LOGIC Mill maintains that we are always, though not necessarily consciously, applying his canons in daily life and in the courts of law Thus, to illustrate the second canon he says, ‘When a man is shot through the heart, it is by this method we know that it was the gunshot which killed him: for he was in the fullness of life immediately before, all circumstances being the same, except the wound.’ Mill’s methods of agreement and disagreement are a sophistication of Bacon’s tables of presence and absence.1 Like Bacon’s, Mill’s methods seem to assume the constancy of general laws Mill says explicitly, ‘The proposition that the course of Nature is uniform, is the fundamental principle, or general axiom, of Induction.’ But where does this general axiom come from? As a thoroughgoing empiricist, Mill treats it as being itself a generalization from experience: it would be rash, he says, to assume that the law of causation applied on distant stars But if this very general principle is the basis of induction, it is difficult to see how it can itself be established by induction But then Mill was prepared to affirm that not only the fundamental laws of physics, but those of arithmetic and logic, including the very principle of non-contradiction itself, were nothing more than very well-confirmed generalizations from experience.2 Frege’s Refoundation of Logic On these matters Frege occupied the opposite pole from Mill While for Mill propositions of every kind were known a posteriori, for Frege arithmetic no less than logic was not only a priori but also analytic In order to establish this, Frege had to investigate and systematize logic to a degree that neither Mill nor any of his predecessors had achieved He organized logic in a wholly new way, and became in effect the second founder of the discipline first established by Aristotle One way to define logic is to say that it is the discipline that sorts out good inferences from bad In the centuries preceding Frege the most important part of logic had been the study of the validity and invalidity of a particular form of inference, namely the syllogism Elaborate rules had been drawn up to distinguish between valid inferences such as See vol III, p 31 100 See Ch below