1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. To (...) follow this method is to introduce the central notions of the subject-matter to be investigated into a system governed by exact rules. For example, the constructionist method of investigating the properties of geometric figures may consist in formulating a system of postulates and definitions which, together with the apparatus of formal logic, generates all necessary truths concerning geometric figures. Similarly, a constructionist analysis of the notion of an individual may take the form of an axiomatic theory whose provable assertions are just those which seem essential to the role played by the concept of an individual in system atic contexts. Such axiomatic theories gain in interest if they are supple mented by precise semantical rules specifying the denotation of all terms and the truth conditions of all sentences of the theory. (shrink)

The conditions are examined under which one theory is said to be replaceable by another, while preserving those features of the original theory which made it serviceable for a given purpose. Among such replacements, special attention is given to ones which qualify as so-called reductions of a theory, and some theorems are proved concerning the notion of a reduction.

A tongue-in-cheek send-up of certain aspects of existentialism written by a well-known logician and philosopher who had a serious affair with existentialism in his youth. It was never submitted for publication and is finally being made available here posthumously with the permission of Helen Eberle. To the best of my recollection it was written some time in the mid/late 1980s. -- Gary H. Merrill.

According to the customary view, logic is a mere subdiscipline or ad junct of philosophy in so far as it is relevant to philosophy at all, and a sub discipline of mathematics to the extent that it is not. Thus, philosophy is taken to have traditional proprietary rights on "its" logic. I would like to examine here the reverse proprietary attitude, according to which philosophy is a branch of logic.

Alonzo Church has repeatedly argued that the semantic analysis of certain contexts requires reference to abstract entities of various kinds. The problem, arising from this argument for nominalists, will be examined first. Then we shall attempt to meet Church’s challenge by constructing and informally describing a semantics which was inspired by Nelson Goodman’s distinction between primary and secondary extensions. According to that semantics, no expression of the object language will make reference to any abstract or non-actual entity while the system (...) is strong enough to lend itself to semantic analysis in Church’s sense. (shrink)