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