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While post-Fregean logicians tend to ignore or even denigrate the traditional logic of Aristotle and the Scholastics, new work in recent years has shown the viability of a renewed, extended, and strengthened logic of terms that shares fundamental features of the old syllogistic. A number of logicians, following the lead of Fred Sommers, have built just such a term logic. It is a system of formal logic that not only matches the expressive and inferential powers of today’s standard logic, but surpasses it and is far simpler and more natural. This book aims to substantiate this claim by exhibiting just how the term logic can shed need light on a variety of challenges that face any system of formal logic.

Logic. --- Aristotle. --- scholasticism. --- syllogism.

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Common sense tells me I can control my life to some extent; should I then, faced with a logical argument for fatalism, reject common sense? There seems to be no place in a physical theory of the universe for the sensory experiences of colours, taste and smells, yet I know I have these experiences. In this book, Gilbert Ryle explores the conflicts that arise in everyday life and shows that the either/or which such dilemmas seem to suggest is a false dilemma: one side of the dilemma does not deny what we know to be true on the other side. This classic book has been revived in a new series livery for twenty-first-century readers, featuring a specially commissioned preface written by Barry Stroud.

Dilemma --- Philosophy --- Philosophy & Religion --- Logic --- Decision making --- Syllogism --- Dilemma.

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Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory. .

Computer science. --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Proof theory --- Data processing. --- Gentzen, Gerhard. --- Mathematics. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Logic, Symbolic and mathematical. --- Informatics --- Science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Gottlob Frege's 'Grundgesetze der Arithmetik', or 'Basic Laws of Arithmetic', was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's "Paradox", which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of 'Reading Frege's Grundgesetze' develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the matrehematical basis of Frege's logicism, explaining and exploring Frege's formal arguments.

Arithmétique --- Philosophie --- Mathematical logic --- Frege, Gottlob --- Arithmetic --- Logic, symbolic and mathematical --- Philosophy --- Frege, Gottlob, --- Philosophie. --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Calculators --- Numbers, Real --- Arithmetic - Philosophy --- Frege, Gottlob, - 1848-1925

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This book includes detailed critical analysis of a wide variety of versions of the indispensability argument, as well as a novel approach to traditional views about mathematics.

Logic, Symbolic and mathematical. --- Mathematics --- Platonists. --- Platonism --- Philosophers --- Philosophy, Ancient --- Logic of mathematics --- Mathematics, Logic of --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Philosophy. --- Quine, W. V. --- Benacerraf, Paul. --- Quine, Willard Van Orman --- Kuaĭn, Uillard van Ormen --- קואיין, ו. ו. א.