Download Fibred Semantics and the Weaving of Logics Part 1: Modal and by Gabbay, D. M PDF

Download Fibred Semantics and the Weaving of Logics Part 1: Modal and by Gabbay, D. M PDF

By Gabbay, D. M

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Extra resources for Fibred Semantics and the Weaving of Logics Part 1: Modal and Intuitionistic Logics [paper]

Example text

Definitions Although certain points about the analysis of definitions belong in the later sections, it is necessary to take the subject up at this pointinorder that we can use the technique. We regard the definition of a new nominal symbol as the introduction of a new ob, the definiendum (which is named by that symbol), together with an axiom relating it to an old ob, the definiens, by a relation of identity which we symbolize by the infix ‘ ’. In a similar manner we treat the definition of certain nominal combinations as the introduction of a new operation (cf 9 B2).

The interpretation of one formal (or semiformal) system in another is important in modern logic. Under certain conditions, too complex to be considered at this stage, this gives rise to “models”. 4. Acceptability 23 We shall consider a few general principles concerning the reasons which lead us to choose a formal system for study. These reasons are relative to some purpose; when they are fulfilled for a given purpose, we say that the formal system is acceptable for that purpose. Naturally the most important criterion for acceptability is the validity of an interpretation in some field we are interested in.

A similar term was used by Legniewski (cf. Tarski [WBF] pp. 267-269 footnotes 3 and 5 ) . 1 SI SUPPLEMENTARY TOPICS 39 quantifier. Except for the present article we therefore pay no attention to the demands of nominalism. It is quite plausible that the conceptualistic manner of speaking which we employ can be translated into a nominalistic one. But the question of exactly how to make such a translation we leave open. For nominalistic theories in general we refer to Goodman [SAP] and to various papers by Quine collected in his [LPV].

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