Peirce's 1870 “Logic Of Relatives ” • Comment 11.3

Post   : Peirce's 1870 =93Logic Of Relatives=94 =95 Comment 11.3
http://inquiryintoinquiry.com/2014/04/30/peirces-1870-logic-of-relatives-%e=
2%80%a2-comment-11-3/
Posted : April 30, 2014 at 3:00 pm
Author : Jon Awbrey

Peircers,

Before I can discuss Peirce's =93number of=94 function in greater detail I =
will need to deal with an =

expositional difficulty that I have been very carefully dancing around all =
this time, but one that =

will no longer abide its assigned place under the rug.

Functions have long been understood, from well before Peirce's time to ours=
, as special cases of =

dyadic relations, so the =93number of=94 function itself is already to be n=
umbered among the types of =

dyadic relatives that we=92ve been explicitly mentioning and implicitly usi=
ng all this time.  But =

Peirce's way of talking about a dyadic relative term is to list the =93rela=
te=94 first and the =

=93correlate=94 second, a convention that goes over into functional terms a=
s making the functional value =

first and the functional argument second, whereas almost anyone brought up =
in our present time frame =

has difficulty thinking of a function any other way than as a set of ordere=
d pairs where the order =

in each pair lists the functional argument first and the functional value s=
econd.

All of these syntactic wrinkles can be ironed out in a very smooth way, giv=
en a sufficiently general =

context of flexible enough interpretive conventions, but not without introd=
ucing an order of =

anachronism into Peirce's presentation that I am presently trying to avoid =
as much as possible. =

Thus, I will need to experiment with various styles of compromise formation.

The interpretation of Peirce's 1870 =93Logic of Relatives=94 can be facilit=
ated by introducing a few =

items of background material on relations in general, as regarded from a co=
mbinatorial point of view.

Regards,

Jon

-- =


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