By Arnold Koslow
This is often surely some of the most innovative books written in philosophy. Koslow's structuralist method of good judgment opens the potential for analogous purposes in different parts of philosophy. Get this e-book. it's going to switch how you do philosophy.
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Additional info for A Structuralist Theory of Logic
We shall, whatever the history of these events may be, keep to the insights of those early papers that set forth a general account of implication relations. Before we turn to a discussion of the various kinds of implication relations and their uses, there are two points that may have raised the reader's curiosity. One concerns the possibility of emending or varying the six conditions that we have used to characterize implication relations. The other point concerns the status of the conditions that we have adopted (see Chapter 10).
An 1= B if and only if every interpretation that assigns "true" to all the A;'s also assigns "true" to B. 2 It is easy to see that "1=" is an implication relation. The details are familiar and need not be reviewed here. Although these examples qualify as implication relations, some of the details of their construction are misleading in regard to the general picture. For one thing, both examples usually concern systems of sentences (of the propositional, predicate, or some higher-order theories).
Belnap's account is satisfactory for the special case that it covers, but it is only a limited case, for it requires that in order for expressions to be conjunctions, each must have a conjunctive sign like "&" embedded in it. Consider, first, what might be called the case of the missing conjunction. " 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.
A Structuralist Theory of Logic by Arnold Koslow