Mathematics : Logic

One of the most famous anagrams of all time was constructed in the Middle Ages. The unknown author contrived it as a Latin dialogue between Pilate and Jesus. Jesus' answer to Pilate's question 'What is truth?' is phrased as an ingenious anagram of the letters of that very question: Pilate: Quid est veritas? ('What is truth?') Jesus: Est virqui adest. ('It is the man before you'). Danesi argues that the fascination with puzzles throughout the ages suggests something more than that they provide a form of constructive entertainment. They serve, in fact, a deeply imbedded need in people to make sense of things. more...

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With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who too more...

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Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs to make the material more accessible. The presentation is based on natural deduction and readers are assumed to be familiar with basic notions of first order logic. more...

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This title provides a series of case studies that introduces students to data analysis. Including a summary of the theory needed to do the analyses, it provides a self-contained introduction to modern statistical practice. more...

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