×

Again on relativistic semantics. (English) Zbl 0970.03507

From the introduction: This paper has two parts: Part I is a continuation of the author’s paper “A semantical theory connected with relativistic space-time” [in: U. Majer et al. (eds.), Semantical aspects of space-time theories, Proc. Symp., Bielefeld 1991, Wissenschaftsverlag, Leipzig, 53–65 (1994)] and as well as this it deals mainly with the logic of an auxiliary (semantical) theory, \({\mathcal S}{\mathcal T}\), in effect generally considered (by textbooks) within the semantics for a typical theory \({\mathcal T}\) of general relativity; and especially the modal features of this auxiliary theory are studied.
Part II deals with the influence by relativistic theories and especially by the new notion of space-time on pragmatic languages (in Carnap’s sense), so that they include, e.g., “now” and “here”. By means of some examples, in effect concerning the nearest star \(\Sigma\), one emphasizes that, in various cases, the causal present (causal past, or causal future) cannot be used as the present (past, or future respectively), ordinarily used in framing pragmatic semantical rules (based on classical physics): this use of the above causal notions would cause big mistakes, or more precisely big discrepancies with the meanings of ordinary pragmatic sentences about times and lengths. In order to frame pragmatic rules based on, e.g., general relativity one suggests the use of certain geodesic manifolds also depending on the 4-velocity of the speaker, or better on a reasonable 4-velocity of the human community being considered. Thus, in case also classical physics can be regarded as a good physical basis, no discrepancy arises.
Comments on this paper are given by M. Urchs in the same volume [ibid. 3, 37–42 (1995; Zbl 0969.03509)].

MSC:

03B30 Foundations of classical theories (including reverse mathematics)
00A30 Philosophy of mathematics
00A79 Physics
83A05 Special relativity

Citations:

Zbl 0969.03509
PDFBibTeX XMLCite
Full Text: DOI