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In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately (...) for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. (shrink)

This chapter situates Mill’s System of Logic (1843/1872) in the context of some of the meta-logical themes and disputes characteristic of the 19th century as well as Mill’s empiricism. Particularly, by placing the Logic in relation to Whately’s (1827) Elements of Logic and Mill’s response to the “great paradox” of the informativeness of syllogistic reasoning, the chapter explores the development of Mill’s views on the foundation, function, and the relation between ratiocination and induction. It provides a survey of the Mill-Whewell (...) debate on the nature of induction, Mill’s account of putatively a priori disciplines such as the science of number, and Frege’s criticisms of the Logic as psychologistic. (shrink)

This paper considers the question of whether Mill's account of the nature and justificatory foundations of deductive logic is psychologistic. Logical psychologism asserts the dependency of logic on psychology. Frequently, this dependency arises as a result of a metaphysical thesis asserting the psychological nature of the subject matter of logic. A study of Mill's System of Logic and his Examination reveals that Mill held an equivocal view of the subject matter of logic, sometimes treating it as a set of psychological (...) processes and at other times as the objects of those processes. The consequences of each of these views upon the justificatory foundations of logic are explored. The paper concludes that, despite his providing logic with a prescriptive function, and despite his avoidance of conceptualism, Mill's theory fails to provide deductive logic with a justificatory foundation that is independent of psychology. (shrink)

'Nobody reads Mill today,' wrote a reviewer in Time magazine a few years ago.! One could scarcely praise Mr Melvin Maddocks, who penned that remark, for his awareness of the present state of Mill studies, for of all nineteenth century philosophers who wrote in English, it is 1. S. Mill who remains the most read today. Yet it would not be so far from the truth to say that very few people pay much serious attention nowadays to Mill's writings about (...) logic and metaphysics (as distinct from those on ethical and social issues), despite the fact that Mill put enormous effort into their composition and through them exerted a considerable influen ce on the course of European philosophy for the rest of his century. But the only sections of A System of Logic (1843) and An Examination of Sir William Hamilton's Philosophy (1865) to which much reference is now made comprise only a small proportion of those very large books, and the prevailing assumption is that Mill's theories about logical and meta physical questions are, with few exceptions, of merely antiquarian in terest. Bertrand Russell once said that Mill's misfortune was to be born at the wrong time (Russell (1951), p. 2). It can certainly appear that Mill chose an inauspicious time to attempt a major work on logic. (shrink)

The philosophical background important to Mill’s theory of induction has two major components: Richard Whately’s introduction of the uniformity principle into inductive inference and the loss of the idea of formal cause.