Extensionalism: The Revolution in Logic

a single life-span. Philosophers, then, do not see more or know more, and they do not see less or know less. They aim to see less detail and more of the abstract. Their details, if you like, are abstractions. Walking on God's earth as a pedestrian, as a farmer working his fields or as a passer-by, one's picture of one's surroundings is every bit as intelligent as that of the pilot riding the sky. The views of the field are radically different, however. One sees only a specific field and in all lively detail: the exact pattern of the land, or even the exact outline of a given leaf, grasshopper, grain of sand even. Acquaintance with minute detail is not without its price: details may stand in the way of conjuring the big picture. It may be difficult to compare whichever field one happens to be in with far off fields, with respect to their size or shape or any other quality. One may wish to inquire if far off fields were already planted, harvested, or even if they exist. A pedestrian mayfind it hard or even impossible to do so. The pedestrian view contains fine points that the pilot's map never would, but it does not necessarily contain more information, for it lacks the general context. After all, there are only so many items that one can observe and account for at a single glance, a single map, a single book, a single life-span.

Provides a broad, concise, accurate and up-to-date overview of the history of logic (up to and including the early modern period) The first history of logic that explains logical theories as philosophical solutions to fundamental epistemological problems: it is the first extended treatment of the history of logic from the point of view of critical rationalism Challenges previous and prevalent histories of logic Unites the history of logic with the history of epistemology The first extensive discussion of the philosophical and historical importance of extensionalism

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This vivid and thought-provoking book by the Israeli logician Nimrod Bar-Am impels one to rethink the place of logic in Western thought. It shows that the history of logic from Aristotle to Tarski is the history of the gradual undoing of the classic conflation of logic and empirical science. It sets tomorrow's agenda for philosophers and historians of logic and scientific method by taking as its starting point the mere fact that, curiously, ancient logic is not as formal as current literature presents it. Rather, as Bar-Am explains, modern formal logic became possible only after a series of bold criticisms of the magnificent Aristotelian system. These criticisms begin with David Hume's declaration that logic does not sanction induction, follow on with Kant's view of logic as an extremely limited system, and culminating with Booles' introduction of logic as an extensional system, and Russell's solution to his own paradox.

The book offers a breathtaking intellectual odyssey; presenting the development of logic as an evolving critical assessment of approaches to an impossible ideal. Bar-Am handles an extremely complex subject matter in a manner that is both accessible to the general educated reader and challenging to the learned expert, by opening to them live background ideas to dead formulas. The book will easily find its place alongside both general introductions to the history of science and advanced reading lists in the philosophy of logic.

Contenu
Preliminary Notes.- Outline of Preliminary Notes.- Setting the Scene: Some Notes on the Pre-history of Logic.- The Mother of All Conflations: Parmenides' Proof.- Early Disagreements Concerning the Power of Proofs: The Uses and Misuses of Dialogues.- The Sophists' Challenge.- Aristotle's Logic: The Rise of Essentialism.- The Beginning is the Term.- Chimera in the Dusk: Essentialism.- Semantics is not Ontology.- The Mother of All Matrices, or, How Terms Spawn Definitions and Syllogisms.- The Conflation of the Source with the True, Good and Beautiful (Source).- Induction as Spell-Casting.- The Birth of Induction from Sea Foam.- Taxonomy of Reality by Syllogism.- Essentialism Besieged.- Ad Hominem Logic: Logic between Aristotle and Boole.- The Neglect of Judgment.- Leibniz as Aristotle and Boole Conflated.- Why Transcendental Logic is no Logic at All.- The Fall of Essentialism.- Extensionalism as Exorcism.- Mathematical Logic: An Oxymoron.- The Last Step.