Re: Categorical Aspects of Abduction, Deduction, Induction

Peircers,

This passage from Peirce has intrigued me, too, for at least a dozen years,
just going by the first discussions that I can remember having about it,
and still find scattered about on the web.  I am less concerned about
the terms of art from Aristotle -- predicables, predicaments, etc. --
than I am about the nature and function of categories in general,
with especial reference to the status of Peirce's 3 categories.

The larger interest of this question for me is this -- that I see a certain continuity
of purpose and "uberty" that extends from Aristotle's categories, up through Peirce's,
and through one potential, as yet unrealized, but perhaps inevitable future development
of category theory as it is understood and used in most mathematical work today, either
as a practical tool, as most will admit it, or as a foundation more natural and more sure
than set theory, as others are inclined to recommend it.

But it's Saturday, and I'm due for a bit of R&R ...

Regards,

Jon

P.S. I copied out the remainder of that section on Objective Logic to these places:

• http://stderr.org/pipermail/inquiry/2012-March/thread.html#3796
• http://stderr.org/pipermail/arisbe/2012-March/thread.html#3660

GF = Gary Fuhrman
GR = Gary Richmond

GF: I'm a little confused as to what the question is here. It seems clear to
     me that in the Prolegomena of 1906, which is the source of the passage in
     question, Peirce does NOT use the term "Categories" in reference to what he
     elsewhere calls categories, or "elements" of the phaneron, or even sometimes
     "universes" -- i.e. the triad of Firstness/Secondness/Thirdness.

GF: The "Prolegomena" is all about diagrams, specifically Existential Graphs, and
     the purpose of these diagrams is to facilitate the analysis of propositions.
     The first use of the term in the Prolegomena, namely CP 4.544-5:

CSP: [[[ As for Indices, their utility especially shines where other Signs fail....
      But of superior importance in Logic is the use of Indices to denote Categories
      and Universes, which are classes that, being enormously large, very promiscuous,
      and known but in small part, cannot be satisfactorily defined, and therefore can
      only be denoted by Indices. Such, to give but a single instance, is the collection
      of all things in the Physical Universe. ...

CSP: Oh, I overhear what you are saying, O Reader: that a Universe and a Category are
      not at all the same thing; a Universe being a receptacle or class of Subjects,
      and a Category being a mode of Predication, or class of Predicates.  I never
      said they were the same thing; but whether you describe the two correctly
      is a question for careful study. ]]]

GF: Peirce then proceeds to take up the question of Universes, returning to Categories
     much later, in the passage Jon quoted; and he begins by saying that he prefers the
     term "Predicaments" for classes of predicates, no doubt because this avoids confusing
     them "with the different Modes of Being" which are elsewhere called "categories.  And
     indeed he never mentions "Categories" again in this very long article; nor does he make
     any explicit reference in the whole article to Firstness, Secondness or Thirdness. I can
     only conclude that the passage you quoted from it, Jon, tells us nothing about *those*
     "categories", which i guess are the ones you referred to as "Peirce's categories."  The
     connection between them and the triad of first, second, and third *intentions* is very
     tenuous, as i think Peirce indicates by saying that his thoughts about the latter triad
     are "not yet harvested" -- something he could hardly say in 1906 about his phaneroscopic
     "categories".

GR: Gary, I think you got this just right.

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