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 jawb...@att.net Reply-To: Jon Awbrey jawb...@att.net Subject: Re: What Peirce Preserves To: Jack Rooney johnphilipda...@hotmail.com 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 Associate Peirce Edition, Institute for American Thought 902 W. New York St. Indiana University-Purdue
Re: [peirce-l] Not Preserving Peirce
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 professor willing and able to join him in working through _Principia Mathematica_. The first textbooks began appearing in the 1923s, led off by Carnap's Abriss; in English, Clarence Irving Lewis and Cooper Harold Langford co-authored the first modern symbolic logic textbook in English, their _Symbolic Logic_ (1932; 2nd ed., 1959). This was followed by Susanne K. Langer's textbook, _An Introduction to Symbolic Logic (1937; 2nd ed., 1953
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 johnphilipda...@hotmail.com Reply-To: Jack Rooney johnphilipda...@hotmail.com Subject: RE: [peirce-l] Not Preserving Peirce To: Irving H. Anellis ianel...@iupui.edu, 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
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 jimwillgo...@msn.com Reply-To: Jim Willgoose jimwillgo...@msn.com 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 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
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 jawb...@att.net Reply-To: Jon Awbrey jawb...@att.net Subject: Re: Not Preserving Peirce To: Jack Rooney johnphilipda...@hotmail.com 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
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 eugene.w.halto...@nd.edu Reply-To: Eugene Halton eugene.w.halto...@nd.edu Subject: RE: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition To: PEIRCE-L@LISTSERV.IUPUI.EDU 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 grinding out of [usually numerical] solutions to particular problems, the other generally thought of as those parts of mathematics taught in catch-all undergrad courses that frequently go by the name of Finite Mathematics
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
...@nyc.rr.com Reply-To: Benjamin Udell bud...@nyc.rr.com 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, 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 bud...@nyc.rr.com - Irving H. Anellis Visiting Research Associate Peirce Edition, Institute for American Thought 902 W. New York St. Indiana University-Purdue University at Indianapolis Indianapolis, IN 46202-5159 USA URL: http
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 bud...@nyc.rr.com Reply-To: Benjamin Udell bud...@nyc.rr.com 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 unfamiliar with Peirce's way of distinguishing theormatic from corollarial, see further below where I've copied my Wikipedia summary with reference links
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
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 richmon...@lagcc.cuny.edu Reply-To: Gary Richmond richmon...@lagcc.cuny.edu 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 some core issues in illuminating ways for at least this general reader. I'm going to pass over a great deal which I found of considerable interest, including the Jerry Chandler matter (I would also like to hear about the nature of chemical logic and its rigor). I have only a few quick questions for now, the first a simple terminological one the answer to which is probably so obvious to you that you might wonder why anyone would ask it. You remarked concerning an older, artificial, and somewhat inaccurate terminological distinction between practical or applied on the one hand
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 jawb...@att.net Reply-To: Jon Awbrey jawb...@att.net Subject: Re: Philosophia Mathematica articles of interest To: Irving ianel...@iupui.edu 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=1index=17992mailbox=INBOXactionID=view_attachid=1mimecache=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 ste...@iase.us Reply-To: Steven Ericsson-Zenith ste...@iase.us 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=1index=17992mailbox=INBOXactionID=view_attachid=1mimecache=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
[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] 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] ?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 jerry_lr_chand...@me.com Reply-To: Jerry LR Chandler jerry_lr_chand...@me.com 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 are included, insofar as they putatively do no more than attempt to algebraicize Aristotle's syllogistic logic) from
[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
[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/cspbr.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]
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, 1999), 145187; On the Origins of Hilbert's 6th Problem: Physics and the Empiricist Approach to Axiomatization, in Marta Sanz-Solé et al (eds.), Proceedings
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 ianel...@iupui.edu Reply-To: Irving ianel...@iupui.edu To: PEIRCE-L@LISTSERV.IUPUI.EDU 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 (1898-1918) (Dordrecht: Kluwer Academic Publishers, 2004); some of his other work includes: David
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 jerry_lr_chand...@me.com Reply-To: Jerry LR Chandler jerry_lr_chand...@me.com 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 very much for your comments on the distinction between Hilbert's formalism and CSPs philosophy of logic. This crisp distinction had eluded me for over a decade! You cannot possibly know
[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
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] 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 ste...@semeiosis.org Reply-To: Steven Ericsson-Zenith ste...@semeiosis.org Subject: Re: [peirce-l] On the Paradigm of Experience Appropriate for Semiotic To: Irving ianel...@iupui.edu Dear Irving, Thank you for the correction regarding the source of Hilbert's remarks. I believe I read it in Unger's translation of The Foundations of Geometry, perhaps in the foreword or annotations, but I still have to check this. I assume that Hilbert is making a remark that appeals to Berkeley's similar comments in stating the case of idealism. Suggesting he was familiar with Berkeley. It isn't clear to me how you can/must infer that there is or is not experiential inference in the distinction between must and can. Must and will appear to me to speak to the over confidence of 1900. But, again, I appreciate both the point and the correction. With respect, Steven On Nov 8, 2011, at 7:43 AM, Irving wrote: In response to posts and queries from Steven, Jon, and Jerry, (1) Regarding Steven's initial post: My initial discomfort stemmed from associating Hilbert's remark with the Peircean idea of logic as an experiential or positive science, since Hilbert as a strict formalist did not regard mathematics (or logic) as in any sense an empirical endeavor. I suggest that the quote from Kant with which Hilbert began his _Grundlagen der Geometrie_ had the dual purpose of paying homage to his fellow Königsberger and, more significantly, to suggest that, although geometry begins with spatial intuition, it is, as a discipline, twice removed from intuition by a series of abstractions. Whether he held space to be a priori or a posteriori, I cannot say for certain, but my strong inclination is to hold that he conceived geometry to be a symbolic science, with points as the most basic of the primitives, in the same sense that he held the natural numbers to be, not mental constructs, but symbols. (Incidentally, the precise formulation of the quote from Hilbert is: Wir müssen wissen. Wir werden wissen. Which should be translated as: We must know. We will know. There is no can in this quote; so no experiential inference would seem to be indicated.) (2) Hilbert did not himself include the comment on tables, chairs, and beer mugs in G.d.G. It was reported by Blumenthal in his 1935 obituary of Hilbert, recorded as a part of a conversation. If it does appear in G.d.G., it does so in an edition that includes a reprint of Otto Blumenthal's obit of Hilbert. (3) Regarding the points made by Jon Awbrey and Jerry Chandler: In attempting to sort out the various notions of formal, whether it applies to Peirce and to Hilbert, to logical positivism, 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 a few of the works published in From Frege to Gödel and his subsequent handful of articles, offers barely hints at the connections that Gerladine Brady exhaustively unraveled in _From Peirce
[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/csphilbert.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
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
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
Re: [peirce-l] Peirce's law ((PQ)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 klkevel...@hotmail.com Reply-To: Keith Kevelson klkevel...@hotmail.com Subject: [peirce-l] Peirce's law ((PQ)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?
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
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USA
URL: http://www.irvinganellis.info
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