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 [email protected] --------- Date: Mon, 07 May 2012 09:25:22 -0400 From: Jon Awbrey <[email protected]> Reply-To: Jon Awbrey <[email protected]> Subject: Re: What Peirce Preserves To: Jack Rooney <[email protected]>
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 [email protected] ----- 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 [email protected] with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to [email protected]
