Re: 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 LISTSERV <at> 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 <at> LISTSERV.IUPUI.EDU