: "It is true that A.N. Whitehead and
B. Russell, in _Principia mathematica_, included the theory of
relations in the whole of logic, made this theory a central part of
their logical system, and introduced many new and important concepts
connected with the concept of relation. Most of these concepts do not
belong, however, to the theory of relations proper but rather establish
relations between this theory and other parts of logic: _Principia
mathematica_ contributed but slightly to the intrinsic development of
the theory of relations as an independent deductive discipline. In
general, it must be said that -- though the significance of the theory
of relations is universally recognized today -- this theory, especially
the calculus of relations, is now in practically the same stage of
development as that in which it was forty-five years ago."
The survival of algebraic logic as a specialized subfield may be due
preeminently, if not exclusively, as much as any factor, to the work of
Tarski and the generations to logicians that he taught and promoted at
U Cal Berkeley from the 1940s to his death.
(3) Since Mr. Rooney spoke of logic at the University of Illinois in
the 1950s, perhaps it would be worth remarking that in the mid-1930s,
one had to take logic, as did my father and Paul Halmos, in the
philosophy department with Oskar ("Oscar") Kubitz, who used the
then-brand-new Cohen & Nagel as the textbook for the course. Kubitz was
a Millian, and the author of the _Development of John Stuart Mill's
System of Logic_ (Urbana: Univ. of Illinois, 1932). My father was a
chem major, and enjoyed Kubitz's logic course (I inherited his copy of
Cohen & Nagel); Halmos was double majoring in philosophy and
mathematics, and his disaffection with that logic course and the drills
in syllogistic was one of the factors in deciding him to become a
mathematician.
(4) For those unafraid of mathematics, between 1910 and 1930, there
were few options in the immediate post-Principia era for studying the
"new" symbolic logic other than to do as Quine did, and that was to
find a profe
Re: [peirce-l] Not Preserving Peirce
Jim, I suggest -- assuming I have not missed the import of your question -- that it would be far more accurate to propose that "Studies in Logic", like most of the work of the algebraic tradition of the "post-Principia" era was a victim rather of the so-called "Fregean revolution" which, when not ignoring algebraic logic, rejected it altogether as "inferior" to the modern logistic. If, for example, on examines introductory logic textbooks from the mid-20th century, in particular those aimed at philosophy students, one continues to find inductive logic and scientific method ensconced in the same introductory textbooks as deductive logic, although then the deductive logic includes propositional calculus (and, depending upon the level of the textbook, first-order predicate calculus), along with syllogistic logic. One of the earliest, popular, post-Principia intro texts aimed at philosophy students was Cohen & Nagel's "Introduction to Logic and Scientific Method", which first appeared in 1934 and still had a strong following until well into the 1960s at least. If differed from newer intro logic textbooks aimed at philosophy students such as Copi's "Introduction to Logic", appearing twenty years later and still going strong, only in preferring the axiomatic approach to prop calc and FOL rather than Copi-style natural deduction. They differ from an older "pre-Principia" textbook such as -- to pull one off the shelf here, Boyd Henry Bode's 1910 "An Outline of Logic" only in that deductive logic meant syllogisms. Even in Peirce's day, few philosophers would touch algebraic logic, taking the tack of Jevons in wanting to get rid of the "mathematical dress" of classical algebraic logic. On a related matter: The fact is, that the classical Boole-Schröder calculus was simply too technically difficult, both in its day and since, to fair well at appealing to any but those with mathematical training. Examine the American Mathematical Society's and Zentralblatt für Mathematik's Mathematical Subject Classification (any edition will do): what you will find is that algebraic logic is listed as a specialty, on a par with model theory, recursion theory, proof theory, set theory, rather than as belonging to general logic that includes propositional calculus, FOL, and the sorts of topics you might expect to find in introductory textbooks. Sorry if this doesn't speak more explicitly to the question you had in mind. - Message from jimwillgo...@msn.com - Date: Wed, 2 May 2012 14:41:18 -0500 From: Jim Willgoose Reply-To: Jim Willgoose Subject: RE: [peirce-l] Not Preserving Peirce To: ianel...@iupui.edu, peirce-l@LISTSERV.IUPUI.EDU Irving and Jon; I wonder if the "Studies in Logic" did not suffer, in part, from a retrospective lack of unity. In other words, from the vantage point of 1950, the various topics (quantification, induction, Epicurus etc.) did not fit the 20th century development of a more narrow-grained classification into history of philosophy of science or formal deductive logic, or philosophy of language and meaning. Another conjecture might be that the first two decades of the 20th century dealt with the formalization and sytematizing of deductive logic for textbook presentation. Only after sufficient time had passed could the book be retrieved for historical and philosophical interest. Of course, there is always the nefarious possibility of an 'institutional apriori" authority having its way. Jim W > Date: Wed, 2 May 2012 11:48:14 -0400 From: ianel...@iupui.edu Subject: Re: [peirce-l] Not Preserving Peirce To: PEIRCE-L@LISTSERV.IUPUI.EDU Jon, I couldn't have said it better myself! Kneale & Kneale, to which Jack referred, was originally written in the late 1950s and published in 1962, and in terms of respective significance pays more attention to Kant even than to Frege, and is best, thanks to Martha Kneale's expertise, on the medievals. Trouble was, in those days, and pretty much even today, it is about all there is in English. My joint paper with Nathan Houser, "The Nineteenth Century Roots of Universal Algebra and Algebraic Logic", in Hajnal Andreka, James Donald Monk, Istvan Nemeti (eds.), Colloquia Mathematica Societatis Janos Bolyai 54. Algebraic Logic, Budapest (Hungary), 1988 (Amsterdam/London/New York: North-Holland, 1991), 1-36, includes a brief analysis of what's WRONG with Kneale & Kneale and its ilk. When Mendelson's translation of Styazhkin's History of Mathematical Logic came out in 1969, it should really have come to serve as a decent supplement to Kneale & Kneale for K & K's grossly inadequate treatment of Boole, Peirce, Schröder, Jevons, Venn, and Peano to help fill in the serious gaps in Kneale & Kneale. Even if one looks at the hugh multi-volume
Re: [peirce-l] Not Preserving Peirce
Jon, I couldn't have said it better myself! Kneale & Kneale, to which Jack referred, was originally written in the late 1950s and published in 1962, and in terms of respective significance pays more attention to Kant even than to Frege, and is best, thanks to Martha Kneale's expertise, on the medievals. Trouble was, in those days, and pretty much even today, it is about all there is in English. My joint paper with Nathan Houser, "The Nineteenth Century Roots of Universal Algebra and Algebraic Logic", in Hajnal Andreka, James Donald Monk, Istvan Nemeti (eds.), Colloquia Mathematica Societatis Janos Bolyai 54. Algebraic Logic, Budapest (Hungary), 1988 (Amsterdam/London/New York: North-Holland, 1991), 1-36, includes a brief analysis of what's WRONG with Kneale & Kneale and its ilk. When Mendelson's translation of Styazhkin's History of Mathematical Logic came out in 1969, it should really have come to serve as a decent supplement to Kneale & Kneale for K & K's grossly inadequate treatment of Boole, Peirce, Schröder, Jevons, Venn, and Peano to help fill in the serious gaps in Kneale & Kneale. Even if one looks at the hugh multi-volume Handbook of the History of Logic under the editorship of Dov Gabbay and John Woods that is still coming out, it's a mixed bag in terms of the quality of the essays, some of which are historical surveys, others of which are attempts at reconstruction based on philosophical speculation. Irving - Message from jawb...@att.net - Date: Wed, 02 May 2012 11:15:05 -0400 From: Jon Awbrey Reply-To: Jon Awbrey Subject: Re: Not Preserving Peirce To: Jack Rooney Jack, All histories of logic written that I've read so far are very weak on Peirce, and I think it's fair to say that even the few that make an attempt to cover his work have fallen into the assimilationist vein. Regards, Jon Jack Rooney wrote: Despite all this there are several books on the history of logic eg Kneale & Kneale[?]. -- academia: http://independent.academia.edu/JonAwbrey inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey word press blog 1: http://jonawbrey.wordpress.com/ word press blog 2: http://inquiryintoinquiry.com/ - End message from jawb...@att.net - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l]
As an addendum to Nathan Houser's "The Fortunes and Misfortunes of the Peirce Papers", it might be well to pass along parts of an email exchange I had over the last few days with Ignacio Angelelli. Ignacio wrote on 29 April, in connection with our discussion of lack of interest in history of logic in some quarters that: "Peirce's personal copy of Studies in Logic is a good example. I.C. Lieb had received it as a gift from P Weiss around 1950 (how did P Weiss get it... oh well...) . Upon his death Lieb gave it to our Phil Dept in Austin. It was stored in the open stacks of the departmental library... can you imagine! It took lots of paper work to have it transferred to the Humanities Research Library (where at least in theory my Hist of Log Collection continued to exist). It was finally catalogued as the little book deserves. But my point is that none of my logician colleagues was interested in such a beautiful volume, with so many handwritten remarks." In reply, I summarized the main points of Nathan's depressing article on the abuse of such historically valuable material, and then reported my recollection that Henry Aiken, whose T.A. I was in the early 1970s, was among those who has alleged to have gleefully composed his own lecture notes on the verso of original Peirce manuscripts that he acquired when the Harvard philosophy department gave away some of Peirce's papers as souvenirs. I personally can neither confirm nor disconfirm these claims; I saw Aiken referring in his class lectures to notes on clearly yellowing paper with writing on both sides, but never got close enough to get a good look at those pages. In his latest communication in this discussion, Ignacio wrote (in part) on 1 May regarding these "interesting comments on the Peirce library" that: "When back in Austin I should look again into those items left to the Phil Dept little library by Chet Lieb, because I seem to remember there was another Peirce volume, a geometry or math book, of course no recollection of who was the author. Alas, things and people change. I somehow forced the librarian to accept the Studies in Logic, as well as a set of papers left by Lieb." ...To be continued...? Irving H. Anellis Visiting Research Associate Peirce Edition, Institute for American Thought 902 W. New York Street Indiana University - Purdue University at Indianapolis Indianapolis, IN 46202-5157 USA - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] a pragmatic approach to quantum theory
Since quantum theory has come up in a number of recent posts, I thought it apropos to mention that I just came across this notice in the British Journal of Philosophy of Science: for: Richard Healey Quantum Theory: A Pragmatist Approach Brit J Philos Sci 2012 : axr054v1-axr054 Irving H. Anellis, Ph.D. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
e infinitesimal calculus, Lübsen (see 5th (1874) ed. [1855, p. 228]) therefore writes that "In dieser wahrhaft schöpferischen Leibniz'schen Method liegt der eigentliche Zauber der Infinitesimalrechnung." Theodor Ziehen defined logicism in his Lehrbuch der Logik auf postivischer Grundlage mit Berücksichtigung der Geschichte der Logik [1920, p. 173] to mean that there is an objective realm of ideal entities, studied by logic and mathematics, and he numbered on that account Lotze, Windelband, Husserl, and Rickert among those adhering to logicism. Having said that: as I wrote in the FOM back in May 2011, I recall that, many years ago (probably some time in the early or mid-1980s), Reuben Hersh gave a colloquium talk in the mathematics department at the University of Iowa. I don't recall the specifics of that talk, but in its general tenor it went along the lines that, in their workaday world. most mathematicians are Platonists, working as though the mathematical structures with which they are working and which are the subject of theorems exist, whereas, on weekends, they deny the real existence of mathematical entities. In the description for Reuben Hersh's What Is Mathematics Really? (Oxford U. Press, 1997), Hersh's position is described (in part) as follows: "Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. ...In What is Mathematics, Really?, renowned mathematician Reuben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism. Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. ..." - Message from eugene.w.halto...@nd.edu - Date: Tue, 13 Mar 2012 17:09:42 -0400 From: Eugene Halton Reply-To: Eugene Halton Subject: RE: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition To: "PEIRCE-L@LISTSERV.IUPUI.EDU" Dear Irving, A digression, from the perspective of art. You quote probability theorist William Taylor and set theorist Martin Dowd as saying: "The chief difference between scientists and mathematicians is that mathematicians have a much more direct connection to reality." This does not entitle philosophers to characterize mathematical reality as fictional. Yes, I can see that. But how about a variant: The chief difference between scientists, mathematicians, and artists is that artists have a much more direct connection to reality. This does not prevent scientists and mathematicians to characterize artistic reality as fictional, because it is, and yet, nevertheless, real. This is because scientist's and mathematician's map is not the territory, yet the artist's art is both. Gene Halton -Original Message- From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf Of Irving Sent: Tuesday, March 13, 2012 4:34 PM To: PEIRCE-L@LISTSERV.IUPUI.EDU Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition Ben, Gary, Malgosia, list It would appear from the various responses that. whereas there is a consensus that Peirce's theorematic/corollarial distinction has relatively little, if anything, to do with my theoretical/computational distinction or Pratt's "creator" and "consumer" distinction. As you might recall, in my initial discussion, I indicated that I found Pratt's distinction to be somewhat preferable to the theoretical/computational, since, as we have seen in the responses, "computational" has several connotations, only one of which I initially had specifically in mind, of hack gri
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
distinction between analytic and synthetic propositions is one of those things that either run out in a triviality or are false." - Message from bud...@nyc.rr.com - Date: Mon, 12 Mar 2012 13:47:10 -0400 From: Benjamin Udell Reply-To: Benjamin Udell Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition To: PEIRCE-L@LISTSERV.IUPUI.EDU Malgosia, Irving, Gary, list, I should add that this whole line of discussion began because I put the cart in front of the horse. The adjectives bothered me. "Theoretical math" vs. "computational math" - the latter sounds like of math about computation. And "creative math" vs. what - "consumptive math"? "consumptorial math"? Then I thought of theorematic vs. corollarial, thought it was an interesting idea and gave it a try. The comparison is interesting and there is some likeness between the distinctions. However I now think that trying to align it to Irving's and Pratt's distinctions just stretches it too far. And it's occurred to me that I'd be happy with the adjective "computative" - hence, theoretical math versus computative math. However, I don't think that we've thoroughly replaced the terms "pure" and "applied" as affirmed of math areas until we find some way to justly distinguish between so-called 'pure' maths as opposed to so-called 'applied' yet often (if not absolutely always) mathematically nontrivial areas such as maths of optimization (linear and nonlinear programming), probability theory, the maths of information (with laws of information corresponding to group-theoretical principles), etc. Best, Ben - Original Message - From: Benjamin Udell To: PEIRCE-L@LISTSERV.IUPUI.EDU Sent: Monday, March 12, 2012 1:14 PM Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition Malgosia, list, Responses interleaved. - Original Message - From: malgosia askanas To: PEIRCE-L@LISTSERV.IUPUI.EDU Sent: Monday, March 12, 2012 12:31 PM Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition [BU] Yes, the theorematic-vs.-corollarial distinction does not appear in the Peirce quote to depend on whether the premisses - _up until some lemma_ - already warrant presumption. BUT, but, but, the theorematic deduction does involve the introdution of that lemma, and the lemma needs to be proven (in terms of some postulate system), or at least include a definition (in remarkable cases supported by a "proper postulate") in order to stand as a premiss, and that is what Irving is referring to. [MA] OK, but how does this connect to the corollarial/theorematic distinction? On the basis purely of the quote from Peirce that Irving was discussing, the theorem, again, could follow from the lemma either corollarially (by virtue purely of "logical form") or theorematically (requiring additional work with the actual mathematical objects of which the theorem speaks). [BU] So far, so good. [MA] And the lemma, too, could have been obtained either corollarially (a rather needless lemma, in that case) [BU] Only if it comes from another area of math, otherwise it is corollarially drawn from what's already on the table and isn't a lemma. [MA] or theorematically. Doesn't this particular distinction, in either case, refer to the nature of the _deduction_ that is required in order to pass from the premisses to the conclusion, rather than referring to the warrant (or lack of it) of presuming the premisses? [BU] It's both, to the extent that the nature of that deduction depends on whether the premisses require a lemma, a lemma that either gets something from elsewhere (i.e., the lemma must refer to where its content is established elsewhere), or needs to be proven on the spot. But - in some cases there's no lemma but merely a definition that is uncontemplated in the thesis, and is not demanded by the premisses or postulates but is still consistent with them, and so Irving and I, as it seems to me now, are wrong to say that it's _always_ a matter of whether some premiss requires special proof. Not always, then, but merely often. In some cases said definition needs to be supported by a new postulate, so there the proof-need revives but is solved by recognizing the need and "conceding" a new postulate to its account. [MA] If the premisses are presumed without warrant, that - it seems to me - does not make the deduction more corollarial or more theorematic; it just makes it uncompleted, and perhaps uncompletable. [BU] That sounds right. Best, Ben ----- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, s
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
Ben Udell asked: Do you think that your "theoretical - computational" distinction and likewise Pratt's "creator - consumer" distinction between kinds of mathematics could be expressed in terms of Peirce's "theorematic - corollarial" distinction? Given that Peirce wrote at MS L75:35-39 that: "Deduction is only of value in tracing out the consequences of hypotheses, which it regards as pure, or unfounded, hypotheses. Deduction is divisible into sub-classes in various ways, of which the most important is into corollarial and theorematic. Corollarial deduction is where it is only necessary to imagine any case in which the premisses are true in order to perceive immediately that the conclusion holds in that case. Ordinary syllogisms and some deductions in the logic of relatives belong to this class. Theorematic deduction is deduction in which it is necessary to experiment in the imagination upon the image of the premiss in order from the result of such experiment to make corollarial deductions to the truth of the conclusion. The subdivisions of theorematic deduction are of very high theoretical importance. But I cannot go into them in this statement." the answer to the question would appear to be: no. Whereas Peirce's characterization of theorematic and corrolarial deduction would seem, on the basis of this quote, to have to do with whether the presumption that the premises of a deductive argument or proof are true versus whether they require to be established to be true, and seems more akin, at least peripherally, to the categorical/hypothetical status of the premises, the distinctions "theoretical - computational" which I suggested and likewise Pratt's "creator - consumer" are not at all about the deriving theorems or the what is assumed about the truth of the premises. Rather the distinction between creator-theoretician vs. consumer-practitioner is a distinction in which the former is concerned (in the main) to develop new mathematics on the basis of the mathematics that has already been established, whereas the consumer practitioner borrows and utilizes already established mathematics for purposes other than establishing new mathematical results. The example which I cited, of Riemann and Minkowski vs. Einstein is applicable here. Riemann expanded known mathematical results regarding three-dimensional geometries to n-dimensional geometries (Riemann manifolds) and contributed to the development of non-Euclidean geometries, and Minkowski starting from non-Euclidean geometries, in particular parabolic and hyperbolic, arrived at his "saddle-shaped" space, and Minkowski taught Einstein the mathematics of Riemannin and Minkowski geometry, who used it to work out the details of relativity, but, unlike Riemann or Minkowski, did not create any new mathematics, just utilized the already given mathematics of Riemann and Minkowski to mathematically solve a particular problem in physics. I think most would agree with the proposition that Einstein was a physicist, rather than a mathematician, albeit unassailably a mathematical physicist, who employed already established mathematics and mathematical equations to advance physics, and along those same lines, I think most would likewise agree with the proposition that Einstein was not a mathematician. This does not, of course, take away from his status as a physicist. By the same token, Newton can be credited as both a mathematician, for his fluxional caculus as well as a physicist, although his invention -- and I would not want to get into the Newton-Leibniz battle here -- of the calculus was developed in large measure for the purpose of doing physics. But the fact that Newton (although he used geometry rather than the calculus in the mathematics of the Principia) obtained the fluxional calculus in part to advance mathematics (a major advance over Cavalieri's ponderous method of indivisibles, and in part to work out and express mathematically the laws of gravity and of terrestrial and celestial mechanics, illustrates that a theoretical/ applied distinction is somewhat artificial as compared with the "theoretical - computational" distinction and "creator - consumer" distinction. - Message from bud...@nyc.rr.com - Date: Wed, 7 Mar 2012 14:41:08 -0500 From: Benjamin Udell Reply-To: Benjamin Udell Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition To: PEIRCE-L@LISTSERV.IUPUI.EDU Irving, Do you think that your "theoretical - computational" distinction and likewise Pratt's "creator - consumer" distinction between kinds of mathematics could be expressed in terms of Peirce's "theorematic - corollarial" distinction? That identification seems not without issues but still pretty appealing to me, but maybe I've missed something. (For readers unfam
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
s examples of mathematicians who were also physicists, e.g. Laplace, even Euler, I think it would be beneficial to adopt Pratt's "creator" and "consumer" distinction. A notable example of the latter would be Einstein, who, with the help of Minkowski, applied the Riemannian geometry to classical mechanics to provide the mathematical tools that allowed formulation of the theory of relativity as requiring a four-dimensional, curved space. You mention the two "conflicting definitions" of mathematics and offer an extraordinarily helpful passage of Hans Hahn's to the effect that mathematicians generally concern themselves with "how a proof goes" while the logician sets himself the task of examining "why it goes this way". Besides arguing that "we should do well to understand necessary reasoning as mathematics" (EP2:318), Peirce also states that theoretical mathematics is a "science of hypotheses" (EP2:51), "not how things actually are, but how they might be supposed to be, if not in our universe, then in some other" (EP2:144). I would now say that "conflicting" was far too strong and too negative a characterization of Hahn's remark. But I would continue to argue that mathematicians who are not logicians and mathematical logicians who are mathematicians still vary in their conception of what constitutes a proof in mathematics, if not of what mathematics is; namely, that the "'working' mathematician" is concerned primarily with cranking out theorems, whereas the logician is primarily concerned with the inner workings of the procedures used in deriving or deducing theorems. It is most unlikely, however, that the person who attempts to prove theorems without some essential understanding of why they [the proofs] go this way, rather than that way or that other way will develop into an original mathematician, but will remain a consumer, capable of carrying out computations, but most unlikely capable of creating any new mathematics. (One is reminded here of all those miserable school teachers who, teaching -- or, more accurately, attempting to teach -- mathematics, could not explain to their students what they were doing or why they were doing it, but probably relied on rote memory and the teachers manual.) This is another reason for preferring to distinguish, if distinguish we must, between theoretical and computational over the older, Aristotelian, distinction of pure and applied mathematics. I believe that your discussion of Peirce's remarks (which Fiske commented on) add this hypothetical dimension to theoretical mathematics. You wrote that there is "a three-fold distinction, of the creative activity of arriving at a piece of mathematics, the mathematics itself, and the elaboration of logical arguments whereby that bit of mathematics is established as valid." For the moment I am seeing these three as forming a genuine tricategorical relationship, which I'd diagram in my trikonic way, thus: Theoretical mathematics: (1ns) mathematical hypothesis formation (creative abduction--that "piece of mathematics") |> (3ns) argumentative proof (of the validity of the mathematics) (2ns) the mathematics itself Does this categorial division make any sense to you? I'm working on a trichotomic (tricategorial) analysis of science as Peirce classified it, but I'm challenged in the areas of mathematics as well as certain parts of what Peirce calls "critical logic", or, "logic as logic" (the second division of logic as semeiotic, sandwiched between semeiotic grammar and rhetoric/methodeutic, all problematic terms for contemporary logic, I'm assuming). I certainly don't want to create tricategorial relations which don't exist, so would appreciate your thoughts in this matter. Sounds okay to me, but that is question perhaps better dealt with by someone more familiar with Peirce's understanding of category theory and his tri-categorical conceptions. Incidentally, I remember ages ago reading Emil Fackenheim's _The Religious Dimension in Hegel's Thought_, which, as I recall, presented the thesis that Hegel's triadism was an abstractification (or "philosophization") and secularization of the religious idea of the Trinity. Does anyone propound the view that Peirce's triadism is something similar? - Message from richmon...@lagcc.cuny.edu - Date: Sat, 18 Feb 2012 19:17:55 -0500 From: Gary Richmond Reply-To: Gary Richmond Subject: Mathematical terminology, was, review of Moore's Peirce edition To: ianel...@iupui.edu, PEIRCE-L@LISTSERV.IUPUI.EDU Irving, Although I am neither a mathematician nor a logician, I learn a great deal from your posts about both of these disciplines and their connections, for example, in this most recent message of yours which takes up s
Re: [peirce-l] review of Moore's Peirce edition
greater "rigor" of chemistry than mathematics, and, along the way, a discussion of what Eugene Wigner famously called the "unreasonable effectiveness of mathematics in the natural sciences" in dealing with physical reality. Is it the claim that a piece of mathematics is valid only if it is experimental(ly confirmed) rather than formal? Is it the claim that a logic system, or a proof within that system, is valid only if it is experimentally tested and demonstrated? So : Expliqué, s'il vous plait. - Message from jerry_lr_chand...@mac.com - Date: Fri, 03 Feb 2012 21:30:44 -0500 From: Jerry LR Chandler Reply-To: Jerry LR Chandler Subject: Re: [peirce-l] review of Moore's Peirce edition To: Irving , PEIRCE-L@LISTSERV.IUPUI.EDU Irving, List: A belated reply to Irving's note on "Wissenschaften" and chemistry and a few speculations about the origins of "logical rigor". On Jan 27, 2012, at 7:32 PM, Irving wrote: Jerry, Kirsti, list, ... That being said, I for one suspect it is very much possible to discuss logic and mathematics without bringing chemistry into the discussion. For those interested in the axiomatization of chemistry, or in employing group theory to study cristaline structures, that of course is a different story altogether. But, as a mathematician, I have no need to consider chemistry. My interest in chemistry, as historian of mathematics extends only so far as Cayley, Kempe, and Peirce were inspired by chemical diagrams to treat logical relations graphically. ... But this is just my own logico-mathematical orientation at play. I certainly agree that nearly all mathematicians can do mathematics, logicians can do logic and mathematical logicians can study the history of logic without addressing the atomic numbers and the particular graphic icons constructed by chemists to symbolize, index and "icononize" material reality. Relative to the ancient history of mathematics, the atomic number are not yet 100 years old and, of course, the mathematics of molecular biology, now incubating in the pregnant minds of biochemists, is yet to be fully born, although biosemioticians are preparing to serve as midwives. Further, I believe that academics have an inviolate obligation to seek to answer the questions of interest to them (within the legal confines of one's community.) I am reminded of a elderly epidemiologist, who patiently explained to me that one expresses one's personal values by WHAT one chooses to study and one's professional values by HOW one studies it. Over the years, I have audited about 2 dozen graduate level math courses; chemistry was not mentioned in any of these, with one exception in a graph theory class. Now, as a professional chemist, I know that chemistry is an entangled mixture of mathematics and empiricism, grounded in the atomic numbers and experimentation. I would add that the rigor of chemical logic probably exceeds the rigor of mathematical logic because chemists do not invoke irrational, transcendental, or surrealistic numbers, chemists do not admit to imaginary numbers and chemists demand proof in nature and as well in the mind. This is an empirical logic or, better yet, a pragmatic logic that CSP understood very well. Within this framework, I study CSP's writings in search of a better understanding of the relation between logic and chemistry, in search of the encoding of chemistry in logic, and in search of the encoding of logic in chemistry (the molecular neuro-sciences.) My philosophical biases are well-known to regular readers of this list - I am a hardcore realist. My immediate goals have been strongly influenced by two colleagues - category theorists Robert Rosen and Andree Ehresmann. Andree argues that category theory is a suitable BASIS for mathematical biology / complex systems theory (See "Memory Evolutive Systems" 2007?). Robert Rosen spent an entire career studying his brand of molecular biology, termed metabolic repair systems. Using category theory, he concluded that formal mathematical logic LACKED the capacity to symbolize natural systems. (See "Life Itself" 1991?) The Rosen and Ehremann hypotheses are not exactly diametrically opposed, but may be considered so for most practical purposes. Through my participation in the Washington Evolutionary Systems Society, I got to know both Robert and Andree as personal friends and colleagues. These friendships fostered deep discussions of the relationships between mathematics, logic and biology, more so with Andree than Robert. Thus, I come to CSP's writings with a trained eye on how and when the sciences influence the works of a mathematician. The subtle influences of chemical thinking AS IT STOOD in CSP lifetime, are abundant in CSP writings. But, he wrote BEFORE the atomic numbers were exactly measured and BEFORE the exact logical rigor of the covalent chemical b
Re: [peirce-l] Philosophia Mathematica articles of interest
You're very welcome, Cathy. It would be useful to have a single venue that would disseminate Peirce-related publications. Perhaps the keepers of Arisbe can be persuaded to have one or more folks volunteer as librarians to post and maintain a list of titles on the Arisbe site. - Message from cl...@waikato.ac.nz - Date: Wed, 15 Feb 2012 15:10:01 +1300 From: Catherine Legg Reply-To: Catherine Legg Subject: RE: Philosophia Mathematica articles of interest To: PEIRCE-L@LISTSERV.IUPUI.EDU Thank you for publicising that, Irving! Both papers were part of a mini-conference myself and Clemency Montelle organized at the NZ Division of the Australasian Association of Philosophy Conference, in Dec '09. Peirce featured prominently in discussions on the day, which is unusual for Australasian philosophy. Another paper from that mini-conference which is still in advance access, and has a similar theme to the Catton & Montelle paper, is Danielle Macbeth, "Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice": http://philmat.oxfordjournals.org/content/20/1/58.abstract?sid=2b61ff33-ea 82-434f-9c8d-67675faf094b I would love to hear more about recent publications on Peirce from other list members, though at the same time cognisant of the danger of tipping off a bibliographic deluge. Cheers, Cathy -Original Message- From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf Of Irving Sent: Tuesday, 14 February 2012 8:36 a.m. To: PEIRCE-L@LISTSERV.IUPUI.EDU Subject: Philosophia Mathematica articles of interest The newest issue of Philosophia Mathematica, vol. 20, no. 1 (Feb. 2012) has some items that may be of interest to members of PEIRCE-L; in particular: Catherine Legg, "The Hardness of the Iconic Must: Can Peirce's Existential Graphs Assist Modal Epistemology?", pp. 1-24 Philip Catton & Clemency Montelle, "To Diagram, to Demonstrate: To Do, To See, and to Judge in Greek Geometry", pp. 25-27 [the title alone of this one puts me in mind of Reviel Netz's book, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, which argues that the demonstrations in Euclid's Elements involved diagrammatic reasoning, rather than logical deductions, using "proof" to mean "argumentation" rather than, say, syllogistic logic, and I suspect that Peirce would have loved to have read this and Netz's book]; and Thomas McLaughlin's review of Matthew Moore's edition of Philosophy of Mathematics: Selected Writings of Charles S. Peirce, pp. 122-128. You can find the preview at: https://webmail.iu.edu/horde/imp/view.php?popup_view=1&index=17992&mailbox =INBOX&actionID=view_attach&id=1&mimecache=c8c67315bb4e056828f0a08507e94ea 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 -- --- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from cl...@waikato.ac.nz - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Philosophia Mathematica articles of interest
Jon, list, I don't know how you got that link; the link I posted was http://philmat.oxfordjournals.org/content/current that is: http://philmat.oxfordjournals.org/content/current repeat: http://philmat.oxfordjournals.org/content/current - Message from jawb...@att.net - Date: Wed, 15 Feb 2012 11:24:17 -0500 From: Jon Awbrey Reply-To: Jon Awbrey Subject: Re: Philosophia Mathematica articles of interest To: Irving Irving, All I get when I follow that link is an IU Webmail login page, but I don't have an account. Regards, Jon Irving wrote: The newest issue of Philosophia Mathematica, vol. 20, no. 1 (Feb. 2012) has some items that may be of interest to members of PEIRCE-L; in particular: Catherine Legg, "The Hardness of the Iconic Must: Can Peirce's Existential Graphs Assist Modal Epistemology?", pp. 1-24 Philip Catton & Clemency Montelle, "To Diagram, to Demonstrate: To Do, To See, and to Judge in Greek Geometry", pp. 25-27 [the title alone of this one puts me in mind of Reviel Netz's book, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, which argues that the demonstrations in Euclid's Elements involved diagrammatic reasoning, rather than logical deductions, using "proof" to mean "argumentation" rather than, say, syllogistic logic, and I suspect that Peirce would have loved to have read this and Netz's book]; and Thomas McLaughlin's review of Matthew Moore's edition of Philosophy of Mathematics: Selected Writings of Charles S. Peirce, pp. 122-128. You can find the preview at: https://webmail.iu.edu/horde/imp/view.php?popup_view=1&index=17992&mailbox=INBOX&actionID=view_attach&id=1&mimecache=c8c67315bb4e056828f0a08507e94ea0 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 -- academia: http://independent.academia.edu/JonAwbrey inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey word press blog 1: http://jonawbrey.wordpress.com/ word press blog 2: http://inquiryintoinquiry.com/ - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from jawb...@att.net - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Conceptions Of Locality In Logic And Computation, A History
Steven, I only very quickly scanned the abstract that you linked to, and would ask: With mereology characterized as a theory of collective sets (in opposition to the Cantorian notion of set), and with collective sets defined by means of the "part of" relation, such that mereology can be described as a theory of this relation; How relevant might Lesniewski's mereology be to this discussion, along with all of the other logicians you mention, besides Peirce and Schöder? Irving - Message from ste...@iase.us - Date: Mon, 13 Feb 2012 22:48:23 -0800 From: Steven Ericsson-Zenith Reply-To: Steven Ericsson-Zenith Subject: Conceptions Of Locality In Logic And Computation, A History To: PEIRCE-L@LISTSERV.IUPUI.EDU Dear List, I am giving a presentation at CiE 2012 in Cambridge (England) in June that may interest list members: Conceptions Of Locality In Logic And Computation, A History http://iase.info/conceptions-of-locality-in-logic-and-computat Your review welcome. With respect, Steven -- Dr. Steven Ericsson-Zenith Institute for Advanced Science & Engineering http://iase.info - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from ste...@iase.us - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] Philosophia Mathematica articles of interest
The newest issue of Philosophia Mathematica, vol. 20, no. 1 (Feb. 2012) has some items that may be of interest to members of PEIRCE-L; in particular: Catherine Legg, "The Hardness of the Iconic Must: Can Peirce's Existential Graphs Assist Modal Epistemology?", pp. 1-24 Philip Catton & Clemency Montelle, "To Diagram, to Demonstrate: To Do, To See, and to Judge in Greek Geometry", pp. 25-27 [the title alone of this one puts me in mind of Reviel Netz's book, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, which argues that the demonstrations in Euclid's Elements involved diagrammatic reasoning, rather than logical deductions, using "proof" to mean "argumentation" rather than, say, syllogistic logic, and I suspect that Peirce would have loved to have read this and Netz's book]; and Thomas McLaughlin's review of Matthew Moore's edition of Philosophy of Mathematics: Selected Writings of Charles S. Peirce, pp. 122-128. You can find the preview at: https://webmail.iu.edu/horde/imp/view.php?popup_view=1&index=17992&mailbox=INBOX&actionID=view_attach&id=1&mimecache=c8c67315bb4e056828f0a08507e94ea0 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] review of Moore's Peirce edition
Jerry, Please explain what "chemical logic" may be, and how it relates if at all, to mathematical logic on the one hand and whether it is not somehow akin to the experimental logic of Mill or Dewey, or perhaps a neurologically, electro-chemically based version of some sort of psychologistic logic. - Message from jerry_lr_chand...@mac.com - Date: Fri, 03 Feb 2012 21:30:44 -0500 From: Jerry LR Chandler Reply-To: Jerry LR Chandler Subject: Re: [peirce-l] review of Moore's Peirce edition To: Irving , PEIRCE-L@LISTSERV.IUPUI.EDU Irving, List: A belated reply to Irving's note on "Wissenschaften" and chemistry and a few speculations about the origins of "logical rigor". On Jan 27, 2012, at 7:32 PM, Irving wrote: Jerry, Kirsti, list, ... That being said, I for one suspect it is very much possible to discuss logic and mathematics without bringing chemistry into the discussion. For those interested in the axiomatization of chemistry, or in employing group theory to study cristaline structures, that of course is a different story altogether. But, as a mathematician, I have no need to consider chemistry. My interest in chemistry, as historian of mathematics extends only so far as Cayley, Kempe, and Peirce were inspired by chemical diagrams to treat logical relations graphically. ... But this is just my own logico-mathematical orientation at play. I certainly agree that nearly all mathematicians can do mathematics, logicians can do logic and mathematical logicians can study the history of logic without addressing the atomic numbers and the particular graphic icons constructed by chemists to symbolize, index and "icononize" material reality. Relative to the ancient history of mathematics, the atomic number are not yet 100 years old and, of course, the mathematics of molecular biology, now incubating in the pregnant minds of biochemists, is yet to be fully born, although biosemioticians are preparing to serve as midwives. Further, I believe that academics have an inviolate obligation to seek to answer the questions of interest to them (within the legal confines of one's community.) I am reminded of a elderly epidemiologist, who patiently explained to me that one expresses one's personal values by WHAT one chooses to study and one's professional values by HOW one studies it. Over the years, I have audited about 2 dozen graduate level math courses; chemistry was not mentioned in any of these, with one exception in a graph theory class. Now, as a professional chemist, I know that chemistry is an entangled mixture of mathematics and empiricism, grounded in the atomic numbers and experimentation. I would add that the rigor of chemical logic probably exceeds the rigor of mathematical logic because chemists do not invoke irrational, transcendental, or surrealistic numbers, chemists do not admit to imaginary numbers and chemists demand proof in nature and as well in the mind. This is an empirical logic or, better yet, a pragmatic logic that CSP understood very well. Within this framework, I study CSP's writings in search of a better understanding of the relation between logic and chemistry, in search of the encoding of chemistry in logic, and in search of the encoding of logic in chemistry (the molecular neuro-sciences.) My philosophical biases are well-known to regular readers of this list - I am a hardcore realist. My immediate goals have been strongly influenced by two colleagues - category theorists Robert Rosen and Andree Ehresmann. Andree argues that category theory is a suitable BASIS for mathematical biology / complex systems theory (See "Memory Evolutive Systems" 2007?). Robert Rosen spent an entire career studying his brand of molecular biology, termed metabolic repair systems. Using category theory, he concluded that formal mathematical logic LACKED the capacity to symbolize natural systems. (See "Life Itself" 1991?) The Rosen and Ehremann hypotheses are not exactly diametrically opposed, but may be considered so for most practical purposes. Through my participation in the Washington Evolutionary Systems Society, I got to know both Robert and Andree as personal friends and colleagues. These friendships fostered deep discussions of the relationships between mathematics, logic and biology, more so with Andree than Robert. Thus, I come to CSP's writings with a trained eye on how and when the sciences influence the works of a mathematician. The subtle influences of chemical thinking AS IT STOOD in CSP lifetime, are abundant in CSP writings. But, he wrote BEFORE the atomic numbers were exactly measured and BEFORE the exact logical rigor of the covalent chemical bond was established. Thus, I ask, what prevents a formal theory of chemical logic that would resolve the conundrums raised by the logics deployed by Rosen and by Ehresmann? The importance of this question i
[peirce-l] The International Interdisciplinary Conference Philosophy, Mathematics, Linguistics: Aspects of Interaction 2012
I just received notification of a conference that may be of interest to some list members: The International Interdisciplinary Conference Philosophy, Mathematics, Linguistics: Aspects of Interaction 2012 The details are in the attachment. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU announcement_PhML_2012_en.pdf Description: Adobe PDF document
Re: [peirce-l] review of Moore's Peirce edition
Jerry, Kirsti, list, I've certainly not yet gone through all of the material in Moore's edition of Peirce. Thus far I have concentrated my attention to those parts dealing with issues in set theory, [infinitesimal] analysis, some number, a bit of geometry, and the role of mathematics in education. My general impression of the whole of the contents so far is that CSP's main, but not necessarily so, concern, is to understand the relationship(s) between mathematics and logic, and more generally, of the place of mathematics in the broader context of rationality, thought, and knowledge (the latter, perhaps, in the German sense of "Wissenschaften", to include, therefore, the Geisteswissenschafteen as well as the Naturwissenschaften). There are a few references to Cayley and to Kempe, and then only referring to their work in geometry, so I consequently find nothing specific of chemistry in these selections, and so, if chemistry is on the agenda at all here for Peirce, it is probably so only very indirectly, within the perspective of one of the Naturwissenschaften, and not in these selections. That being said, I for one suspect it is very much possible to discuss logic and mathematics without bringing chemistry into the discussion. For those interested in the axiomatization of chemistry, or in employing group theory to study cristaline structures, that of course is a different story altogether. But, as a mathematician, I have no need to consider chemistry. My interest in chemistry, as historian of mathematics extends only so far as Cayley, Kempe, and Peirce were inspired by chemical diagrams to treat logical relations graphically. ... But this is just my own logico-mathematical orientation at play. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] review of Moore's Peirce edition
In the alert I received this morning from the journal Philosophia Mathematica, I could not help but notice the review by Thomas McLaughlin of Matthew Moore (ed.), Philosophy of Mathematics: Selected Writings of Charles S. Peirce. The review starts off: "The importance of C.S. Peirce as a philosopher of mathematics has long been less than a matter of consensus. For a goodly portion of the twentieth century, those who championed his stature in this regard were rather few, and his significant if admittedly not numerous contributions to mathematics per se (e.g., his independent proof of the Frobenius theorem on associative division algebras with real scalars) went largely overlooked. Gradually, however, the work of scholars such as Brady, Herron, Herzberger, Levy, Putnam, and Roberts (the list is by no means exhaustive) brought Peirce's writings in the area to the more respectful, if not always concurring, attention of a wider audience." The link is http://philmat.oxfordjournals.org/content/early/2012/01/18/philmat.nkr044.short?rss=1 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] The Peirce house at 4 Kirkland Place
Thanks to LinkedIn, I was able to locate my fellow Brandeisian, Jan Wald, who took his Ph.D. at the same time as I (1977). Wald had written his dissertation on mass terms, which was doubly supervised by Jean van Heijenoort at Brandeis and Helen Cartwright at Tufts. After getting his doctorate, Wald taught for a while at Middlebury College in Vermont, but then dropped out of sight of academia, I believe in the early 1980s (he's now an analyst specializing in medical devices for a major investment firm). As an aside, but Peirce-relevant, van Heijenoort's "Peirce" file contained nothing more by Charles than the entries from the Baldwin Dictionary "Modality", "'Necessary' and 'Necessity'", and "Vague", photocopies from Hartshorne & Weiss, and which, one might suppose, relate directly or indirectly to Wald's dissertation. None of Peirce's major publcations on algebraic logic occur in van Heijenoort's notes. For those of you who have read my book on van Heijennort, you might recall that Wald was van Heijenoort's housemate at the former Peirce house at 4 Kirkland Place. I'm hoping that Wald might be able to definitely answer the question as to whether or not van Heijenoort was ever aware of the Peirce association of that house. I'm still fairly certain that I learned about the Peirce association of that house directly from Willard Quine, and that van Heijenoort never mentioned it to me; and that Quine must have told me about it shortly after van Heijenoort died (in 1986), but before the Peirce Sesquicentennial conference at Harvard in September 1989, when Max Fisch's "Walk a Mile in Peirce's Shoes" was distributed to conference attendees. It should be interesting to get Wald's reply. So stay tuned. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] How Peircean was the 'Fregean Revolution' in Logic?
The full preprint of my paper "How Peircean was the 'Fregean Revolution' in Logic?" is now accessible online on Arisbe at: http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp-frege-revolu.pdf and on arXivMath, at: http://arxiv.org/abs/1201.0353 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Doctrine Of Individuals
Jon, Auke, Jim W., list members, My intention is and was not to withdraw from the list, but from the particular discussion regarding the role of individuals had played in Peirce's logic -- or, according to van Heijenoort had not played in Peirce's logic. My question was meant to sort out and distinguish my claims from van Heijenoort's, as it seemed -- to me, at least -- that the arsenal of quotations which Jon presented were designed to establish that the usual view, as enunciated by van Heijenoort, was incorrect. Indeed, van Heijenoort's claim that there are no individuals in Peirce's universe of discourse, as I myself have noted many times, is patently incorrect. But since the quotations were listed without explanation or qualification, it was unclear to me whether they were misdirected at me, or directed, and correctly so, at van Heijenoort. So my question was really intended to ascertain whether or not I had been misunderstood. All this by way of explanation. More crucially, I wish to thank all those who wrote to encourage me to continue on the lis, and to apololgize for the misunderstandings and confusions that ensued. I suppose we can take this as an example of one point at which I would agree with van Heijenoort, and probably most formal logicians: that natural or ordinary language embeds a vagueness that an ideal language is intended to override. Once again, thanks to all for your encouragement! I'm not planning on going anywhere. Irving Irving H. AnellisVisiting Research AssociatePeirce Edition Project, Institute for American Thought902 W. New York St.Indiana University-Purdue University at IndianapolisIndianapolis, IN 46202-5159USAURL: http://www.irvinganellis.info - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Doctrine Of Individuals
The sample quotes from Peirce regarding individuals are much appreciated.
Nevertheless: ...
Did Anellis claim that there are no individuals in Peirce's logical system? No.
Did Anellis say that van Heijenoort claim that there are no individuals in Peirce's logical system? Yes.
Did Anellis say that Bertrand Russell claimed that there are no individuals in Schroeder's logic? Yes.
Did Bertrand Russell tell Norbert Wiener that he had judged that Peano's logic was better than Schroeder's because Peano was able to refer to individuals in his system (had a notation for 'the'), whereas Schroeder's did not? Yes.
Did Anellis claim that it was Bertrand Russell (and by implication also van Heijenoort, had he known of Russell's account of that discussion with Wiener) who denied that there are individuals in the classical Boole-Schroeder calculus? Yes
Did Anellis claim that there are no individuals in Schroeder's logic? No.
Is it perhaps time for Anellis to withdraw from the discussion? Yes? / No?
Dec 8, 2011 05:28:41 PM, jawb...@att.net wrote:
Peircers,Writing "in reference to the doctrine of individuals" in his"Description of a Notation for the Logic of Relatives" (1870),Peirce's approach is, in its basic principles, so far ahead ofhis time that it overleaps the dustbin of Logical Atomism andanticipates ideas about element-free set theory that will notcome into their own until the latter part of the 20th Century.Here is a collection of excerpts that I gathered forseveral previous occasions, here and elsewhere, whenthe topic of Peirce's approach to individuals arose.o~o~o~o~o~oDOI. Doctrine Of Individualso~o~o~o~o~oDOI. Note 1o~o~o~o~o~o| In reference to the doctrine of individuals, two distinctions should be| borne in mind. The logical atom, or term not capable of logical division,| must be one of which every predicate may be universally affirmed or denied.| For, let 'A' be such a term. Then, if it is neither true that all 'A' is 'X'| nor that no 'A' is 'X', it must be true that some 'A' is 'X' and some 'A' is| not 'X'; and therefore 'A' may be divided into 'A' that is 'X' and 'A' that| is not 'X', which is contrary to its nature as a logical atom.|| Such a term can be realized neither in thought nor in sense.|| Not in sense, because our organs of sense are special -- the eye,| for example, not immediately informing us of taste, so that an image| on the retina is indeterminate in respect to sweetUess and non-sweetness.| When I see a thing, I do not see that it is not sweet, nor do I see that it| is sweet; and therefore what I see is capable of logical division into the| sweet and the not sweet. It is customary to assume that visual images are| absolutely determinate in respect to color, but even this may be doubted.| I know of no facts which prove that there is never the least vagueness| in the immediate sensation.|| In thought, an absolutely determinate term cannot be realized,| because, not being given by sense, such a concept would have to| be formed by synthesis, and there would be no end to the synthesis| because there is no limit to the number of possible predicates.|| A logical atom, then, like a point in space, would involve for| its precise determination an endless process. We can only say,| in a general way, that a term, however determinate, may be made| more determinate still, but not that it can be made absolutely| determinate. Such a term as "the second Philip of Macedon" is| still capable of logical division -- into Philip drunk and| Philip sober, for example; but we call it individual because| that which is denoted by it is in only one place at one time.| It is a term not 'absolutely' indivisible, but indivisible as| long as we neglect differences of time and the differences which| accompany them. Such differences we habitually disregard in the| logical division of substances. In the division of relations,| etc., we do not, of course, disregard these differences, but we| disregard some others. There is nothing to prevent almost any| sort of difference from being conventionally neglected in some| discourse, and if 'I' be a term which in consequence of such| neglect becomes indivisible in that discourse, we have in| that discourse,|| ['I'] = 1.|| This distinction between the absolutely indivisible and that which| is one in number from a particular point of view is shadowed forth| in the two words 'individual' ('to atomon') and 'singular' ('to kath| ekaston'); but as those who have used the word 'individual' have not| been aware that absolute individuality is merely ideal, it has come to| be used in a more general sense.|| C.S. Peirce, 'Collected Papers', CP 3.93Peirce defines the "number" ['t'] of a logical term 't' as follows:| I propose to assign to all logical terms, numbers; to an absolute term,| the number of individuals it denotes; to a relative term, the av
Re: [peirce-l] SLOW READ: On the Paradigm of Experience Appropriate for Semiotic
Assuming that you are referring to Louis Couturat and the First International Congress of Philosophy in Paris in 1900, the answer is: Yes. He was one of the congress organizers, and the organizer for the section on logic and philosophy of science. He also spoke at that congres, on "Le système de Platon exposé dans son développement". On the issue of his treatment of functions, should I also assume that you are referring to his _Traité de logique algorithmique_. Message from jimwillgo...@msn.com - Date: Wed, 7 Dec 2011 19:30:58 -0600 From: Jim Willgoose Reply-To: Jim Willgoose Subject: RE: [peirce-l] SLOW READ: On the Paradigm of Experience Appropriate for Semiotic To: peirce-l@LISTSERV.IUPUI.EDU 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 n
Re: [peirce-l] "On the Paradigm of Experience Appropriate for Semiotic"
Certainly model theory is a general theory of interpretation of axiomatic set theory, but as such it is not committed to any extra-systematic objects, only to the sets themselves as defined by the axioms. Rather, model theory studies the mathematical structures by examining first-order sentences true of those structures and the sets definable in those structures by first-order formulas. So, model theory is neither more nor less than the structure and sets that are definable within an axiomatic theory. In other words, we require extra-logical individuals to be extensional. And since, according to Russell, and van Heijenoort, as I said in my previous post, there are no individuals in the classical Boole-Schröder calculus, that system would, again according JvH, be intensional rather than extensional. Since we have a universe of discourse in Aristotle, De Morgan, Boole, et al,m rather than THE UNIVERSE (i.e. the universal domain), "individuals" in their logic are merely representatives of a class that is given by definition, rather than an element of a set or a collection of individuals with a specified property. To employ Husserl's terminology (for example in his debates with Voigt) in order to avoid our contemporary expectations regarding the meaning and implications of "intensional" and "extensional", if that would help clarify matters, JvH would have said, as Husserl did w.r.t. Schröder's Algebra der Logik (again, had he employed the alternative terminology) the logics of Aristotle, Boole, et al are *conceptual* [a Begriffskalkul or Folgerungscalcul] rather than *contentual* [a Inhaltslogik]. One final point. So far as I recall, I did not say that "model theory necessarily intensional"; in any case, I know that I did not say *necessarily*, although it can (and should) be inferred that JvH would, as I noted, consider the classical Boole-Schroder logic to be (again in Husserlian terms, if you prefer, a Folgerungslogik, or intensional, rather than a an Inhaltslogik, or extensional. Irving - Message from michael...@comcast.net - Date: Wed, 7 Dec 2011 10:39:51 -0500 From: "Michael J. DeLaurentis" Reply-To: "Michael J. DeLaurentis" Subject: RE: [peirce-l] "On the Paradigm of Experience Appropriate for Semiotic" To: 'Jon Awbrey' , PEIRCE-L@LISTSERV.IUPUI.EDU In what sense is model theory necessarily intensional? In standard modern usage, a model simply extensionally assigns interpretations [individuals and sets, sometimes ordered] to categories of symbols in the object language. Where's the intensionality? [Leave aside for the moment modal/opaque contexts.] -Original Message- From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf Of Jon Awbrey Sent: Wednesday, December 07, 2011 9:40 AM To: PEIRCE-L@LISTSERV.IUPUI.EDU Subject: Re: [peirce-l] "On the Paradigm of Experience Appropriate for Semiotic" * 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 IA: 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. This has been coming pretty thick and fast, so let me see if I can sift it out. Aristotelian-Boolean . | Fregean logic as calculus | logic as language model-theoretic .. | set-theoretic intensional .. | extensional syntactic | semantic relative . | absolute Did you intend to align things that way? Or did you intend them as coordinate axes? Jon CC: Arisbe, Inquiry, Peirce List -- facebook page: https://www.facebook.com/JonnyCache inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey knol profile: http://knol.google.com/k/Jon-Awbrey# oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey polmic: www.policymic.com/profiles/1110/Jon-Awbrey - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - No virus found in this message. Checked by AVG - www.avg.com Version: 2012.0.1873 / Virus Database: 2102/4665 - Release Date: 12/07/11
Re: [peirce-l] ?On the Paradigm of Experience Appropriate for Semiotic?
Jerry, I think I need to make it clear that I have been providing an exposition of van Heijenoort's characterizations of the history of logic and his classifications. In fact, I do not myself adhere to these. (Indeed, as Volker Peckhaus had correctly noted, I myself, in my book on van Heijenoort, made it patently clear that I hold van Heijenoort's classificatory scheme to embrace a false dichotomy.) Van, for example, did not himself think that either Peirce or Schröder had room in the classical Boole-Schröder calculus for individuals, or that they had articulated a full quantification theory. Apropos the question, e.g. of whether the classical Boole-Schröder calculus handled individuals, JvH would surely, had he known about Bertrand Russell's discussions with Norbert Wiener, have referred to Russell's account of how it was precisely hearing the discussion between Peano and Schröder at the Paris Philosophy Congress in 1900, and the capability of Peano's pasigraphy of articulating "the" within his logical system, and Schröder's [presumptive] inability to do so in his calculus, that convinced him of the superiority of Peano's logic to the Boole-Schroöder calculus. I deal elsewhere, separately, with where and how Van got Peirce and Schröder WRONG in "How Peircean was the "Fregean" Revolution in Logic?" (forthcoming Logicheskie issledovaniya, Pt. 1 (2012); Pt. 2 (2013); preprint: http://vfc.org.ru/eng/events/conferences/smirnov2011/members/; http://vfc.org.ru/rus/events/conferences/smirnov2011/members/). I demonstrate there that virtually all of the criteria that JvH listed as Frege's unique original innovations contributing to the development of "modern" logic can in fact be found in Peirce's (and Schröder's) algebraic logic. With respect to the Stoic logicians, Van dealt with them only to the very limited extent of noting that J. M. Bochenski, in his little paper "Spitzfindingkeit", included them among the logicians who were spitzfinding (subtle -- or better, rigorous), and did not raise the question of where they might fit in the Aristotelian/Boolean or the Fregean stream. They play no role whatever in any other of Van's published work outside of his review of Bochenski's paper. I shall leave the question of the role that chemical bonding had for CSP in bonding [pun intended] the Stoic concept of consequence with Aristotelian logic aside for another time, as a bit off topic from the traditional/modern question. I am for the moment able to say little more than that Kempe contributed to the logic of relations, applications of the logic or relations to geometry and foundations of geometry, and his chemically-inspired diagrams, together with Cayley's analytical trees, had indubitably formed part of the inspiration for CSP's entitative and existential graphs for logic. Beyond that, in any event, I think others would be much better prepared than I to handle any philosophical issues that might be involved. Irving - Message from jerry_lr_chand...@me.com - Date: Wed, 07 Dec 2011 13:39:40 -0500 From: Jerry LR Chandler Reply-To: Jerry LR Chandler Subject: Re: [peirce-l] ?On the Paradigm of Experience Appropriate for Semiotic? To: PEIRCE-L@LISTSERV.IUPUI.EDU Irving, List: A well articulated response that motivates me to push the ill-formed questions yet another step. If the first primitive binary separation of the primitive notion of a meaningful logic is Aristotelian (Boolean) / Fregean, then where would one place the Stoic notion of Antecedent / Consequence? Secondly, CSP speaks of copulative logic (presumably from the notion of a copula) in contrast to predicate logic; where would this sort of grammatical distinction fit in such a binary primitive of the classification of adjectives describing forms of logic? This question arises from the basic notion of a chemical bond as expressed by the conjunction of two terms to form a third terms such that the two parts create (form) a new whole. Clearly, CSP was aware of Cayley's work on both graph theory and group theory and yet proceeded with basing his graphic notation for logic on chemical relations. (See EP 2, 362-70.) The philosophical importance of this question emerges from the text describing how he chose to base his Phaneron on "indecomposable elements" (logically) analogous to the chemical elements. Is it possible that CSP was attempting to bridge the gap between Aristotelian and Stoic logic in this attempt to give meaning to the notion of scientific observations? Cheers Jerry On Dec 7, 2011, at 12:12 PM, Irving wrote: I'm not certain that I fully understand the question here. These two disparate sets of properties are part of an interacting complex that, for JvH, typify and help distinguish the traditional logic (in which the "Booleans" or algebraic logicians a
Re: [peirce-l] ?On the Paradigm of Experience Appropriate for Semiotic?
I'm not certain that I fully understand the question here. These two disparate sets of properties are part of an interacting complex that, for JvH, typify and help distinguish the traditional logic (in which the "Booleans" or algebraic logicians are included, insofar as they putatively do no more than attempt to algebraicize Aristotle's syllogistic logic) from the "Fregeans". I suppose that the best that can be said in terms of attempting to organize the list is that those in the first column are characteristic -- I suppose I would say in varying degrees, although JvH did not explicitly include that modifier -- of the traditional logic, those in the second column "modern", and specifically mathematical, logic, which, he says unequivocally, begins with Frege's Begriffsschrift. On the other hand, there is some implicit equivocation, since JvH also described Hilbert as standing between these two groups -- in which case, we have, indeed, to allow some flexibility rather than arbitrarily assign every characteristic in one column exclusively to the one or the other of the traditional or the modern logic. (I suppose if you want some principle of organization for each property in these two sets of properties, they therefore should perhaps better be thought of as rays, rather than either strictly and rigidly aligned or as lying on absolute coordinate axes. That is why I preferred to describe these two sets of properties as forming a "complex of related dichotomies" rather than, as "defining characteristics" and now call them the set of characteristics that for JvH "typify and help distinguish" the two traditions or streams of logic. Irving - Message from jawb...@att.net - Date: Wed, 07 Dec 2011 09:40:26 -0500 From: Jon Awbrey Reply-To: Jon Awbrey Subject: Re: ?On the Paradigm of Experience Appropriate for Semiotic? To: Jon Awbrey's Inquiry Project * 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 IA: 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. This has been coming pretty thick and fast, so let me see if I can sift it out. Aristotelian-Boolean . | Fregean logic as calculus | logic as language model-theoretic .. | set-theoretic intensional .. | extensional syntactic | semantic relative . | absolute Did you intend to align things that way? Or did you intend them as coordinate axes? Jon CC: Arisbe, Inquiry, Peirce List -- facebook page: https://www.facebook.com/JonnyCache inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey knol profile: http://knol.google.com/k/Jon-Awbrey# oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey polmic: www.policymic.com/profiles/1110/Jon-Awbrey - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from jawb...@att.net - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] SLOW READ: On the Paradigm of Experience Appropriate for Semiotic
y 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
Reply-To: Benjamin Udell
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 Bool
Re: [peirce-l] ?On the Paradigm of Experience Appropriate for Semiotic?
ntial, the experimental and the empirical from certain other complexes of ideas with which they have become associated by accident rather than necessity. The thoughts that occur to me on reading this statement are as follows. On the one hand I am much in favor of seeking deeper-lying continuities where only divisions appear to rule the superficial aspects of phenomena. That is one of the things that attracts me to Peirce's theory of inquiry, that succeeds in connecting our everyday problem-solving activities with the more deliberate and disciplined methodologies of scientific research. On the other hand I cannot help noticing the facts of usage. For example, even though the words "experiential", "empirical", and "experimental" may be near enough synonyms in some contexts, in other contexts a person will tend to use "empirical" to emphasize a shade of distinction between casual experience and the deliberate collection of data, perhaps even bearing the motive of testing a specific array of hypotheses. In that empirical setting, a person will tend to use "experimental" to suggest an even more deliberate manipulation of events for the purpose of generating data that can serve to sift the likely from the unlikely stories in the heap of hypotheses in view. Sufficient unto the day ... Jon AB: It would be handy if 'reply' gives a reply to the list message instead of a reply to the sender. Yes, it seems that different browsers handle that differently. I try to remember always to hit "reply to all", but often don't. AB: You wrote a sentence that raises some questions, at least in my mind. JA1: An equivocation is a variation in meaning, or a manifold of sign senses, and so Peirce's claim that three categories are sufficient amounts to an assertion that all manifolds of meaning can be unified in just three steps. AB: In comparison with the sentence you wrote earlier in the same mail there are two differences: JA2: Peirce's claim that three categories are necessary and sufficient for the purposes of logic says that a properly designed system of logic can resolve all equivocation in just three levels or steps. AB: a. unification of all manifolds of meaning is not without further qualifications the same as disambiguation. So, in principle at least I could support JA2 and not support JA1. AB: b. In JA1 the problem of the meaning of 'meaning' presses itself upon the reader, in JA2 meaning is given, the only problem that remains is to make a choice between alternatives that are supposed to be given. AB: So, JA1 is a much stronger claim than JA2. Since you wrote in JA2 about levels or steps, but in JA1 just about steps, your claim seems to amount to the proposition that all manifolds of meaning can be unified in a single run of a procedure that consists of three steps. Of course unification can be taken as quite empty (for instance as "signs written on the same sheet are unified", but then "unification of all manifolds of meaning", is rather unsatisfying on the meaning side of the issue. AB: I am inclined to reason that, given: JA3: Peirce's distinctive claim is that a type hierarchy of three levels is generative of all that we need in logic. AB: It is possible to design a procedure with the three steps of JA1 that unifies all manifolds of meaning, not in three steps. -- facebook page: https://www.facebook.com/JonnyCache inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey knol profile: http://knol.google.com/k/Jon-Awbrey# oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey polmic: www.policymic.com/profiles/1110/Jon-Awbrey - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from jawb...@att.net - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] SLOW READ: On the Paradigm of Experience Appropriate for Semiotic
Ben Udell wrote [begin quote]: Gary F., list, ... You wrote: Abstraction (in the sense above) obviously has its uses in the process of learning from experience, but not to the degree that it can *replace* experience. My guess is that this is the same issue that Irving and others have been dealing with in this thread with regard to ?formalism?, but not being a mathematician, i don't always follow their idiom. I'm not a mathematician either, and Irving can correct me if he wants to plow through my prose, but I agree that the issue is related. There's a related issue of model theorists and semanticists, versus proof theorists, who are more like formalists. Model theorists and semanticists see formal languages as being _about_ subject matters which are 'models' for the formalism. Somebody once told me that when I say that, in a deduction, the premisses validly imply the conclusions, that's proof-theoretic in perspective, but when I say that, in a deduction, if the premisses are true then the conclusion is true, that's model-theoretic in perspective. Peirce is usually classed on the model theorist/semanticist side, and Goedel's aim is said to have been to show that mathematics can't be regarded as pure formalism, a show about nothing. Proof theorists and formalists are more inclined to see math as formal calculi, systems of marks transformable according to rules, not as language _about_ things. Now, calculation, as far as I can tell, is (deductive mathematical) reasoning with terms. E.g., (trivially) "5 ergo 5"*, instead of "there is a horse ergo there is a horse". I can kind of see how propositions (a.k.a. zero-place terms) versus (other) terms, would align with facts, real objects, etc., versus marks. If you look at propositions as marks, then they're like term-inviting clumpish things (as opposed to proposition-inviting facts or states of affairs.) But it's an alignment by some sort of affinity or correlation, not identity. Semantics is concerned not just with reference by propositions but with reference by terms to things; the terms are not ideally non-referring marks in semantics. For a formalist, the marks _are_ the things. [end quote] If I understand aright, one of the issues being raised by Ben and Gary is the link between abstraction and formalism, and whether there is a connection as well between model theorists and semanticists on the one hand, and proof theorists on the other, where the latter are close to formalists as being abstractionist. The first part of my reply in this case is that neither intuitionists (such as Brouwer) or logicists (such as Frege or Russell) abjure abstraction any more than formalists. Indeed, Piaget formulated his genetic "constructive epistemology" for his developmental psychologist Jean Piaget, describing abstract reasoning as the final stage of cognitive development by referring directly to Brouwer. The expression "constructivist epistemology" was first used by Piaget in 1967, in the article "Logique et Connaissance scientifique" in the Encyclopédie de la Pléiade. Piaget refers directly to the Brouwer and his radical constructivism. (See, e.g., my "La psicologia di Piaget, la matematica costruttivista e l'interpretazione semantica della verita secondo la teoria degli insiemi" (Nominazione: Rivista Internazionale di Logica 2 (1981), 174-188) on how Piaget's psychology describes the epistemology of number and set theory. Setting aside, therefore, the issue of abstraction, the more complex issue under consideration is that regarding the perceived distinction between "model theorists and semanticists on the one hand and proof theorists on the other. This is an erroneous distinction insofar as the historical and philosophical literature, from van Heijenoort forward, distinguishes between two types of semantics, namely the set-theoretic (or extensional, which would also include Frege's course-of-values, or Werthverlauf, semantics) and the model-theoretic (or intensional). (Actually, van Heijenoort's terminology is itself at first somewhat misleading, insofar as he initially associated the limited universes of discourses of the algebraic logicians with the set-theoretic, and not with the course-of-values of Frege and the set theory of Russell; although he then immediately corrected himself by associating the Russello-Fregean extensional semantics with the set theoretical.) Having said that, there is, for van Heijenoort and those who came after him, a complex of dichotomies that are bound together to distinguish the algebraic logic of De Morgan, Boole, Peirce, and Schröder on the one hand from the "quantification-theoretic -- or more properly, despite van Heijenoort, function-theoretic and set-theoretic logic of Frege, Peano, and Russell. All of the elements of this complex are to be brought together in my forthc
[peirce-l] forthcoming Peirce titles
Dear colleagues, In case you have not yet heard about it, there is a new publisher, Docent Press, that focuses on history of mathematics, including history of logic, with Ivor Grattan-Guinness among those serving on its editorial board, and is interested primarily in works on history of mathematics. Two of their forthcoming titles are directly relevant to Peirce; they are: Paul Shields, Charles S. Peirce on the Logic of Number and Alison Walsh, Relations between Logic and Mathematics in the Work of Benjamin and Charles S. Peirce Many of you, in particular PEIRCE-L members, Peircean scholars, and historians of logic, may be familiar with my "Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic", Modern Logic 5 (1995), 270328; electronic version at: http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp&br.htm. and my "Some Views of Russell and Russells Logic by His Contemporaries", Review of Modern Logic 10:1/2 (2004-2005), 67-97; especially the electronic version: "Some Views of Russell and Russell's Logic by His Contemporaries, with Particular Reference to Peirce", at http://www.cspeirce.com/menu/library/aboutcsp/anellis/views.pdf. Now my Evaluating Bertrand Russell: The Logician and His Work which, however, is much more tangentially relevant specifically to Peirce, has also been added to their list of forthcoming titles. The URL for Docent Press's web page is: http://docentpress.com/ Irving 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] Hilbert and Peirce
On Nov. 27, I wrote: "... I would have to say that he would agree that there is a strong empiricism underlying Hilbert's work, and that this is the philosophical import of his quote from Kant's K.d.r.V. in the Grundlagen der Geometrie: "So fängt denn alle menschliche Erkenntnis mit Anschauungen an, geht von da zu Begriffen und endigt mit Ideen." I would argue, however, that this is about how we obtain our information, and, assuming Corry is correct, how Hilbert thought we select the elements of our universe of discourse; but I would also argue that it has nothing to do with how axiomatic systems operate, which is to say, having established the axioms, chosen the inference rules for the system, and selected the primitives from which theorems are constructed from the axioms in accordance with the inference rules, is strictly mechanical, and it does not, working within the axiom system, whether what is being manipulated are points, lines and planes, or tables, chairs, and beer mugs, or integers, , or whatever we may require for the axiomatizing task at hand. What matters within the system, while the calculations are occurring, is that complex formulas (theorems) are being constructed on the basis of the formulas that do duty as axioms, in accordance with the rules. (It is this distinction, of having inference rules in place, that renders Hilbert's systems not merely axiomatic systems, but formal deductive systems.) Hilbert's formalism amounts to the mechanization of these manipulations, and for practical purposes, the formulas are combinations of marks, and these marks become signs as soon as an interpretation is give, that is, a universe of discourse - - whether points, lines, and planes, or tables, chairs and beer mugs, or the integers. What concerns me is whether, in considering what (else) or what different Hilbert might have meant by his formalism, and whether or not there was an underlying empiricism behind this, is that we might be demanding too much of Hilbert, who was, I understand, concerned with mathematics and only peripherally with philosophy of mathematics. (Having said this,I have to also confess that I have not seen or read the contents of Hilbert's late, unpublished, lectures on foundations, but I believe that Corry has, and it is on that basis that Corry proposes an empiricist epistemology behind Hilbert's formalism.) "The only other point I would make w.r.t. Hilbert on physics, is that, at least according to Corry, part of Hilbert's empiricism is exhibited by the requirement that his axiomatization depends upon his axiomatization of geometry, and that the Kantian root of geometry is spatial intuition." Since then, I have come across some preprints (headed for publication in Erkenntnis or Synthese) that stress the empiricist aspect of Hilbert's philosophy, such as Helen De Cruz & Johan De Smedt's "Mathematical Symbols as Epistemic Actions" that takes Hilbert to be a radical empiricist in the style of, or at least very close to, Husserl's pre-phenomenological psychologism, and Soren Stenlund's "Different Senses of Finitude: An Inquiry into Hilbert's Finitism". And then there is Solomon Feferman's "And so on...: Reasoning with Infinite Diagrams", in which, in footnote 10, Sol, who I had known primarily and essentially as a mathematician specializing in recursion-theoretic aspects of proof theory and a disciple of Georg Kreisel, and secondarily as a friend and associate of Jean van Heijenoort and as editor-in-chief of Gödel's Collected Works, straightforwardly and unequivocally asserts that it is a mistake to regard Hilbert as a formalism. (What this all suggests to me is that, *if* correct, everything about Hilbert and twentieth-century formalist foundational philosophy of mathematics that I was -- and probably many of us were -- taught 47 years and more ago ... is just plain *wrong*.) 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Reply to Steven Ericsson-Zenith & Jerry Chandler re Hilbert & Peirce
Apologies for sending out the following message previously without the
subject line; the IMAP connection was temporarily broken and causing
transmission and other difficulties.
- Message from ianel...@iupui.edu -
Date: Sun, 27 Nov 2011 11:20:02 -0500
From: Irving
Reply-To: Irving
To: "PEIRCE-L@LISTSERV.IUPUI.EDU"
On 18 Nov. Steven Ericsson-Zenith wrote:
My own interpretation may be substantively different, it may not.
I take Hilbert's position to be that the formalism is independent of
the subject matter. That is, I
take his view of formal interpretation to be mechanistic, specifying
valid transformations of the
structure under consideration, be it logical, geometric or physical.
I am confused because you use
"signs" instead of "marks" here. In addition, since the formalism is
independent of the subject - as suggested by his appeal to Berkeley -
a theorem of the formalism
remains a theorem of the formalism despite the subject.
In this view, how one selects an appropriate formalism for a given
subject - if there is a fitness
("suitability") requirement as you suggest for the "different parts of
mathematics" - appears to be a mystery, unless you think empiricism
is required at this point.
And on 26 Nov., Jerry Chandler wrote:
The separate and distinct axiom systems for mathematical structures
is a thorn in my mind as it
disrupts simpler notions of the rules for conducting calculations
with numbers. While I eventually
came to accept the category theorists view of the emergence of
mathematic structures as a
historical fact, the separation of formal axiom systems causes
philosophical problems.
Firstly, physicists often speak of "first principles" or "ab initio"
foundations. These terms are used in such a sense as to imply a
special connection exists between
physics and the universals and to further imply that other sciences
do not have access to such
"first principles".
If such ab initio calculations were to be invoked as something more
serious than a linguistic
fabrication, what mathematical structure would one invoke? In the mid
and late 20 th Century, group
theory and symmetry were the popular choice among philosophically
oriented physicists and applied
mathematicians.
Philosophically, the foundations of Aristotelian causality come into
play. Philosophers abandoned
material causality, substituted the formalism of efficient causality
for formal causality and
summarily dissed telic reasoning of biology. The four causes so
widely discussed in medieval logic
and the trivium were reduced to one cause. Obviously, if every axiom
system is a formalism and
every formalism is to be associated with efficient causality, the
concept of "ab initio"
calculations is seriously diminished as every axiom system becomes a
new form of "ab
initio" calculations and conclusions.
Does anyone else see this as a problem for the philosophy of physics?
A second question is perhaps easier for you, Irving, or perhaps more
challenging.
You write:
... the only mathematically
legitimate characteristic of axiom systems is that they be
proof-theoretically sound, that is, the completeness, consistency, and
independence of the axiom system,...
I am puzzled on how to interpret the phrase,
and
independence of the axiom system,...
Many axiom systems may use the same axioms, just extend the number of
axioms in the system; the
formal axiom systems are interdependent on one another.
So, what is the sense of 'independence' as it is used in this phrase?
I would note in passing that I have attempted to write a set of
axioms for chemical relations on
several occasions and have been amply rewarded, initially with
exhilaration and subsequently with
deep remorse for having wasted my energies on such an intractable
challenge. :-) :-) :-)
I would like to take the easiest question first.
Independence, like consistency or completeness, is a model-theoretic
property of axiom systems. To put it in simplest terms, by the
independence of the axiom system, the mathematician means nothing more
nor less than that there are no axioms in the set of axioms that could
be pr oven as a theorem from the other axioms.
The issue arose when, ever since Euclid, mathematicians attempted to
determine the status of the parallel postulate. It came to a head in
1733 when Saccheri claimed to prove the parallel postulate(Vth) from
all of Euclid's axioms other than the Vth postulate, using a reductio
argument. What Beltrami showed in 1868 was that Saccheri had in fact pr
oven the independence of Euclid's Vth postulate, since in fact,
Saccheri ended up with a hyperbolic parallel postulate.
I don't know very much about Hilbert's axiomatization of physics, other
than that Leo Corry has written the most about them, including the book
David Hilbert and the Axiomatization of Physics
(1898-
[peirce-l]
On 18 Nov. Steven Ericsson-Zenith wrote:
My own interpretation may be substantively different, it may not.
I take Hilbert's position to be that the formalism is independent of
the subject matter. That is, I
take his view of formal interpretation to be mechanistic, specifying
valid transformations of the
structure under consideration, be it logical, geometric or physical. I
am confused because you use
"signs" instead of "marks" here. In addition, since the formalism is
independent of the subject - as suggested by his appeal to Berkeley - a
theorem of the formalism
remains a theorem of the formalism despite the subject.
In this view, how one selects an appropriate formalism for a given
subject - if there is a fitness
("suitability") requirement as you suggest for the "different parts of
mathematics" - appears to be a mystery, unless you think empiricism is
required at this point.
And on 26 Nov., Jerry Chandler wrote:
The separate and distinct axiom systems for mathematical structures is
a thorn in my mind as it
disrupts simpler notions of the rules for conducting calculations with
numbers. While I eventually
came to accept the category theorists view of the emergence of
mathematic structures as a
historical fact, the separation of formal axiom systems causes
philosophical problems.
Firstly, physicists often speak of "first principles" or "ab initio"
foundations. These terms are used in such a sense as to imply a special
connection exists between
physics and the universals and to further imply that other sciences do
not have access to such
"first principles".
If such ab initio calculations were to be invoked as something more
serious than a linguistic
fabrication, what mathematical structure would one invoke? In the mid
and late 20 th Century, group
theory and symmetry were the popular choice among philosophically
oriented physicists and applied
mathematicians.
Philosophically, the foundations of Aristotelian causality come into
play. Philosophers abandoned
material causality, substituted the formalism of efficient causality
for formal causality and
summarily dissed telic reasoning of biology. The four causes so widely
discussed in medieval logic
and the trivium were reduced to one cause. Obviously, if every axiom
system is a formalism and
every formalism is to be associated with efficient causality, the
concept of "ab initio"
calculations is seriously diminished as every axiom system becomes a
new form of "ab
initio" calculations and conclusions.
Does anyone else see this as a problem for the philosophy of physics?
A second question is perhaps easier for you, Irving, or perhaps more
challenging.
You write:
... the only mathematically
legitimate characteristic of axiom systems is that they be
proof-theoretically sound, that is, the completeness, consistency, and
independence of the axiom system,...
I am puzzled on how to interpret the phrase,
and
independence of the axiom system,...
Many axiom systems may use the same axioms, just extend the number of
axioms in the system; the
formal axiom systems are interdependent on one another.
So, what is the sense of 'independence' as it is used in this phrase?
I would note in passing that I have attempted to write a set of axioms
for chemical relations on
several occasions and have been amply rewarded, initially with
exhilaration and subsequently with
deep remorse for having wasted my energies on such an intractable
challenge. :-) :-) :-)
I would like to take the easiest question first.
Independence, like consistency or completeness, is a model-theoretic
property of axiom systems. To
put it in simplest terms, by the independence of the axiom system, the
mathematician means nothing
more nor less than that there are no axioms in the set of axioms that
could be proven as a theorem
from the other axioms.
The issue arose when, ever since Euclid, mathematicians attempted to
determine the status of the
parallel postulate. It came to a head in 1733 when Saccheri claimed to
prove the parallel postulate
(Vth) from all of Euclid's axioms other than the Vth postulate, using a
reductio argument. What
Beltrami showed in 1868 was that Saccheri had in fact proven the
independence of Euclid's Vth
postulate, since in fact, Saccheri ended up with a hyperbolic parallel
postulate.
I don't know very much about Hilbert's axiomatization of physics, other
than that Leo Corry has
written the most about them, including the book David Hilbert and the
Axiomatization of Physics
(1898-1918) (Dordrecht: Kluwer Academic Publishers, 2004); some of his
other work includes:
"David Hilbert and the Axiomatization of Physics", Archive for History
of Exact Sciences
51 (1997), 83-198;
"Hilbert and Physics (1900-1915)," In Jeremy Gray (ed,), The Symbolic
Universe: Geometry
and Physics (18901930) (New York, Oxford University Press,
[peirce-l] Reply to Jerry Chandler, on Hilbert and Peirce
Jerry, I suggest that this is a very good question, but I think that we have to consider Hilbert's position as an unfinished product and a moving target. Probably the best indication can be gotten by considering that there is not so much *a* "Hilbert program" as there are "Hilbert programs" (see, e.g. Wilfried Sieg's SIEG, "Hilbert's Programs, 19171922", Bulletin of Symbolic Logic 5 (1999), 1-44). I would therefore preface my answer by noting that I think it important to remember that Hilbert was a mathematician first and foremost, and that, although interested in philosophical issues in foundations of mathematics, did not systematically develop his formalism. He is better considered an amateur at philosophy. Apart from his handful of brief publications such as "Axiomatische Denken" and "Die logischen Grundlagen der Mathematik", there is, e.g. his correspondence with Frege and his unpublished lectures. The best early articulation of Hilbert's formalism is probably that given by John von Neumann in the round-table discussion in 1930 on foundations, in which Heyting also presented Brouwer's intuitionism and Carnap presented logicism, all published in Erkenntnis in 1931. All of this having been said, the best answer I can give is that, the "points, lines, and planes" and "tables, chairs, and beer mugs" remark aside, Hilbert would give different axiomatizations for different parts of mathematics. That is to say, therwe is one set of axioms and primitives suitable to develop, say, projective geometry, and another for algebraic numbers; there is one suitable for Euclidean geometry and another for metageometry. In the case of the latter, for example, one needs to devise an axiom set that is powerful enough to develop all of the theorems required for the articulation not only required for Euclidean geometry, but also for hyperbolic geometry and elliptical geometry, but which do not also generate superfluous theorems of other theories. Hilbert's axiom system for geometry, then, is not the same athat which he erected for physics. What I think is the correct understanding of Hilbert's "throw-away" remark about points, lines and planes and tables, chairs, and beer mugs, is the more profound -- or perhaps more mundane -- idea that axiom systems are sets of signs which are meaningless unless and until they are interpreted, and by themselves, the only mathematically legitimate characteristic of axiom systems is that they be proof-theoretically sound, that is, the completeness, consistency, and independence of the axiom system, and capable of allowing valid derivation of all, and only those, theorems, required for the piece of mathematics being investigated. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic
Jerry, I suggest that this is a very good question, but I am not certain that I can give you a straightforward answer. In particular, I have to altogether beg off attempting to respond to the part of your question concerning Aristotelian causality. I think that we have to consider Hilbert's position as an unfinished product and a moving target. Probably the best indication can be gotten by considering that there is not so much *a* "Hilbert program" as there are "Hilbert programs" (see, e.g. Wilfried Sieg's SIEG, "Hilbert's Programs, 19171922", Bulletin of Symbolic Logic 5 (1999), 1-44). I would therefore preface my answer by noting that I think it important to remember that Hilbert was a mathematician first and foremost, and that, although interested in philosophical issues in foundations of mathematics, did not systematically develop his formalism. He is better considered an amateur at philosophy. Apart from his handful of brief publications such as "Axiomatische Denken" and "Die logischen Grundlagen der Mathematik", there is, e.g. his correspondence with Frege and his unpublished lectures. The best early articulation of Hilbert's formalism is probably that given by John von Neumann in the round-table discussion in 1930 on foundations, in which Heyting also presented Brouwer's intuitionism and Carnap presented logicism, all published in Erkenntnis in 1931. All of this having been said, the best answer I can give is that, the "points, lines, and planes" and "tables, chairs, and beer mugs" remark aside, Hilbert would give different axiomatizations for different parts of mathematics. That is to say, there is one set of axioms and primitives suitable to develop, say, projective geometry, and another for algebraic numbers; there is one suitable for Euclidean geometry and another for metageometry. In the case of the latter, for example, one needs to devise an axiom set that is powerful enough to develop all of the theorems required for the articulation not only required for Euclidean geometry, but also for hyperbolic geometry and elliptical geometry, but which do not also generate superfluous theorems of other theories. Hilbert's axiom system for geometry, then, is not the same athat which he erected for physics. What I think is the correct understanding of Hilbert's "off-the-cuff" remark about points, lines and planes and tables, vs. chairs, and beer mugs, is the more profound -- or perhaps more mundane -- idea that axiom systems are sets of signs which are meaningless unless and until they are interpreted, and by themselves, the only mathematically legitimate characteristic of axiom systems is that they be proof-theoretically sound, that is, the completeness, consistency, and independence of the axiom system, and capable of allowing valid derivation of all, and only those, theorems, required for the piece of mathematics being investigated. Irving - Message from jerry_lr_chand...@me.com - Date: Sun, 13 Nov 2011 23:16:40 -0500 From: Jerry LR Chandler Reply-To: Jerry LR Chandler Subject: Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic To: PEIRCE-L@LISTSERV.IUPUI.EDU Irving, Jon, List; From Jon's Post: "Peirce's most detailed definition of a sign relation, namely, the one given in 2 variants in NEM 4, 20-21 & 54." "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. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic." My question is simple and regards the singular and the plural as grammatical units. In the sentence, "Logic will here be defined as formal semiotic.", is the term 'semiotic' singular or plural? Did CSP assert that only one formal semiotic exists? Or, does this sentence allow for multiple formal semiotics? For example, would the formal semiotic of Aristotelian causality be necessarily the same as the formal semiotic of material causality? By extension, signs for music, dance, electrical circuits, genetics,...; the same formal semiotic or different? This sentence reflects on the meaning of the following sentence: "Namely, a sign is something, A, which brings something, B,..." In short, what is the nature of the active process of "brings" - the same meaning for all formal semiotic, or is the fetching process tailor-made for the category of the sign? Irving: Thank you ver
Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic
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 Reply-To: Steven Ericsson-Zenith Subject: Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic To: Irving 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, formalism, intuitionism, logicism, or to any of the philosophy of logic "isms", as well as how to treat logical inference, I suggest that it helps to keep in mind Jean van Heijenoort's useful, if somewhat controversial, classification of logic of logic as calculus and logic as language and the properties associated with these. I will preface what I have to say about that, admittedly sketchily here, by noting, as a mere curiosity, of no obvious significance other than biographical, that van Heijenoort, who was my Doktorvater, resided in the house, at 4 Kirkland Place, Cambridge, formerly owned by members of the Peirce family, including Charles's father Benjamin, Charles's brother, James Mills, and Charles's Aunt "Lizzie". I first learned of the Peirce association of the house from Quine. I cannot imagine that Quine would not have told Van, since they were good friends as well as colleagues. What is ironic, then, is that Van had so little to say about Peirce and his logic. What little Van said, in his intros to
Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic
ng/events/conferences/smirnov2011/members/; http://vfc.org.ru/rus/events/conferences/smirnov2011/members/. In any case, this is a rather complicated complex of characteristics which has elicited considerable discussion since Van initially published his "Logic as Calculus and Logic as Language" (1967) and related articles, especially his "Set-theoretic Semantics" (1976); Hans Sluga's "Frege Against the Booleans" (1987) was really the first to take up some of the themes enunciated by Van in his "Logic as Calculus and Logic as Language", and my dealing with it in my _Van Heijenoort: Logic and Its History in the Work and Writings of Jean van Heijenoort_ (1994) is somewhat scattered throughout that book. The attempt to elucidate and compare Peirce's and Hilbert's takes on these issues, as well as mine, would, unfortunately, really require more time and space than would be feasible for posting on this list; I will therefore at this point plead inability to provide a simple or succinct reply to the questions asked, and refer those interested in pursuing this further to begin with Van's "Logic as Calculus and Logic as Language" (1967) and "Set-theoretic Semantics" (1976) and one or both of my "Jean van Heijenoort's Conception of Modern Logic, in Historical Perspective" and "How Peircean was the "Fregean" Revolution in Logic?". (And, yes, it's also a bit of a cop-out on my part as well, since I haven't really been thinking about these issues since completing those two papers.) Irving 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] SLOW READ: On the Paradigm of Experience Appropriate for
Steven, You quote Peirce as saying in CP 7.526 that "Logic is a branch of philosophy. That is to say it is an experiential, or positive science, but a science which rests on no special observations, made by special observational means, but on phenomena which lie open to the observation of every man, every day and hour. There are two main branches of philosophy, Logic, or the philosophy of thought, and Metaphysics, or the philosophy of being. Still more general than these is High Philosophy which brings to light certain truths applicable alike to logic and to metaphysics. It is with this high philosophy that we have at first to deal." A few paragraphs later, you then say: 'To echo Hilbert, "We can know, we will know." Only it is not mathematics alone that will inform us (and a revolution in the Foundations of Logic is required).' I do not think that Hilbert would have accepted the interpretation that seems to be implied in placing his remark in juxtaposition with the quote from Peirce calling logic an experiential or positive science. At the very least, this juxtaposition of Peirce and Hilbert runs counter to Hilberts conception of logic and mathematics as purely formal. When Hilbert quotes his Königsberg brethren Kant as the motto for his _Grundlagen der Geometrie_, he does so to make what I would call a Kantian-Piagetan point; true, we learn numbers by counting objects, and in counting different collections of objects, begin to extrapolate the concept of number; but there is a further abstraction of the abstraction before we reach the concept of number as something fundamentally UN-experiential. Or, in the passage that Hilbert quotes from Kants K.d.r.V., "So fängt denn alle menschliche Erkenntnis mit Anschauungen an, geht von da zu Begriffen und endigt mit Ideen." I suggest that the import of Hilbert's remark, as recorded in his biography by Otto Blumenthal, that we should be able to replace points, lines, and planes with tables, chairs, and beer mugs as the primitives with which our axioms deal and which we manipulate when deriving theorems from our axioms, means that our concern with logic and mathematics is entirely formal and abstract. Hilbert as we know, was a formalist, and whether. When Hilbert made the remark that we can know, we will know, he did so within the context of his Problems list at the ICM in 1900, listing and sketching what he considered to be the most interesting and important open problems in mathematics remaining at the start of the twentieth century, and which he hoped mathematicians would work on and solve. What he was saying is that he had the expectation that new and sharper mathematical tools would be devised which would give mathematicians the analytical means to solve those open problems. What he was NOT saying, I would argue, is that there are physical experiments or observations that would be undertaken that would allow mathematicians to point to some so-to-speak new or hitherto undiscovered mathematical animal as a result of experiment or observation. I think that what is wanted is a deep clarification of what Peirce may or may not have meant in asserting that logic is "an experiential, or positive science." Therefore, I guess my point is that I initially feel uncomfortable if the suggestion, in quoting Hilbert, is that Hilbert would endorse an empiricist reading of logic or mathematics. And I guess my question is whether Hilbert and Peirce would or would not agree with this "Kantian-Piagetan" position and with each other regarding the "Kantian-Piagetan" point as I have outlined it. Being an historian of logic and mathematics, rather than a philosopher of logic or mathematics, and probably a bit dense in general, I will not myself attempt to unpack this any further. Rather, I would require a tutorial to elucidate in what sense Peirce was calling logic "an experiential, or positive science" and what connection, if any, this has with (a) Kant's views, and (2) with Peirce's. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] two more papers on Peirce on math and logic coming soon
My apologies if you receive duplicate copies of this post. I've got two papers on Peirce that will be appearing shortly: "Peirce's Truth-functional Analysis and the Origin of the Truth Table" is scheduled to appear in the journal History and Philosophy of Logic; an electronic preprint is available on matharXiv(cite as arXiv:1108.2429v1 [math.HO]): http://arxiv.org/abs/1108.2429, and can also be accessed through Arisbe. The abstract and access is now available from the publisher, Taylor & Francis, at: http://www.tandfonline.com/doi/abs/10.1080/01445340.2011.621702. "Did Peirce Have Hilbert's Ninth and Tenth Problems?" is now being prepared for publication in the Spanish-language history and philosophy of mathematics journal Mathesis. The English preprint is available through Arisbe at: Arisbe; http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp&hilbert.pdf. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Some Leading Ideas of Peirce's Semiotic
ning, and inference. This may call for some discussion. He then claims that 90% of Peirce's "prodigious philosophical output" is directly concerned with semiotic." This is an odd claim in a way since it does not seem to be straightforwardly true. How can we make sense of it? From my sense of Peirce's work, I would have say that I agree with the claim that Joe makes on this point, even if I can't say whether it would be for any of the same reasons he had in mind. Understanding Peirce's pragmatism depends on understanding sign relations, triadic relations, and relations in general, all of which forms the conceptual framework of his theory of inquiry and his theory of signs. Regards, Jon -- facebook page: https://www.facebook.com/JonnyCache policy mic: www.policymic.com/profile/show?id=1110 inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey knol: http://knol.google.com/k/-/-/3fkwvf69kridz/1 oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from richmon...@lagcc.cuny.edu - 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Sciences as Communicational Communities
Not sure how relevant this is to the discussion, which I havent followed very closely, but I suggest that it is not only useful, but necessary to draw a distinction between the scientist and organization (whether governmental, academic, or entrepreneurial) for who the scientist works. It is probably doubtful that most scientists go into research to get rich, or even famous, rather than because of their curiosity to understand the natural world, or even through a moral decision to use science to improve life. Does this mean that the scientific community, or at least some members of that community, cannot be corrupted by the organizations with whom they are employed? Of course not. Those on whom the scientist depend for their survival, who pay for the research, who provide the funds for needed and elaborate experimental equipment, define the immediate goals towards which scientific research is directed. The scientist is not, by definition, entirely immune from the pressures and blandishments, ranging from publish-or-no-tenure to build-a-better-bomb-or-we-execute-your-family, that organizations might employ. Along the same lines, then, it is also important to distinguish the goals, interests, and motivations of the scientist from those of the societies or organizations and the technocrats that govern them who employ the scientific work for their own purposes. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] new Peirce related paper
It's just come to my attention that a new Peirce-related paper is available on-line and being published in the journal History and Philosophy of Logic; it's: Ahti-Veikko Pietarinen, "Existential Graphs: What a Diagrammatic Logic of Cognition Might Look Like", History and Philosophy of Logic, vol. 32 no, 3, (2011), pages 265-281, and the abstract is available at: http://www.tandfonline.com/doi/abs/10.1080/01445340.2011.06 Irving H. AnellisVisiting Research AssociatePeirce Edition Project, Institute for American Thought902 W. New York St.Indiana University-Purdue University at IndianapolisIndianapolis, IN 46202-5159USAURL: http://www.irvinganellis.info - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] email problems?
Dear Colleagues, I seem to be having some problems receiving email at my IUPUI address. So far as I can tell, this effects only email from PEIRCE-L. However, as a precaution, if anyone needs or wishes to reach me by email, it would probably be a good idea to also send back-up copies to one or both of my personal email addresses as well: irvanel...@lycos.com and/or irving.anel...@gmail.com Thanks! Irving 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Precursors Of Category Theory
Please note first of all that as a result of the glitch of the transfer of the list from Texas Tech to IUPU, I am for some inexplicable reason no longer receiving PEIRCE-L posts at the ianellis[at]iupui[dot] address. If you want to get seriously beyond Wikipedia for a history of category theory, consider
Ralf Kr{o"}mer, Tool and Object: A History and Philosophy of Category Theory (Basel/Boston/Berlin: BirkhauserBirkh{a"}user, 2007)
for an over-all history of category theory, from Aristotle to the present, including a discussion of Peirce, and
Jean-Pierre Marquis, From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory (Heidelberg/Berlin/New York, 2009)
as a follow-up from Felix Klein to the present for a discussion of mathematical category theory.
Irving H. Anellis
Visiting Research Associate
Peirce Edition Project, Institute for American Thought
Indiana University-Purdue University a Indianapolis
Aug 18, 2011 10:45:07 PM, jawb...@att.net wrote:
Peircers,Time has not been permitting me to keep up with the slow readings,but I did notice a passing discussion of "Category Theory" and therelation between various notions of categories over the years, so Ithought the following sketch might be of interest, where I tried totrace the continuities of the concept from Aristotle, thorough Kantand Peirce, Hilbert and Ackermann, to contemporary mathematical use.Precursors Of Category Theoryhttp://mywikibiz.com/Directory:Jon_Awbrey/Notes/PrecursorsRegards,Joncc: Arisbe, CG, Inquiry-- facebook page: https://www.facebook.com/JonnyCacheinquiry list: http://stderr.org/pipermail/inquiry/mwb: http://www.mywikibiz.com/Directory:Jon_Awbreyknol: http://knol.google.com/k/-/-/3fkwvf69kridz/1oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey-You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
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You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] test; ignore
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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?" - Concept of category?
- Message from stevenzen...@me.com - Date: Mon, 25 Jul 2011 02:00:59 -0700 From: Steven Ericsson-Zenith Reply-To: Steven Ericsson-Zenith Subject: Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?" - Concept of category? To: Irving We are referring to two different things Irving: the term overloading (of "category") and, distinctly, the use of author identification in mathematics, that is - as you say - usage in a given context. I don't know what you mean by overloading";, and I never used that term. I do not view the convention in mathematics to be idiosyncratic. I never said that. The "equivalence" between definitions that you refer to here has to do with very different definitions in diverse frameworks reducing to the same necessary distinctions. It is not "term overloading." Re: equivalence" between definitions that you refer to here has to do with very different definitions in diverse frameworks reducing to the same necessary distinctions. That's essentially what I was saying, too. Re: It is not "term overloading." Again, don't know what you mean by overloading", and I never used that term. In any case, I find the convention creates a private language that is an unnecessary barrier to entry. I haven't a clue what you mean here, but it sounds dubious. Do you mean personal convention, or profesional convention of generally accepted usage agreed upon by the community of practicioners? With respect, Steven On Jul 23, 2011, at 6:03 PM, Irving wrote: Steve wrote: It seems to me to be something of a problem if the claimed distinctions cannot be concisely enumerated and it is even more of a problem if we refuse to do so by the waving of hands with the claim that such definition would "easily fill a small book." Mathematical Journal editors manifestly fail in any "attempt to ensure that the usage is not individualized by authors." To suggest this is the case seems ridiculous to me given the plethora of theories, theorems and conjectures named after the founding mathematician that constitute contemporary mathematical >literature. The practice has made mathematical text useless for any outsider and personally I wish such editors would return to insisting upon self-contained papers and reject this private language. There are, as every mathematician will readily confess, equivalent definitions within and across mathematical disciplines. Consider, for example, that in set theory, Zorn's Lemma is equivalent to Zermelo's Axiom of Choice and bothe are equivalent to Hausdorff's maximal principle in topology, which is equivalent to Tychonov's Product Theorem, also in topology, and to the Boolean Prime Ideal Theorem in algebra, to mention but a very few. For references, see Herman Rubin and Jean E. Rubin, Equivalents of the Axiom of Choice (Amsterdam: North-Holland, 1963), which was later added to and updated in their Equivalents of the Axiom of Choice II (Amsterdam: North-Holland, 1985) and contains a selection of over 250 propositions which are equivalent to AC. Granted, AC and its equivalents are an extreme example. Of course there are also slight variations in jargon between subfields, witness "homomorphism" vs. "homeomorphism", the former familiar from algebra, especially group theory, and category theory, used in the sense of a general morphism, that is, as a map between two objects in an abstract category (category theory) or between two algebraic structures or groups (abstract algebra, group theory). , the latter found in geometry and topology and referring to a continuous transformation, namely an equivalence relation and one-to-one correspondence; but these are also well-known and do not cause anyone confusion. The editors and readers of mathematics journals are generally sufficiently astute to recognize, from the context, and without confusion, which formulation and branch or sub-branch of mathematics a particular definition or theorem is being referred to. It is not that usages are being "individualized" or idiosyncratically set forth, but rather that each "version" does duty for within a given specified context. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from ste
Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?" - Concept of category?
Steve wrote: It seems to me to be something of a problem if the claimed distinctions cannot be concisely enumerated and it is even more of a problem if we refuse to do so by the waving of hands with the claim that such definition would "easily fill a small book." Mathematical Journal editors manifestly fail in any "attempt to ensure that the usage is not individualized by authors." To suggest this is the case seems ridiculous to me given the plethora of theories, theorems and conjectures named after the founding mathematician that constitute contemporary mathematical >literature. The practice has made mathematical text useless for any outsider and personally I wish such editors would return to insisting upon self-contained papers and reject this private language. There are, as every mathematician will readily confess, equivalent definitions within and across mathematical disciplines. Consider, for example, that in set theory, Zorn's Lemma is equivalent to Zermelo's Axiom of Choice and bothe are equivalent to Hausdorff's maximal principle in topology, which is equivalent to Tychonov's Product Theorem, also in topology, and to the Boolean Prime Ideal Theorem in algebra, to mention but a very few. For references, see Herman Rubin and Jean E. Rubin, Equivalents of the Axiom of Choice (Amsterdam: North-Holland, 1963), which was later added to and updated in their Equivalents of the Axiom of Choice II (Amsterdam: North-Holland, 1985) and contains a selection of over 250 propositions which are equivalent to AC. Granted, AC and its equivalents are an extreme example. Of course there are also slight variations in jargon between subfields, witness "homomorphism" vs. "homeomorphism", the former familiar from algebra, especially group theory, and category theory, used in the sense of a general morphism, that is, as a map between two objects in an abstract category (category theory) or between two algebraic structures or groups (abstract algebra, group theory). , the latter found in geometry and topology and referring to a continuous transformation, namely an equivalence relation and one-to-one correspondence; but these are also well-known and do not cause anyone confusion. The editors and readers of mathematics journals are generally sufficiently astute to recognize, from the context, and without confusion, which formulation and branch or sub-branch of mathematics a particular definition or theorem is being referred to. It is not that usages are being "individualized" or idiosyncratically set forth, but rather that each "version" does duty for within a given specified context. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
[peirce-l] Peirce, Mac Lane and Categories; was: Slow Read: "Is Peirce a Phenomenologist?"
Gary Fuhrman writes: "there is at least one mathematical site online, http://kea-monad.blogspot.com/2007/11/peirce-and-de-morgan.html, which refers to Peirce as "the originator of Category Theory", a real connection between Peircean and current mathematical Category Theory appears to be arguable" I'd want to know who the author of that blog site would be, and what expertise and credentials the author possesses. Note that the line in question asserts that Peirce was the "originator of Category Theory"; apparently the author of this statement has never heard or Aristotle, or Kant, either, and fails to explain what she means by "Category Theory", never mind stating whether she has in mind category theory as per Aristotle, Kant, et al., or Eilenberg & Mac Lane, et al., or whether or not there is a connection. Jerry LR Chandler wrote: "Mathematical categories are of recent origin (Eilenberg / MacLean, 1940?)" You of course mean Mac Lane; and the reference you presumably have in mind is Samuel Eilenberg & Saunders Mac Lane, "General Theory of Natural Equivalences", Transactions of the American Mathematical Society 58 (1945), 231-294. Jerry also noted that he "had the opportunity to discuss the meaning of category theory with Saunders MacLane himself. He was well into his 90's at the time - and firmly believed that category theory was the first basis for mathematics (not set theory)." The journal Philosophia Mathematica these days has quite a number of articles devoted to the idea of employing [mathematical] category theory, rather than set theory, as a foundation. I was instrumental in getting Mac Lane to publish his "Structure in Mathematics" in the second series of Phil. Math. 4 (1996), 174-183. I renew my offer to provide either a Word doc or pdf version of my 18-page "lecture" on [mathematical] "Category Theory and Categorical Logic" for Advanced Symbolic Logic for anyone interested in a "quick-and-dirty" account of the technical basics, which also includes some history. 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Peirce's law ((P>Q)>P)>P
It's a simple exercise, using mathematical induction, that Peirce's Law is is independent under axioms (1) and (2) with the Rule of Detachment, but not under (1) and (3): (1) A --> (B --> A) (2) A --> (B --> C) --> ((A --> B) --> (A --> C)) (3) (~A --> ~B) --> (B --> A) Not certain how "non-trivial", but this is a good illustration of how selection of one's axioms can be crucial, or perhaps "non-trivial". - Message from klkevel...@hotmail.com - Date: Thu, 21 Jul 2011 23:43:51 -0400 From: Keith Kevelson Reply-To: Keith Kevelson Subject: [peirce-l] Peirce's law ((P>Q)>P)>P To: PEIRCE-L@LISTSERV.IUPUI.EDU Dear list, I was wondering if anyone has come up with some good, non-trivial examples of Peirce's law holding when Q is false. I've come up with some examples, but they all imply the truth of Q. How can you have a false logical relationship still imply the truth of its initial proposition? Thanks,Keith - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - End message from klkevel...@hotmail.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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?"
allow for more specialization,
in my opinion. For example, while I put a high value on John Sowa's
work in critical logic and, to a lesser extent, in philosophy of
science (== science of review in Peirce), I have not seen him attempt
much work in semeiotic grammar or methodeutic. But the
phenomenologist should be capable of all three moves, in my opinion.
GF: Yes. And yet there is something ?primal? about the first move
that is deeper than its relation to the other two, or to science; and
this is what actually drew me into the study of phaneroscopy, though
i'm quite sure it is not what drew Peirce to it. I think i'll have to
step outside of the Peircean ethics of terminology in order to say
anything meaningful about this Original Face (to borrow from another
idiom), and even then, it will only be meaningful to those whose
practice has already acquainted them with it. Peirce says that
?Phenomenology can only tell the reader which way to look and to see
what he shall see? (CP 2.197), but even this is questionable: Can
anything that can be read can really tell the reader which way to
look? There is however a helpful hint here and there in Peirce's
work, especially in his late remarks about time (bearing in mind that
the phaneron is whatever is present to the mind):
[[[ As for the Present instant, it is so inscrutable that I wonder
whether no sceptic has ever attacked its reality. I can fancy one of
them dipping his pen in his blackest ink to commence the assault, and
then suddenly reflecting that his entire life is in the Present,?the
?living present,? as we say,?this instant when all hopes and fears
concerning it come to their end, this Living Death in which we are
born anew. It is plainly that Nascent State between the Determinate
and the Indeterminate ? ]] EP2:358]
Anyway i think i'll leave it there for now.
Gary F.
} Everything which is present to us is a phenomenal manifestation of
ourselves. [Peirce] {
www.gnusystems.ca/PeircePhenom.htm }{ Peirce on Phaneroscopy
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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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Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?"
I suggest that it is very crucial to keep in mind when using the term "category theory" that when used by a mathematician, it is not necessarily synonymous with anything obviously resembling the Kantian -- or even Peircean -- doctrine of categories. But in its mathematical usage, it has been suggested as an alternative foundation for mathematics in a sense that perhaps Peirce would necessarily approve. There is, however, a connection: a _functor_ is the mechanism which is the operation that carries out morphisms in category theory, and when working on creating category theory, Samuel Eilenberg and Saunders Mac Lane borrowed the term "category" from philosophy, and specifically from Aristotle, Kant, and Peirce, while giving it is mathematical meaning. For a mathematician, category theory is that part of abstract algebra that studies a class or category of objects or structures. A category consists of three things: (1) a collection of objects, (2) for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and (3) a binary operation defined on compatible pairs of morphisms called composition. The category must satisfy an identity axiom and an associative axiom which is analogous to the monoid axioms. The morphisms must obey the following laws: 1. If u is a morphism from a to b (in short, u: a * b), and v: b * c, then there is a morphism u * v (commonly read "u composed with v") from a to c. 2. Composition of morphisms where defined, is associative, so if u : a * b, v: b * c), and w : c *d, then (u * v) * w = u * (v * w). 3. For each object a, there is an identity morphism Ia, such that for any u : a * b, Ia * u = u, and u * Ib = u. Category theory can be applied to the study of logical systems in which case category theory is called categorical doctrines at the syntactic, proof-theoretic, and semantic levels. Category theory has been proposed as an alternative to set theory as a foundation for mathematics, and so raises many issues about mathematical ontology and epistemology. Category theory consists of a characteristic language and collection of methods and results that have become common-place in many mathematics-based disciplines. It is a branch of abstract algebra invented in the tradition of the Erlanger Programm of Christian Felix Klein (1849-1925) as a way of studying different kinds of mathematical structures in terms of their "admissible transformations". The general notion of a category provides an axiomatization of the notion of a "structure-preserving transformation", and thereby of a species of structure admitting such transformations. As an abstract theory of mappings, with such great generality, it is not surprising that category theory should have wide-spread applications in many types of foundational work. The applications of category theory in logic often involve the use of topology, sheaf theory, and other ideas imported from geometry, particularly in constructing models. This occurs, for example, in domain theory or topos theory. But as in algebraic topology, where category theory was first invented, extensive use is also made of algebraic techniques, for example in the treatment of logical theories as "generalized algebras". In this way, categorical logic typically treats the classical, logical notions of semantics as "geometry" and syntax as a kind of "algebra", to which general category theory can then be applied, in order to study the connections between the two. Francis William "Frank" Lawvere was the first mathematician to advocate category theory in this mathematical sense as a foundation for mathematics. For some places to look, see, e.g. F. William Lawvere, "The Category of Categories as a Foundation for Mathematics", in Samuel Eilenberg, et al. (eds.), Proceedings of the Conference on Categorical Algebra, La Jolla, 1965; held June 7-12, at the San Diego, University of California (Berlin/ Heidelberg/New York: Springer-Verlag, 1966), 121. ; Saunders Mac Lane, "Categorical Algebra and Set-Theoretic Foundations", in Dana S. Scott & Thomas Jech (eds.), Axiomatic Set Theory (Providence: American Mathematical Society, 1971), vol. 1, 231240, and Mac Lane, _Categories for the Working Mathematician_ (Berlin/New York: Springer-Verlag, 2nd ed., 1998); see also M. C. Pedicchio & W. Tholen, _Categorical Foundations_ (Cambridge/New York: Cambridge University Press, 2004). Meanwhile, for starters,if anyone is interested in the basic essentials of category theory as a branch of mathematics I can provide off-list a copy of either the Word doc or pdf text of my "lecture" on category theory for my graduate course in advanced logic. Irving H. Anellis Visiting Research Associate Peirce Edition, Institute for American Thought 9
Re: [peirce-l] FW: Slow Read: "Is Peirce a Phenomenologist?" parts 1-3 reposted
Just as a bibliographic aside to Gary Fuhrman's point, from the July 8th contribution, that As JR points out, it is highly unlikely that Peirce adopted the name of the discipline from Husserl; by his own account he took it from Hegel, partly because he saw his own three ?categories? as virtually identical with Hegel's ?three stages of thinking? (search "Hegel" in http://www.gnusystems.ca/PeircePhenom.htm ). It is even less plausible that Peirce would have changed his terminological preference from ?phenomenology? to ?phaneroscopy? in 1904 as a way of distancing himself from Husserl. I would just add that it would appear that Husserl's first use of the term "phenomenology" occurred in the _Logische Untersuchungen_ (1900-01), and that, although Peirce began work on "phenomenology, or the Doctrine of Categories" (at (C.P. 1.280)) starting in 1867, his first employ of the term was in the work from which I just quoted (at (C.P. 1.280)). This of course certainly does NOT mean, let alone prove, that Peirce borrowed the term from Husserl rather than from Hegel, and in particular from Hegel's _Pha"nomenologie des Geistes_. I just accidentally came across the book by William L. Rosensohn, _The Phenomenology of Charles S. Peirce: From the Doctrine of Categories to Phaneroscopy" (Amsterdam: B. R. Gru"ner, B.V., 1974), which is available online (apertum.110mb.com/apoteka/Rosensohn_Fenomenologia_CSP.pdf) and which has three pages (pp. 77-79), sect. A of chapter V: "Phaneroscopy: The Description of the Phaneron", on "Phaneroscopy or Pure Phenomenology: Peirce and Husserl". I expect that most of those following this discussion are already familiar with this work; is it worth downloading and going through? P.S. Can we get people to stop sending to the list rather than to the LISTSEV their requests to unsubscribe from the list? 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 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?"
I received a note off-list that part of one of the sentences in my previous message to the list had been cut off. The paragraph in question begins: "I am not sure that I would agree with the assertion that one point on which Peirce's phenomenology differs from all others ... It was the last few words of that paragraph got dropped off the final sentence, which should read: The answer to the question of the applicability of the dichotomy in considering this issue is probably wrapped up with the fact that Husserl in fact did not deal in LU with the formal logic or its laws. - Message from g...@gnusystems.ca - Date: Thu, 14 Jul 2011 09:16:57 -0400 From: Gary Fuhrman Reply-To: Gary Fuhrman Subject: Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?" To: PEIRCE-L@LISTSERV.IUPUI.EDU Thanks for this, Irving -- it clarifies some of the issues regarding "psychologism" and Husserlian phenomenology. There is one point i'd like to comment on, in order to clear up an ambiguity in my previous response to your question. You write: [[I am not sure that I would agree with the assertion that one point on which Peirce's phenomenology differs from all others is in Peirce?s requirement that it must "reckon with pure mathematics" if it is not to be as distorted as Hegel's. I say that because Husserl, both in his psychologistic phase, in his _Philosophie der Arithmetik_ (1891) and in his phenomenological phase, and certainly at least in his _Logische Untersuchungen_ (1900-1901), took it as his mission to provide a philosophical foundation for pure mathematics. ]] I think this is the mission Peirce took on in his 1896 "Logic of Mathematics" paper; or more exactly, he drew upon his categories to provide an experiential foundation for mathematics. In this sense, he was trying to base mathematics on phenomenology (6 years before he called it that). But by the time of the Harvard Lectures in 1903 (the source of the reference to Hegel that you quote), it seems to be the other way round: he is basing phenomenology on mathematics. Thus his Comtean classification of the sciences ends up placing mathematics first and phenomenology second, followed by the normative sciences of esthetics, ethics and logic. And it is this founding phenomenology on mathematics which i claimed was unique to Peirce -- not the effort to provide a phenomenological foundation for mathematics. However -- as documented on the Phaneroscopy page on my website -- what Peirce called phenomenology really consists of two practices, which he usually called "observing" and "generalizing". I call these two "stages" of the process because they are sequential, or at least i don't see how generalization about the elements of the phaneron can precede observation of it. My understanding is that the dependence of phenomenology on pure mathematics applies to the generalizing stage, but not to the observation stage, as phaneroscopic "observing" involves an effort not to be influenced by preconceptions, presuppositions or perceptual habits (as is the case with Husserl as well). Needless to say, this understanding of mine is fallible and does not represent a broad consensus; but it does aim to represent Peirce's own writings on the subject, many of which are included in www.gnusystems.ca/PeircePhenom.htm. Gary F. -Original Message- From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf Of Irving Sent: July-14-11 7:08 AM Thank you, Gary, very much, for your reply. I recall taking three graduate courses on Husserl at Duquesne University during the period 1970-72, but confess that I don't remember very much of anything about them. (I am, however, willing to bet that no efforts whatever were made to consider Husserl's philosophy of mathematics or philosophy, or to consider how his views compared with Frege's, Husserl's, or Peirce's.) So please take the rest of what I say here, again, as the ramblings of a rank amateur. I am not sure that I would agree with the assertion that one point on which Peirce's phenomenology differs from all others is in Peirce?s requirement that it must "reckon with pure mathematics" if it is not to be as distorted as Hegel's. I say that because Husserl, both in his psychologistic phase, in his _Philosophie der Arithmetik_ (1891) and in his phenomenological phase, and certainly at least in his _Logische Untersuchungen_ (1900-1901), took it as his mission to provide a philosophical foundation for pure mathematics. Before venturing into philosophy, Husserl was a mathematics student who was well-versed in contemporary mathematics, having been the student of Weierstrass and Kronecker in Berlin, becoming Weierstrass's assistant for a short time, writing his doctoral thesis at the University of Vienna on the calculu
Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?"
a language, and first and foremost a language. In summarizing Mahnke's comparison between Hilbert and Husserl, Judson Chambers Webb (b. 1936) in his intro to the English translation (1976 p. 71) tells us that Mahnke elucidated "the surprisingly close connections between Husserl's phenomenology with its reductions and Hilbert's metamathematics with its strict formalization," and thinks (in his intro to Boyer's translation of Mahnke's paper, p. 71) that: in order to motivate the possibility of a pure consistency for the axioms of euclidean geometry for someone who, like Frege, found the question pointless in view of the presumed truth of its axioms, there would have been no better terminology available to Hilbert than Husserl's: during such a proof this truth must be bracketed, we must hold the axioms in epoche'," that is, suspend belief in the existence of that which is being bracketed. It is this bracketting, the deprivation of an assumption of ontological status of objects of thought, mathematical entities in particular in this instance, which gives, we may conclude, a logical system the character of a calculus rather than a language. Husserl, even after breaking away from his early psychologism, was unconcerned in his L.U. with formal logic or its laws, with the nature or technicalities of deduction. He had already contested Schröders conception of logic, regarding algebraic logic as all, and only deductive logic. Husserl claimed that the only element of mathematical activity was merely deduction, but included calculation as well. Indeed, for Husserl, a large portion of mathematics involved computation. By deduction Husserl understood devise in a calculus for deduction. He held Schröder to conceive of mathematics as being concerned only with signs. Husserl, however, asserted that mathematics is not about signs, but about the contents of signs. Husserl, rather than being concerned with formal logic and its laws, with the nature or technicalities of deduction, instead was concerned with the structures of pure consciousness that allowed for the formation and articulation of the formal laws of thought. In "The Task and Significance of the Logical Investigations", Husserl (as quoted in Jitendra Nath Mohanty (ed.), _Readings on Husserl's Logical Investigations_ (The Hague: Martinus Nijhoff, 1977), p. 197; this is a translation by Mohanty of an unidentified portion of Husserls Phänomenologisches Psychologie, composed for lectures for the summer semester of 1925 and published in Husserl ((Walter Biemel, hsg.), Phänomenologische Psychologie. Vorlesungen Sommersemester. 1925. The Hague, Netherlands: Martinus Nijhoff, 1968) describes the project of the L.U. to be to clarify the idea of pure logic by going back to the sense-bestowing or cognitive achievements being effected in the complex of lived experience of logical thinking. In this respect, Freges review of Husserls Philosophie der Arithmetic (Zeitschrift für Philosophie und philosophische Kritik 103, 313332; English translation by Eike-Henner W. Kluge: Mind (n.s.) 81 (1972), 321-337) concerns and criticisms regarding Husserls philosophy of arithmetic remain untouched. And indeed, Robert Hanna (p. 254,"Logical Cognition: Husserl's Prolegomena and the Truth in Psychologism", Philosophy and Phenomenological Research 53, 251275) recognizes that a number of Husserl's contemporaries -- who, regrettably, he fails to name -- saw a contradiction in Husserl's claim that his phenomenology dispensed with psychologism, when at the same time seeking to found pure logic of cognitive achievements, although, relying upon the distinction between "strong" and "weak" psychologism, Hanna (pp. 254ff.) defends Husserl's position as a rejection of -- strong -- psychologism. And for Hanna (e.g. Hanna, pp. 251-253), Frege is, on the issue of psychologistic logic, the exemplary and principal adversary. - Message from g...@gnusystems.ca - Date: Mon, 11 Jul 2011 18:03:35 -0400 From: Gary Fuhrman Reply-To: Peirce Discussion Forum Subject: RE: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?" To: Peirce Discussion Forum Irving, if you're ?an amateur on the question at stake?, i'm even more so ... although i have been trying for some time ?to articulate in what specific sense the term "phenomenology" was employed by Peirce?. I often call it ?phaneroscopy? for the same reason that he did (after 1904), namely to distinguish it from other usages (just as he adopted ?pragmaticism? to distinguish it from ?pragmatism?). I'm not well enough acquainted with the other ?phenomenologies? to make authoritative comparisons, but here's a few notes (mostly drawn from www.gnusystems.ca/PeircePhenom.htm) in response to specific questions you pose: [[ (1) whether, if Peirce was a phenomenologist, he was so
