Download e-book for kindle: A Structuralist Theory of Logic by Arnold Koslow

By Arnold Koslow

ISBN-10: 0521023726

ISBN-13: 9780521023726

ISBN-10: 0521412676

ISBN-13: 9780521412674

This can be surely 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 booklet. it is going to switch how you do philosophy.

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A z , ... , and that "~" satisfies these conditions: (1) Ai ~ Aj if and only ifj is less than or equal to i + 1, and (2) Ail' ... , Ai" ~ Ai. if and only if Ai, ~ Ai. for some r belonging to {1, ... , n}. It is easy to see that "~" satisfies all the conditions 1-5 in Chapter 1, but that condition 6 (Cut) fails because Al ~ A z , and A z ~ A 3 , but Al :f:> A 3 · Thus, the Cut condition is not redundant for the characterization of implication relations. We include it because it is a feature of most concepts of inference and therefore is central to the notion of an implication relation - even though there are examples of implication relations that do not correspond to rules of inference.

2. For implication relations "~" (on S) and "~'" (on S'), we shall say that "::::;>'" is a conservative extension of "~" if and only if (1) it is an extension of "~" and (2) for any AI, ... , An and B in S, if AI. , An ~' B, then AI. , An ~ B. Similarly, one implication structure is a conservative extension of another if and only if its implication relation is a conservative extension of that of the other. Thus, in passing from an implication structure 1= (S, ~) to a conservative extension, the two implication relations will be coextensional on S.

Tonking" yields an item that is indicated as the value of the function T, that is, as T(A, B), and that element of the structure is related implicationally to A and to B by Tl and T2 , respectively. Any implication structure I = (S, ~) in which T(A, B) exists for all A and B must be trivial. Its members are equivalent to each other. The reason is that for any A and B, A ~ T(A, B), and T(A, B) ~ B. By transitivity, A ~ B for all A and B in the structure. However, the trivial structures are exactly those in which the distinction between the various logical operators vanishes.

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A Structuralist Theory of Logic by Arnold Koslow


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