Re: Categorical Aspects of Abduction, Deduction, Induction

Peircers,

There is a continuity of purpose that unites all the various category systems,
from Aristotle through the present day.  Clearly, the categories of Aristotle,
Kant, Peirce, and contemporary mathematics are the same in neither number nor
content, but the logical function and semiotic utility they serve is the same.

The problem for which categories are proposed as a solution by Aristotle is
that signs are equivocal, perhaps inherently and even necessarily, at least,
for creatures like us, and so we have need of additional signs for reducing
their ambiguities to the point where logic can begin to apply, as it cannot
apply to words that are used in incompatible categories of meaning or sense.

Here is that inaugural passage from Aristotle again —

| Things are equivocally named, when they have the name only in common,
| the definition (or statement of essence) corresponding with the name
| being different. For instance, while a man and a portrait can properly
| both be called animals (ζωον), these are equivocally named. For they
| have the name only in common, the definitions (or statements of essence)
| corresponding with the name being different. For if you are asked to
| define what the being an animal means in the case of the man and the
| portrait, you give in either case a definition appropriate to that
| case alone.
|
| Things are univocally named, when not only they bear the same name but the
| name means the same in each case — has the same definition corresponding.
| Thus a man and an ox are called animals. The name is the same in both cases;
| so also the statement of essence. For if you are asked what is meant by their
| both of them being called animals, you give that particular name in both cases
| the same definition.
|
| Aristotle, Categories, 1.1a1–12.
|
| Translator's Note. “Ζωον in Greek had two meanings, that is to say, living creature, and,
| secondly, a figure or image in painting, embroidery, sculpture.  We have no ambiguous noun.
| However, we use the word ‘living’ of portraits to mean ‘true to life’.”  (H.P. Cooke).
|
| http://mywikibiz.com/Directory:Jon_Awbrey/Notes/Precursors#Aristotle

As I commented —

In the logic of Aristotle categories are adjuncts to reasoning that are designed to resolve ambiguities
and thus to prepare equivocal signs, that are otherwise recalcitrant to being ruled by logic, for the
application of logical laws.  The example of ζωον illustrates the fact that we don't need categories
to make generalizations so much as we need them to control generalizations, to reign in abstractions
and analogies that are stretched too far.

Regards,

Jon

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