ARISTOTLE’S LOGIC
Consider the argument:
All animals of the dog family are carnivores.
Foxes are animals belonging to the dog family.
Therefore foxes are carnivores.
Is it valid? Well, according to the root definition of validity, it is valid if the denial of the conclusion is incompatible with the truth of the premises.
Clearly, you can’t deny that foxes are carnivores while holding to the truth of both premises, so it is definitely valid. Yet when we try to analyze its validity using statement logic, we get nowhere. The premises and conclusion have no component statements (they do not even have any parts that are themselves statements). So they are simple statements (see the definitions in chapter 3). Nevertheless, the validity of the argument seems to depend on certain elements of these statements that get repeated in an identifiable pattern. If we replace “animals of the dog family” by D, “foxes” by F, and “carnivores” by C, we get an abstract argument of a clearly identifiable form:All D are C.
All F are D.
Therefore all F are C.
Here the capital letters are not standing for statements but categories of things: if C instead stood for the category of things that are “descended from Cynodictis ” we would have another valid argument, indeed another sound argument, since all the premises would again be true. If we use the Greek letters A, B, Γ to stand for any arbitrary categories of things, we may identify the following as a valid form:
All A are B.
All B are Γ.
Therefore all A are Γ.
This is exactly how Aristotle proceeded in setting up his logical system. He followed the practice of the other Ancient Greek logicians of analyzing complex arguments into a series of basic arguments or syllogisms (the Greek for argument), each of which consists of two premises and a conclusion. But he seems to have had a low opinion of the logic of statements begun by the Megarians (and completed after his death by the Stoics, especially Chrysippus).
For him the real logical work in reasoning was done using arguments like the one above that involved connections among categories of things. So he proceeded to establish, apparently single-handed, a complete system for determining the validity or invalidity of arguments of this kind. Thus, in Aristotelian logic each of the premises and the conclusion is a categorical statement, i.e., one that asserts a connection between two categories or terms, the subject term and the predicate term; and each term appears in the argument twice. Such a syllogism is a categorical syllogism. Here’s an example of a categorical syllogism with an invalid form:Beans are vegetables.
Some vegetables are not legumes.
Therefore some beans are not legumes.
Here the categories are “beans,” “vegetables,” and “legumes.” Denying the conclusion is the same as claiming that all beans are legumes. But this is true! Clearly it is also compatible with both premises (which are also true).
That Aristotle regarded categorical logic as the “real logic” was probably fostered by the prevalence of this kind of reasoning in field biology, his greatest passion. It is said that when his former pupil Alexander (soon to be “the Great”) set off on his campaign of conquest, he was under instructions from his teacher to bring back specimens of exotic flora and fauna from distant lands. Now Aristotle was a keen biologist not just in the sense of an enthusiastic amateur, but, as the first to subject the Chiefbiological categories to systematic study, the founder of the discipline of biology. Even his physics is cast in terms that seem more suitable to biology, with each elemental type of body having a natural place in the universe towards which it tends, like so many plants seeking the sunlight. At any rate, as soon as Aristotle’s physics and logic were introduced to the West at the end of the so-called Dark Ages, they took root. In fact his thought dominated these subjects in the universities from their inception in Padua, Bologna, Paris, and Oxford in the thirteenth and fourteenth centuries till the Scientific Revolution in the case of physics, and till the twentieth century in the case of logic. (Actually, in the Middle Ages Logic, along with Rhetoric and Grammar, was part of the Trivium, the three-fold curriculum that you undertook prior to university studies: hence our word trivial—I thought you’d appreciate this bit of trivia!)
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