Re: 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.)

-- 

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