Tuesday, April 4, 2017

Aristotle : Propositions and categories

Aristotle’s writings show that even he realized that there is more to logic than syllogistic. The De interpretatione, like the Prior Analytics, deals mainly with general propositions beginning with Every, No, or Some. But its main concern is not to link these propositions to each other in syllogisms but to explore the relations of compatibility and incompatibility between them. Every swan is white and No swan is white clearly cannot both be true; Aristotle calls such pairs of propositions “contraries.” They can, however, both be false, if—as is the case—some swans are white and some are not. Every swan is white and Some swan is not white, like the former pair, cannot both be true, but—on the assumption that there are such things as swans—they cannot both be false either. If one of them is true, the other is false; and if one of them is false, the other is true. Aristotle calls such pairs of propositions “contradictories.”

The propositions that enter into syllogisms are all general propositions, whether universal or particular; that is to say, none of them is a proposition about an individual, containing a proper name, such as the proposition Socrates is wise. To find a systematic treatment of singular propositions, one must turn to the Categories. This treatise begins by dividing the “things that are said” (the expressions of speech) into those that are simple and those that are complex. Examples of complex sayings are A man runs, A woman speaks, and An ox drinks; simple sayings are the particular words that enter into such complexes: man, runs, woman, speaks, and so on. Only complex sayings can be statements, true or false; simple sayings are neither true nor false. The Categories identifies 10 different ways in which simple expressions may signify; these are the categories that give the treatise its name. To introduce the categories, Aristotle employs a heterogeneous set of expressions, including nouns (e.g., substance), verbs (e.g., wearing), and interrogatives (e.g., where? or how big?). By the Middle Ages it had become customary to refer to each category by a more or less abstract noun: substance, quantity, quality, relation, place, time, posture, vesture, activity, and passivity.

The categories are intended as a classification of both the kinds of expression that may function as a predicate in a proposition and of the kinds of extralinguistic entity such expressions may signify. One might say of Socrates, for example, that he was human (substance), that he was five feet tall (quantity), that he was wise (quality), that he was older than Plato (relation), and that he lived in Athens (place) in the 5th century bce (time). On a particular occasion, his friends might have said of him that he was sitting (posture), wearing a cloak (vesture), cutting a piece of cloth (activity), or being warmed by the sun (passivity).

If one follows Aristotle’s lead, one will easily be able to classify the predicates in propositions such as Socrates is potbellied and Socrates is wiser than Meletus. But what about the term Socrates in propositions such as Socrates is human? What category does it belong to? Aristotle answers the question by making a distinction between “first substance” and “second substance.” In Socrates is human, Socrates refers to a first substance—an individual—and human to a second substance—a species or kind. Thus, the proposition predicates the species human of an individual, Socrates.(See below Physics and metaphysics: Form.)

Aristotle’s logical writings contain two different conceptions of the structure of a proposition and the nature of its parts. One conception can trace its ancestry to Plato’s dialogue the Sophist. In that work Plato introduces a distinction between nouns and verbs, a verb being the sign of an action and a noun being the sign of an agent of an action. A proposition, he claims, must consist of at least one noun and at least one verb; two nouns in succession or two verbs in succession—as in lion stag and walks runs—will never make a proposition. The simplest kind of proposition is something like A man learns or Theaetetus flies, and only something with this kind of structure can be true or false. It is this conception of a proposition as constructed from two quite heterogeneous elements that is to the fore in the Categories and the De interpretatione, and it is also paramount in modern logic.

In the syllogistic of the Prior Analytics, in contrast, the proposition is conceived in quite a different way. The basic elements out of which it is constructed are terms, which are not heterogeneous like nouns and verbs but can occur indifferently, without change of meaning, as either subjects or predicates. One flaw in the doctrine of terms is that it fosters confusion between signs and what they signify. In the proposition Every human is mortal, for example, is mortal predicated of humans or of human? It is important to distinguish between use and mention—between the use of a word to talk about what it signifies and the mention of a word to talk about the word itself. This distinction was not always easy to make in ancient Greek, because the language lacked quotation marks. There is no doubt that Aristotle sometimes fell into confusion between use and mention; the wonder is that, given his dysfunctional doctrine of terms, he did not do so more often.

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