Re: Categorical Aspects of Abduction, Deduction, Induction

Peircers,

I think it's true that some of the difficulties of this discussion may be due to
different concepts of predicates, or different ways of using the word "predicate"
in different applications, communities, and contexts.

If I think back to the variety of different communities of interpretation
that I've had the fortune or misfortune of passing through over the years,
I can reckon up at least this many ways of thinking about predicates:

1.  In purely syntactic contexts, a predicate is just a symbol,
     a syntactic element that is subject to specified rules of
     combination and transformation.

As we pass to contexts where predicate symbols are meant to have meaning,
most disciplines of interpretation will be very careful, at first, about
drawing a firm distinction between a predicate symbol and the object it
is intended to denote.  For example, in computer science, people tend
to use forms like "constant name", "function name", "predicate name",
"type name", "variable name", and so on, for the names that denote
the corresponding abstract objects.

When it comes to what information a predicate name conveys,
what kind of object the predicate name denotes, or finally,
what kind of object the predicate itself is imagined to be,
we find that we still have a number of choices:

2.  Predicate = property, the intension of a concept or term.
3.  Predicate = collection, the extension of a concept or term.
4.  Predicate = function from a universe domain to a boolean domain.

It doesn't really matter all that much in ordinary applications which you prefer,
and there is some advantage to keeping all the options open, using whichever one
appears most helpful at a given moment, just so long as you have a way of moving
consistently among the alternatives and maintaining the information each conveys.

Regards,

Jon

SE = Steven Ericsson-Zenith

SE: Ben and I appear to be speaking across each other and, possibly, agreeing fiercely.

SE: Recall that in the 1906 dialectic Peirce is drawing a distinction between the wider usage
     of "Category" at the time, i.e., Aristotle's Categories considered by "you" in the dialog,
     and saying that he prefers to call these "Predicaments".  Having made this distinction he
     then speaks about the indices that are his categories.

SE: As I said earlier, the index in this case does not point to the elements of the category
     but the category itself. "There is Firstness" as opposed to "x is a first."  The confusion
     may be that Ben thinks I am saying that a category is some set of indices to its members.
     That is not the case, a category stands alone and we can point to it (index).  Icons are
     the selection mechanisms of properties of classes, not indices.

SE: Predicaments are higher order, assertions about assertions, predicates of predicates,
     I prefer to say "predicated predicates" or "assertions about assertions" which is more
     generally understood today.

SE: Being as careful as he is, I see no evidence to cause us to suppose that the categories that
     Peirce attributes to himself in 1906 are different than those he identifies as early as 1866.

-- 

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