This choice of newly comissioned essays by way of overseas members deals a consultant review of crucial advancements in modern philosophical logic.
•Presents controversies in philosophical implications and functions of formal symbolic common sense.
•Surveys significant developments and provides unique insights.
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This ebook offers an advent to Kurt Godel's theorems via a suite of puzzles interspersed with an account of symbolic good judgment. Godel's argument has been transferred from the formal area of mathematical platforms in an try to make its crucial principles extra available to the final reader.
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Extra resources for A Companion to Philosophical Logic
On Megarian and Stoic logic Baltzly, Dirk (2000) Stoicism. Stanford Encyclopedia of Philosophy. ) Döring, Klaus (1974) Die Megariker: kommentierte Sammlung der Testimonien. ) Frede, Michael (1974) Die stoische Logik. Vandenheck and Ruprecht. ) 22 ANCIENT GREEK PHILOSOPHICAL LOGIC Long, A. A. and Sedley, D. N. (1987) The Hellenistic Philosophers. 2 vols. Cambridge: Cambridge University Press. (Comprehensive discussion of all the Hellenistic schools, including the Stoics, as well as Diodorus Cronus.
However, in medieval logic, si (if), igitur (therefore), sequitur (follows) and quia (because) are all indicator-words for one and the same notion of a consequentia. This notion survives terminologically in modern logic under two different guises, namely, on the one hand, as the notion of (logical) consequence between WFFs that derive from Bolzano’s Ableitbarkeit and that was made famous by Tarski, and, on the other hand, as the sequents (German Sequenzen) that were used by Gentzen. The medieval theory of consequences, accordingly, can rightly be seen as a partial anticipation of contemporary sequent-calculus renderings of logical systems.
Logic did not progress in this way; no dominant theory commanded it (a tapestry more than a chain) until the first decades of the twentieth century. No self-sustaining internal theory held sway before then, nor was there much rigor externally imposed. Even Aristotle, as one commentator put it, was more venerated than read, and most versions of syllogistic logic proposed after the Middle Ages did not measure up to the sophistication of his own system. 1 The Dark Ages of Logic In 1543 the French humanist and logician Peter Ramus (1515–72), who had made a name for himself with his dissertation Whatever Aristotle Has Said is False, published his Dialectic, a slim book that went through 262 editions in several countries and became a model for many other textbooks.
A Companion to Philosophical Logic