By Arnold Koslow

This can be surely some of the most progressive 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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**Additional info for A Structuralist Theory of Logic**

**Example text**

In addition, we shall say that the condition *(A, B, T) is the Elimination condition for the operator cp, and if (A, B, R) holds for some R [(R) holds for some R in S], then we shall say that cP eliminates the element R. Similarly, we shall say that the condition [(E) if and only if E ~ T] (for all E in S) is the Introduction condition for the operator cp, and if [(E) if and only if E ~ R] (for all E in S) holds for some R in S, then we shall say that R is introduced by the Introduction condition for the operator cpo It is more perspicuous to write (GG) as follows: For any logical operator *

The introductions represent, as it were, the 'definitions' of the symbols concerned, and the eliminations are no more, in the final analysis, than the consequences of these definitions. This fact may be expressed as follows: in eliminating a symbol we are dealing 'only in the sense afforded it by the introduction of that symbol'. An example may clarify that is meant: We were able to introduce the formula d :J g(l when there existed a derivation of g(l from the assumption formula d. , d :J g(l V fl, V -I), we could do this precisely by inferring g(l directly, once d has been proved, for what d :J g(l attests is just the existence of a derivation of g(l from d.

The second condition corresponds to what is usually known as the deduction theorem, when the context is some standard logical language, and the implication relation is taken to be a deducibility relation. There 2 THE PROGRAM AND ITS ROOTS 17 is no assurance that in general there is a hypothetical with antecedent A and consequent B for arbitrary members of the structure. Is there any assurance of the existence of hypotheticals on our account in the special case in which the structure is the set of sentences of some formulation of first-order logic, and the implication relation is a deducibility relation?