By Arnold Koslow

ISBN-10: 0521023726

ISBN-13: 9780521023726

ISBN-10: 0521412676

ISBN-13: 9780521412674

This is often absolutely some of the most innovative books written in philosophy. Koslow's structuralist method of good judgment opens the potential for analogous functions in different components of philosophy. Get this ebook. it is going to switch how you do philosophy.

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First released in 2004. Routledge is an imprint of Taylor & Francis, an informa corporation.

**Extra resources for A Structuralist Theory of Logic**

**Sample text**

Since R => Rand R* => R*, it follows that R ~ R*. Gentzen thought that an analysis should show how to display the E-inferences as unique functions of their corresponding I-inferences, and he believed that the Elimination rules were consequences of their corresponding Introduction rules (Gentzen, 1934, pp. 80-1). 2 Elimination conditions as uniquely determined by Introduction conditions The generalized E-conditions are, in the following sense, unique functions of their corresponding I-conditions: The Introduction conditions 1'9 have no slack with respect to Elimination conditions E'9' for if there such that were another Elimination condition for the operator, say I'9(R) was given by E'9(U) ~ U => R (for all U), as well as by E;(U) ~ U => R (for all U), then it would follow that E'9(U) ~ E;(U) for all U in S.

There is one possible condition, independent of the rest, that seems a natural candidate for addition. It concerns the case in which an implication relation fails to hold. If we think of the special case of a consequence relation on the set of sentences of a first-order language that has conjunction, then we know that if AI> ... , An -:j::;> B, then there is an element of the structure that implies each of the A;'s but does not imply B - namely, their conjunction. Thus, we might entertain a "star" -condition as an addition to our theory of implication relations: (*).

1 Thus, in nonmonotonic variants of implication relations, Projection does not hold. That is, for some AI> ... , An and Ak, AI> ... , An -=F> A k . This has suggestively been called a "forgetting" notion of implication, although it is, strictly speaking, not an implication relation. 36 II IMPLICATION RELATIONS There is an extensive variety of implication relations to be had. Not all of them are of theoretical interest. There are some very familiar and favored examples (syntactic and semantic concepts of logical consequence) that are part of the story that needs to be told, but these familiar examples are not nearly the whole story about implication relations.

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