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Attempts to Rethink Logic
To appear in The Cambridge History of Philosophy in the Nineteenth Century (1790-1870) (Cambridge, 2011)
The period between Kant and Frege is widely held to be an inactive time in the history of logic, especially when compared to the periods that preceded and succeeded it. By the late eighteenth century, the rich and suggestive exploratory work of Leibniz had led to writings in symbolic logic by Lambert and Ploucquet.1 But after Lambert this tradition effectively ended, and some of its innovations had to be rediscovered independently later in the century. Venn characterized the period between Lambert and Boole as “almost a blank in the history of the subject” and confessed an “uneasy suspicion” that a chief cause was the “disastrous effect on logical method” wrought by Kant’s philosophy.2 De Morgan began his work in symbolic logic “facing Kant’s assertion that logic neither has improved since the time of Aristotle, nor of its own nature can improve.”3
De Morgan soon discovered, however, that the leading logician in Britain at the time, William Hamilton, had himself been teaching that the traditional logic was “perverted and erroneous in form.”4 In Germany, Maimon argued that Kant treated logic as complete only because he omitted the most important part of critique – a critique of logic itself.5 Hegel, less interested in formal logic than Maimon, concurs that “if logic has not undergone any change since Aristotle, . . . then surely the conclusion which should be drawn is that it is all the more in need of a total reconstruction.”6 On Hegel’s reconstruction, logic “coincides with metaphysics.”7 Fries argued that Kant thought logic complete only because he neglected “anthropological logic,” a branch of empirical psychology that provides a theory of the capacities humans employ in thinking and a basis for the meager formal content given in “demonstrative” logic.8 Trendelenburg later argued that the logic contained in Kant’s Logic is not Aristotle’s logic at all, but a corruption of it, since Aristotelian logic has metaphysical implications that Kant rejects.9
Indeed, one would be hard pressed to find a single nineteenth-century logician who agrees with Kant’s notorious claim. However, this great expansion of logic – as some logical works branched out into metaphysics, epistemology, philosophy of science, and psychology, while others introduced new symbolic techniques and representations – threatened to leave logicians with little common ground except for their rejection of Kant’s conservatism. Robert Adamson, in his survey of logical history for the Encyclopedia Britannica, writes of nineteenth-century logical works that “in tone, in method, in aim, in fundamental principles, in extent of field, they diverge so widely as to appear, not so many expositions of the same science, but so many different sciences.”10 Many historians of logic have understandably chosen to circumvent this problem by ignoring many of the logical works that were the most widely read and discussed during the period – the works of Hegel, Trendelenburg, Hamilton, Mill, Lotze, and Sigwart, for example.
The present article, however, aims to be a history of “logic” in the multifaceted ways in which this term was understood between Kant and Frege (though the history of inductive logic – overlapping with the mathematical theory of probabilities and with questions about scientific methodology – falls outside the purview of this article). There are at least two reasons for this wide perspective. First, the diversity of approaches to logic was accompanied by a continuous debate in the philosophy of logic over the nature, extent, and proper method in logic. Second, the various logical traditions that coexisted in the period – though at times isolated from one another – came to cross-pollinate with one another in important ways. The first three sections of the article trace out the evolving conceptions of logic in Germany and Britain. The last three address the century’s most significant debates over the nature of concepts, judgments and inferences, and logical symbolism.
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