* Comments on the Peirce List slow reading of Joseph Ransdell,
"On the Paradigm of Experience Appropriate for Semiotic",
http://www.cspeirce.com/menu/library/aboutcsp/ransdell/paradigm.htm
Re: Comments by Claudio Guerri (cont.)
I realize that many of us have been through these sorts of discussions
many times before, so let me just highlight what I consider to be some
of the most important points.
1. We must not confuse the roles in a sign relation or the components
of a sign relational 3-tuple, that is, Object, Sign, Interpretant,
with the Peircean categories of Firstness, Secondness, Thirdness.
These two sets of concepts reside at very different logical levels,
as one can tell from the fact that Peirce described his Categories
as "Predicaments", that is, predicates of predicates.
To make the shortest possible shrift of the matter, Category k is the
category of k-adic predicates or k-adic relations. Viewing categories
as Aristotle initially described them, as disambiguating references or
devices for resolving the equivocation of terms by indicating the type
of object intended for their interpretation, Peirce's claim that three
categories are necessary and sufficient for the purposes of logic says
that a properly designed system of logic can resolve all equivocation
in just three levels or steps.
For a more detailed discussion, here is an excerpt from the section I wrote
on Peircean categories for the Wikipedia article on Peirce several years ago.
This material can now be found at the MyWikiBiz article on Peirce.
Cf. http://mywikibiz.com/Charles_Sanders_Peirce#Theory_of_categories
In the logic of Aristotle categories are adjuncts to reasoning that are designed
to resolve equivocations and thus to prepare ambiguous signs, that are otherwise
recalcitrant to being ruled by logic, for the application of logical laws. An
equivocation is a variation in meaning, or a manifold of sign senses, and so
Peirce's claim that three categories are sufficient amounts to an assertion
that all manifolds of meaning can be unified in just three steps.
The following passage is critical to the understanding of Peirce's Categories:
CSP: I will now say a few words about what you have called Categories,
but for which I prefer the designation Predicaments, and which you
have explained as predicates of predicates.
CSP: That wonderful operation of hypostatic abstraction by which we seem to
create
entia rationis that are, nevertheless, sometimes real, furnishes us the
means
of turning predicates from being signs that we think or think through, into
being subjects thought of. We thus think of the thought-sign itself, making
it the object of another thought-sign.
CSP: Thereupon, we can repeat the operation of hypostatic abstraction, and from
these
second intentions derive third intentions. Does this series proceed
endlessly?
I think not. What then are the characters of its different members?
CSP: My thoughts on this subject are not yet harvested. I will only say that
the subject
concerns Logic, but that the divisions so obtained must not be confounded
with the
different Modes of Being: Actuality, Possibility, Destiny (or Freedom from
Destiny).
CSP: On the contrary, the succession of Predicates of Predicates is different in
the different Modes of Being. Meantime, it will be proper that in our
system
of diagrammatization we should provide for the division, whenever needed,
of
each of our three Universes of modes of reality into Realms for the
different
Predicaments.
CSP: Peirce, CP 4.549, "Prolegomena to an Apology for Pragmaticism",
The Monist 16, 492–546 (1906), CP 4.530–572).
The first thing to extract from this passage is the fact that Peirce's
Categories,
or "Predicaments", are predicates of predicates. Meaningful predicates have both
extension and intension, so predicates of predicates get their meanings from at
least two sources of information, namely, the classes of relations and the
qualities of qualities to which they refer. Considerations like these tend
to generate hierarchies of subject matters, extending through what is
traditionally called the logic of second intensions, or what is handled
very roughly by second order logic in contemporary parlance, and continuing
onward through higher intensions, or higher order logic and type theory.
Peirce arrived at his own system of three categories after a thoroughgoing study
of his predecessors, with special reference to the categories of Aristotle,
Kant,
and Hegel. The names that he used for his own categories varied with context and
occasion, but ranged from moderately intuitive terms like quality, reaction, and
symbolization to maximally abstract terms like firstness, secondness, and
thirdness,
respectively. Taken in full generality, k-ness may be understood as referring to
those properties that all k-adic relations have in common. Peirce's distinctive
claim is
