Sunday, August 03, 2008

Logic I, Lesson 6: The Ten Categories (in general)


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Introduction: The ten "categories" or "predicaments" (praedicamenta)--to be distinguished from the predicables (praedicabilia)--are the ten ultimate genera (genera generalissima) into which terms may be classified. They are "ultimate" because they are not themselves part of a more universal genus "being." Hence every term that signifies a real being* is reducible to one of these ten; e.g., "horse" is reducible to substance, "swimming" to action, "science" to quality, etc.


*NB. As we will see in the science of metaphysics, two exceptions must be made: God and the transcendentals ("being," "good," "truth," "oneness"--terms which refer to beings existing throughout all the categories and hence "transcend" the categories) cannot be classified as belonging to any one of the categories. It must also be noted that privations (a lack of something that should be there, e.g., deafness) and negations (a pure absence of something, e.g., nothingness) cannot be categorized.


From Aristotle's Categories, 4:

Expressions which are in no way composite signify (1) substance, (2) quantity, (3) quality, (4) relation, (5) place, (6) time, (7) position, (8) state [or 'habit'], (9) action, or (10) affection [or 'passion'].

To sketch my meaning roughly, examples of (1) substance are 'man' or 'the horse', of (2) quantity, such terms as 'two cubits long' or 'three cubits long'; of (3) quality, such attributes as 'white', 'grammatical'. 'Double', 'half', 'greater', fall under the category of (4) relation; 'in a the market place', 'in the Lyceum', under that of (5) place; 'yesterday', 'last year', under that of (6) time. 'Lying', 'sitting', are terms indicating (7) position; 'shod', 'armed', (8) state; 'to lance', 'to cauterize', (9) action; 'to be lanced', 'to be cauterized', (10) affection [i.e., 'passion'].

No one of these terms, in and by itself, involves an affirmation; it is by the combination of such terms that positive or negative statements arise. For every assertion must, as is admitted, be either true or false, whereas expressions which are not in any way composite such as 'man', 'white', 'runs', 'wins', cannot be either true or false.


From Simmons' The Scientific Art of Logic, p. 90:

To illustrate: [...] of the ten ultimate types of being [i.e., the categories] mathematics fits into the category of quality. Then it is significant to note that of the four species of quality mathematics falls under the first as a habit. Habits are either entitative or operational, and mathematics is of the second type. Operational habits are either good or bad. Good habits are virtues, and mathematics is a virtue. Virtues in turn are either moral or intellectual, depending on whether they perfect the will or the intellect. Mathematics is an intellectual virtue, and that special kind of intellectual virtue which we call science. Science itself is either practical or speculative, depending on whether its end is action or truth. Mathematics aims at truth, and so is a speculative science. Speculative science, finally, is either ordered to a knowledge of physical being, quantified being, or being as such. Mathematics is the second type, namely speculative science of quantified being.
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