By Arnold Koslow

This is often surely some of the most progressive books written in philosophy. Koslow's structuralist method of common sense opens the potential for analogous functions in different components of philosophy. Get this publication. it is going to switch how you do philosophy.

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Extra resources for A Structuralist Theory of Logic

Example text

Conversely, suppose conditions 1 and 2, and suppose that C(A) is a filter condition. Conditions 1 and I' are identical. Moreover, given condition 2, we have only to show that for any E, if E ~ T, then C(E), to obtain 2'. Suppose that E ~ T. Then from C(1), and the assumption that Cis a filter condition, C(E). Thus, (I) and (I') are equivalent for any filter condition. In fact, it is also true that any condition C that is used in the strengthened schema (I') has to be a filter condition. In the remainder of this study we shall use schemata of the form (I).

An ~T B and only if some Ai is in K or B is in L. 1 The theoretical interest in bisections and the implication relations based upon them lies in the result that certain kinds of bisections provide a general concept of a truth-value assignment on arbitrary implication structures, with membership in L corresponding to "truth" [an insight essentially due to Scott (1974)]. With the aid of such bisections, a general concept of the extensionality of logical operators on arbitrary implication structures can be defined (see Chapter 19), and the extensionality or non extensionality of the logical operators in various implication structures can be studied.

This is fine if all one wants to do is characterize some syntactically designated set of sentences, called conjunctions, that are distinguished in form by their having the shape of "P & Q", where P and Q are sentences. Consequently, there are no conjunctions in the set S of "&"-less sentences with which Belnap begins his construction. On his account, one obtains conjunctions of the sentences of S only in the extension S& of S. On our view, however, there are situations in which there are conjunctions in S that Belnap's account misses - indeed, that cannot be picked out given his account of conjunction.