Various suggestions have been made as to why Aristotle should have limited himself in this way. Fairly plausible is the idea that, although he is interested in arguments as such, Aristotle is most concerned to formalize the type of argument which finds its home in his model of a completed science or body of knowledge, one in which what is at stake is the relations of kinds of thing, and claims about what holds universally are particularly important. Arguments involving individuals find no place in this logical system (though they appear in fleeting thoughts on Aristotle’s part about a ‘practical’ logic of arguments that lead to action).
Aristotle hints at ideas, developed further by his pupil Theophrastus, of systematizing arguments where what is studied are the relations between the statements, rather than the terms which form part of them. Real progress here, however, was left to the Stoics, in particular Chrysippus. Stoic logic concerns statements or axiomata, which assert or deny something. Compound statements are produced by joining simple statements by various connectives, such as ‘and’, ‘or’ and ‘if’. Stoic logic studies arguments which are made up of premisses and conclusion, where these are all statements; much of it overlaps with modern ‘propositional logic’, though there are differences. Five argument-schemata are taken as basic (the schematic letters P and Q stand in for statements). These are: (1) If P, then Q, P; therefore, Q (still familiar, as ‘modus ponens’), (2) If P, then Q, not-Q; therefore not-P (‘modus tollens’), (3) Not both P and Q, P; therefore not-Q, (4) Either P or Q, P; therefore, not-Q, (5) Either P or Q, not-P, therefore Q. From this basis Stoic logic developed in sophisticated and powerful ways.
As with Aristotle, the Stoics were not merely interested in argument for its own sake. They were concerned to produce arguments which were also ‘proofs’ – arguments which, as they put it, ‘by way of agreed premisses, reveal by deduction an unclear conclusion’. Logical form is studied in the service of representing our claims to knowledge, in this case the way we claim to reach knowledge of ‘unclear’ or theoretical matters by way of what we can agree on in our experience.
Epicurus and his school affected to despise formal logic as a trivial waste of time. But they also spent energy on studying what were called ‘signs’ on the basis of which we make inferences from what we experience to matters that are beyond our own experience; so they engaged other schools in discussion about logic to some extent.
Students of philosophy in the ancient world could (unless they were Epicureans) expect to study both Aristotelian and Stoic logic, which were seen as complementary, although there could be disputes as to which was the more important. By historical accident, Stoic logic was lost, along with much early Stoicism, at the end of antiquity, whereas Aristotle’s logic not only survived but became regarded as all there was to logic. It was elaborated in the Middle Ages, regarded as complete by Kant and dislodged from its place in the syllabus only by the rediscovery of propositional logic by Frege and Russell at the beginning of the twentieth century.
The third part of the philosophical curriculum, ‘physics’, no longer sounds as though it even belongs to philosophy. This is partly because of our narrowing of a term which originally meant the study of nature or phusis. Nature is just everything that there is, or the world (including humans, who are part of the world). Hence the study of nature can cover a number of very different things, and ‘physics’ covers a range of enquiries which for us have got segregated into different subject-matters and taught in very different ways.
One type of enquiry seeks explanations for the puzzling things we see around us and are exposed to. What explains the regularities of the sun and the moon? What brings about the seasons, so crucial for farmers? Why are there hurricanes, earthquakes, eclipses? In the ancient world these were regarded as issues which were part of the study of nature as philosophers undertook that. As philosophy developed, however, and especially after Aristotle, these questions lost much of their interest, since there were numbers of theories about them, but no decisive ways of deciding between these, and so no convincing way of showing any given answer to be correct. They became regarded as suitable material for dinner-party discussion rather than live philosophical questions. In the modern world, of course, the advances of science, whatever their other drawbacks, have provided us with firm answers to questions like these. They no longer seem remotely philosophical, and ancient discussions of them are often put into the history of science.
The study of nature narrowed in another way also, especially in the period after Aristotle, with the development of bodies of scientific knowledge separate from philosophy. Medicine, though crude by modern standards, developed as a specialized science, with differing schools. It was the mathematical sciences, however, which made the greatest strides, with Euclid’s Elements a high point. Archimedes was not only a great mathematician, but developed astronomy and also applied branches like engineering. Historians of science sometimes lament the fact that sophisticated technical ideas were applied in trivial ways; Heron of Alexandria describes a machine for making figures mechanically pour libations on an altar. But basic facts about the ancient economies precluded anything like the development of our industrial technology. Whether we are obviously the winners here is another matter.
The study of nature, or ‘physics’ in the ancient sense, however, covered more than what became narrow scientific enquiries. From the beginning, ‘nature’ could be used for ‘what there is’, everything that there is to be studied. Hence much of ancient ‘physics’ is so broad as to correspond to what we think of as metaphysics. Is change a necessary feature of our world? What is change, anyway? In the world around us, what are the real entities, the things that are basic to a true view of the way the world really is? Are living things, like animals and humans, such basic entities? They seem to be the subjects of changes, the things changes happen to. But if what is real is the subject of change, then perhaps in looking for what is real we should not stop with the living things, but look for whatever it is which in them is the subject of change. Perhaps this is the material they are made out of. Issues like this are central to the philosophical enquiries of many of the so-called Presocratics and of Aristotle, who engaged with their ideas and is our major source for many of them. They are not part of modern science, but of more abstract philosophical enquiries, generally called metaphysical. Often the dividing-line between Aristotle’s ‘physics’ and his ‘metaphysics’ is a thin one.
Such questions were thought to arise naturally in the context of a general view of the world as a whole. Given the less ambitious scope of modern metaphysics, they are often studied in relative isolation. Thus we tend to see Plato’s ‘theory of Forms’, for example, as a metaphysical theory that has nothing to do with what we think of as physics or the study of nature. In the ancient world, however, it was mostly seen as one aspect of Plato’s ‘physics’ or theory of the world, which was primarily studied in the Timaeus, a dialogue not very popular today which contains Plato’s cosmology or account of the universe and its structure. (See box, p.82).