INDUCTIVE LOGIC

The idea of inductive logic as providing a gene-ral, quantitative way of evaluating arguments is a relatively modern one. Aristotle’s conception of ‘induction ’ (epagog!Z)—which he contrasted with ‘reasoning ’ (sullogism!oB)—involved moving only from particulars to universals (Kneale and Kneale 1962, 36). This rather narrow way of think-ing about inductive reasoning seems to have held sway through the Middle Ages and into the seven-teenth century, when Francis Bacon (1620) devel-oped an elaborate account of such reasoning. During the eighteenth and nineteenth centuries, the scope of thinking about induction began to broaden considerably with the description of more sophisticated inductive techniques (e.g., those of Mill [1843]), and with precise mathematical ac-counts of the notion of probability. Intuitive and quasi-mathematical notions of probability had long been used to codify various aspects of uncertain reasoning in the contexts of games of chance and statistical inference (see Stigler 1986 andDale 1999), but a more abstract and formal approach to proba-bility theory would be necessary to formulate the general modern inductive-logical theories of nonde-monstrative inference. In particular, the pioneering work in probability theory by Bayes (1764), Laplace (1812), Boole (1854), and many others in the eigh-teenth and nineteenth centuries laid the ground-work for a much more general framework for inductive reasoning. (Philosophical thinking about the possibility of inductive knowledge was most famously articulated by David Hume 1739–1740 and 1758) (See Problem of Induction). The contemporary idea of inductive logic (as a general, logical theory of argument evaluation) did not begin to appear in a mature form until the late nineteenth and early twentieth centuries. Some of the most eloquent articulations of the basic ideas behind inductive logic in this modern sense appear in John Maynard Keynes’s Treatise on Probability. Keynes (1921, 8) describes a ‘‘logical relation be-tween two sets of propositions in cases where it is not possible to argue demonstratively from one to another.’ ’ Nearly thirty years later, Rudolf Carnap (1950) published his encyclopedic work Logica