Re: Categorical Aspects of Abduction, Deduction, Induction

Ben & All,

At any rate, there is no particular hurry to come to a decision.
As I get time, I'll go back and review the passage in the context
of that paper and others.  For now, let me make a first pass over
your comments and say what I can say off the cuff, subject to the
usual risk of backtracking later.

BU = Ben Udell
JA = Jon Awbrey

BU: The passage by Peirce that you quoted below has nagged at me for some time.
     On your mywikibiz page to which you linked, as regards that passage, you
     said "The first thing to extract from this passage is the fact that
     Peirce's Categories, or 'Predicaments', are predicates of predicates".

Let us call that H_1.  "Categories = Predicates of Predicates".

I was tempted into that interpretation, despite the possibility
of becoming the foil of a subsequent aporia, by the simple fact
that it appears to help me make sense, not only of what Peirce
might mean by a category, but of all the other claims that he
makes for their properties.

As a general rule, I interpret Peirce's categories as categories of relations.
I suppose I am led to do this by the fact that Peirce makes very strong claims
about his categories -- the claim that three are necessary and sufficient, etc. --
and I see nothing else that could anchor these claims except the extremely hard
facts of mathematics that he emphasizes throughout his work under the heading of
triadic irreducibility.

If Peirce intends to explain his categories by means of words like
Actuality, Possibility, Destiny -- words whose meanings are hardly
fixed across traditions of interpretation but range from the fluid
to the flighty and fanciful -- then I can but take him at his word,
at any given moment, whether he means the same thing by them as he
means by First, Last, Middle, in that order or some other, or then
again Quality, Reaction, Representation, or any of the other terms.

But if he means to turn it about, and explain those arrays of highly variable
and traditionally volatile terms by means of mathematical relations, where we
have some hope of probating, proving or disproving, the properties attributed
to these categories, then that is reason to think we are moving in a positive
direction, clarifying obscure words in the light of more determinate concepts.

BU: In the editors' footnote to CP 4.549, the editors say that what there
     Peirce calls the Modes of Being are "Usually called categories by Peirce.
     See vol. 1, bk. III".  Maybe they're wrong, but what here he calls the
     "Modes of Being" -- "Actuality, Possibility, and Destiny (or Freedom from
     Destiny)" do at least comprise one of his formulations of his categories,
     even if not the definitive formulation.

BU: Peirce says "[...] what you have called Categories, but for which I prefer
     the designation Predicaments, and which you have explained as predicates of
     predicates ..." Peirce everywhere else prefers the name Categories for his
     own categories and who is the "you" who would have been speaking of Peirce's
     own categories?

In Peirce's dialogue, formally speaking, "you" addresses the Reader.
I initially read "you" as referring to Peirce's alter ego in a dialogue
with himself, but it occurs to me that another possibility might be Hegel.

BU: Peirce says,

CSP: [...] the divisions so obtained must not be confounded with the different
      Modes of Being:  Actuality, Possibility, Destiny (or Freedom from Destiny).
      On the contrary, the succession of Predicates of Predicates is different in
      the different Modes of Being.

Given what I said above, I am content to leave it open at present whether Categories,
Modalities, Modes of Being, Predicaments, Predicates of Predicates, and all the rest
are exemplifying the same formal structure or not.  What is less variable for me is
the fact that no other reason is given anywhere in Peirce's work for claiming the
necessity and sufficiency of three categories except the mathematical facts about
the valences of relations.

Regards,

Jon

BU: Where else does he say that the successions of his categories are
     "different in the different Modes of Being"?  Where in his other
     writings does he call his own categories "predicates of predicates"?
     It's hard not to think that by "Predicates of Predicates" he does not
     mean his own categories, and instead that, at most, 1st-intentional,
     2nd-intentional, and 3rd-intentional entities, on which he says that
     his "thoughts are not yet harvested," will end up being treated by him
     as Firsts, Seconds, Thirds -- instances or applications of his categories.

JA: We have of course discussed the bearing of Peirce's categories on his
     other triads several times before, even to the point of going through
     his early writings in excruciating detail.  I do not think I have the
     strength to do that again, but it may be possible to recover the gist
     of those examinations from various archives here and there on the web.

JA: One of the nagging things about that passage is of course that Peirce
     is presenting his analysis in the form of a dialogue, which leaves us
     the task of deciding how much of his own thought he is placing in the
     speeches of his interlocutor and how often his dialogue partner plays
     but the part of a foil for his own conclusions.

JA: I have come to learn that there are many different ways of resolving
     questions like these.  I suppose I am leaning more these days toward
     a particular idea -- that if there is an objective reality addressed
     by each observer's mind on a matter, then we ought above all to keep
     our eyes on that prize if we want to settle the question in due time.

JA: If there is an objective reality addressed by the statements that Peirce makes
     about categories, then we have reason to pursue them in a manner more hopeful
     of consensual resolution then, let us say, the purely scholastic matter of
     whether all his statements reflect one and the same authorial perspective.

JA: By way of stating my own perspective at the outset, I value Peirce's work
     primarily for its mathematical character and content, and this means that
     I take his writings to be addressing realities, even if they be realities
     that others may regard as abstract or even fictitious.  That interpretive
     stance determines everything that follows in the way I read Peirce's work.

-- 

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