Aristotle: A Very Short Introduction

Aristotle's classes of predicates are themselves now called 'categories', the term 'category' having been transferred from the things classified to the things into which they are classified, so that it is normal to talk of ' Aristotle's ten categories'. More importantly, the categories are generally referred to as categories 'of being' - and indeed Aristotle himself will sometimes refer to them as 'the classes of the things that exist'. Why the switch from classes of predicates to classes of beings?

Chapter 10
Reality
Science is about real things. That is what makes it knowledge rather than fantasy. But what things are real? What are the fundamental items with which science must concern itself? That is the question of ontology, and a question to which Aristotle devoted much attention. One of his ontological essays, the Categories, is relatively clear; but most of his ontological thought is to be found in the Metaphysics, and in some of the most obscure parts of that obscure work.
'Now the question which, both now and in the past, is continually posed and continually puzzled over is this: What is being? That is, what is substance?' Before sketching Aristotle's answer to that question we must ask about the question itself. What is Aristotle after? What does he mean by 'substance'? This preliminary question is best approached by a circuitous route.

Chapter 9
Ideal and Achievement
Aristotle has emerged as a systematic thinker. The various sciences are autonomous but systematically interrelated. Each individual science is to be developed and presented in the form of an axiomatic system -- 'in the geometrical manner', as later philosophers put it. Moreover, the set of concepts within which Aristotle's notion of science finds its place was itself systematically examined and ordered. Perhaps none of that is surprising. Philosophy, after all, is nothing if not systematic, and Aristotle's system -- his 'world picture' -- has for centuries been held up for admiration and praise.

Some modern philosophers have rejected - and ridiculed - Aristotle's talk of essences. But Aristotle shows himself the better scientist; for an important part of the scientific endeavour consists in explaining the various quirks and properties of substances and stuffs in terms of their fundamental natures - that is to say, in terms of their essences. Aristotle's axiomatic sciences will start from essences and successively explain derivative properties. The theorems of animal biology, say, will express the derived properties of animals, and the deduction of the theorems from the axioms will show how those properties are dependent upon the relevant essences.

Chapter 8
Knowledge
The logic of the Prior Analytics serves to derive the theorems of a science from its axioms. The Posterior Analytics is primarily concerned to study the nature of the axioms themselves, and hence the general form of an axiomatized deductive science. To a surprising extent, the Posterior Analytics is independent of the syllogistical theory developed in the Prior Analytics: whatever the explanation for this fact may be, it has a happy consequence - the deficiencies in Aristotle's theory of inference are not all inherited by his theory of axiomatization.

Aristotle's account of the nature of axioms is based upon his conception of the nature of knowledge; for a science is meant to systematize our knowledge of its subject-matter, and its component axioms and theorems must therefore be propositions which are known and which satisfy the conditions set upon knowledge.

The logical theory of the Prior Analytics is known as ' Aristotle's syllogistic'. The Greek word 'sullogismos' is explained by Aristotle as follows: 'A sullogismos is an argument in which, certain things being assumed, something different from the things assumed follows from necessity by the fact that they hold'. The theory of the Prior Analytics is a theory of the sullogismos -- a theory, as we might put it, of deductive inference.

Aristotle makes great claims for his theory: 'every proof and every deductive inference (sullogismos) must come about through the three figures that we have described'; in other words, every possible deductive inference can be shown to consist of a sequence of one or more arguments of the type which Aristotle has analysed. Aristotle is, in effect, claiming that he has produced a complete and perfect logic; and he offers a complex argument in favour of the claim. The argument is defective, and the claim is false. Moreover, the theory inherits the weaknesses of the account of propositions on which it is based -- and it contains a number of internal deficiencies to boot. None the less, later thinkers were so impressed by the power of Aristotle's exposition that for more than a thousand years Aristotelian syllogistic was taught as though it contained the sum of logical truth. And indeed on any account, the Prior Analytics -- the very first attempt to develop a science of logic -- is a work of outstanding genius. It is elegant and systematic; its arguments are orderly, lucid, and rigorous; and it achieves a remarkable level of generality.

In order to achieve generality, Aristotle introduced a simple device. Instead of employing particular terms -- 'man', 'horse', 'swan' -- in order to describe and characterize arguments, he used letters -- A, B, C. Instead of genuine sentences, such as 'Every octopus has eight tentacles', he used quasi-sentences or sentence patterns, such as 'Every A is B.' This use of letters and sentence patterns allows Aristotle to speak with full generality; for what holds true of a pattern, holds true of every particular instance of the pattern. For example, Aristotle needs to show that from 'Some sea-creatures are mammals' we may infer 'Some mammals are sea-creatures', that from 'Some men are Greeks' we may infer 'Some Greeks are men', that from 'Some democracies are illiberal' we may infer 'Some illiberal regimes are democratic', and so on -- he wants to show (as the jargon has it) that every particular affirmative proposition converts. He does so by considering the sentence pattern 'Some A is B', and by proving that from a sentence of that pattern we can infer the corresponding sentence of the pattern 'Some B is A'. If that has been shown to hold for the pattern, then it has been shown, at one blow, to hold for all of the indefinitely many instances of the pattern.

Aristotle invented this use of letters. Logicians are now so familiar with the invention, and employ it so unthinkingly, that they may forget how remarkable an invention it was.