Re: [peirce-l] What Peirce Preserves
Re: Studies in Logic and Its Vicissitudes At: http://thread.gmane.org/gmane.science.philosophy.peirce/8116 Irving All, Between 1865 and 1870, C.S. Peirce had already begun to set out the rudiments of an information-theoretic semantics for inquiry, communication, and thought in general, along with a logic of relatives that is powerful enough to handle polyadic relations, in particular, the triadic relations that one requires in the theory of signs and throughout mathematics. This is the palette of ideas that Peirce found himself forced to develop to paint a picture of inquiry that could even hope to be “true to life”. Many of these ideas we would not see again until the late 20th century. When it comes to the reception of this picture, this style, by judges from another school, I think we have to sort the aesthetic or affective impacts from the cognitive or intellectual factors. Personally, I don't suppose I will ever have the investigative resources or skills to find out what really happened in the case of Peirce, but common sense tells me that handing out his relics like favors at a scalping party must betoken some form of active, if unconscious hostility. And if I were to speculate on the springs and catches of that hostility, I would guess that there is probably a link between fearing the message and counting coup on the messenger. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache - 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] What Peirce Preserves
Re: Peirce Preservation (Studies in Logic and Its Vicissitudes) At: http://thread.gmane.org/gmane.science.philosophy.peirce/8116 Irving All, The question of how logic, mathematics, phenomenology, and philosophy in general relate to one another has come up again several times in recent discussions, so let me refer once again to a statement from Peirce that I always find enlightening on that score, at least, with respect to how Peirce himself viewed their dependencies and their relative standings as foundations. | Normative science rests largely on phenomenology and on mathematics; | Metaphysics on phenomenology and on normative science. | | C.S. Peirce, CP 1.186 (1903) Here is a digram of these relations, with the more basic inquiries at the bottom and those that rest on them higher up in the ordering. | | | o Metaphysics | /| |/ | | / | |Normative Science o | | / \ | |/ \ | | / \| | Mathematics o o Phenomenology | Cf. http://stderr.org/pipermail/inquiry/2004-March/001262.html 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/ - 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] What Peirce Preserves
Re: Peirce Papers Preservation At: http://thread.gmane.org/gmane.science.philosophy.peirce/8116 Irving, Turning to your list of points ... IA: My points were -- to put them as simplistically and succinctly as possible -- that: IA: (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: IA: (i) philosophers either mathophobic or innumerate were unprepared or unable to tackle the algebraic logic; while: IA: (ii) the mathematician who were capable of handling it did not ignore _Studies in Logic_ 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 in Logic_ by Venn, Schröder, and even Bertrand Russell's recommendation to Couturat that he read _Studies in Logic_); IA: (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 the logical analysis of language in eliminating metaphysics). IA: (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.) I need to say something about the use of the terms algebraic and functional, as they tend to have a diversity of meanings, and some of their connotations have shifted over the years, even in the time that I have observed them being applied to styles of logical notation. We used to use terms like algebraic logic and algebra of logic almost as pejoratives for the older tradition in symbolic logic, going back even as far Leibniz, but that was due to using the term algebra in a very narrow sense, connoting a restriction to finitary operations, those that could be built up from a finite basis of binary operations. More often lately, algebraic tends to be used for applications of category theory, but category theory is abstracted from the concrete materials of functions mapping one set to another, making category theory the apotheosis of functions as a basis for mathematical practice. Moreover, Peirce's use of ∏ and ∑ for quantifiers is actually more functional in spirit than the later use of symbols like ∀ and ∃. These are just some of the reasons that I find myself needing another criterion for distinguishing Peirce's paradigm of logical notation from later devolutions. 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/ - 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] What Peirce Preserves
Re: Peirce Preservation (Studies in Logic and Its Vicissitudes) At: http://thread.gmane.org/gmane.science.philosophy.peirce/8116 IA = Irving Anellis (also, Intelligence Augmentation) IA: 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. IA: I would thoroughly concur. IA: 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). Oh, I didn't mean to suggest that logicians and mathematicians are mutually exclusive categories. I don't see any necessary contradiction between being a logician and being a mathematician, but logicists distinguish themselves as striving to reduce mathematics to logic — and even that need not be extreme in its aims, depending on what an individual inquirer means by logic — but when someone sets out to reduce logic itself to a style of purely syntactic analysis, then I find myself needing to draw a line. Thanks a million for the summary below, as it will help me catch up after many distractions of travel and daily events. Regards, Jon IA: My points were -- to put them as simplistically and succinctly as possible -- that: IA: (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 IA: (i) philosophers either mathophobic or innumerate were unprepared or unable to tackle the algebraic logic; while IA: (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..._); IA: (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). IA: (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.) -- 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
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
