A Companion to Philosophical Logic

Logic

This number of newly comissioned essays through overseas participants deals a consultant assessment of an important advancements in modern philosophical logic.

•Presents controversies in philosophical implications and functions of formal symbolic good judgment.

•Surveys significant developments and provides unique insights.

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This at once imposes two critical limits on demonstrations: nothing can be demonstrated except what is necessarily so, and nothing can be demonstrated except that which has a cause or explanation (the force of the latter restriction will be evident shortly). Since demonstrations are valid arguments, whatever holds of valid arguments in general will hold of them. Therefore, a natural place to begin the discussion of demonstrations would be with a general account of validity. ’ However, Aristotle thought that all valid arguments could be ‘reduced’ to a relatively limited set of valid forms which he usually refers to as ‘arguments in the figures’ (modern terminology refers to these forms as ‘syllogisms’; this can lead to confusion in discussing Aristotle’s theory).

However, sometimes a philosopher is committed to (uses of) both conceptions. It seems more likely, though, that the alternative conceptions of truth-conditions pertain to different kinds of predication, than that the philosopher in question wavers between two absolute, all-encompassing theories. For instance, the substantival predication [Man is an animal] is held to be true because the terms man and animal stand for the same entity, whereas the denominative predication [A man is white] is deemed true because whiteness inheres in what man stands for.

Is a descent to a disjunctive proposition. One can also descend with respect to terms: All men are mortal. Therefore: John and Simon are mortal. Aristotelian logic, when cast in the mold of traditional syllogistic theory, is a termlogic, rather than a logic of propositions. The medievals liberated themselves from the term-logical straitjacket of the Aristotelian syllogistics, first by considering also 29 E. P. BOS AND B. G. SUNDHOLM syllogisms with singular judgments, that is, categorical [S is P] propositions of the form [s is P], where s is a singular term.

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