A Companion to Philosophical Logic by Dale Jacquette

By Dale Jacquette

This selection of newly comissioned essays by way of foreign members bargains a consultant assessment of crucial advancements in modern philosophical logic.

  • Presents controversies in philosophical implications and functions of formal symbolic logic.
  • Surveys significant traits and provides unique insights.

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2. 3. 4. 5. If the first, then the second; the first; therefore the second. If the first then the second; not the first; therefore not the second. Not both the first and the second; the first; therefore not the second. Either the first or the second; the first; therefore not the second. Either the first or the second; not the first; therefore the second. The Stoics then demonstrated the validity of other valid arguments by means of these indemonstrables (unfortunately, our knowledge of their views is very fragmentary: see Kneale and Kneale 1978; Mates 1953; Mueller 1978 for reconstructions).

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.

Two other topics that stand out in this respect are the question whether God’s existence can be demonstrated and the treatments of the various Names of God. Thomas Aquinas does not enjoy a high reputation as a logician; his fame rests on his contribution to metaphysics and the philosophy of mind. Nevertheless, his Summa Theologica contains much that is of great relevance for contemporary philosophy of logic and language. Thus, for instance, in his discussion of the Names of God in Question 13 Aquinas anticipates Frege’s ideas concerning names with different modes of presentation of the same object.

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