A modal view of the semantics of theoretical sentences

Abstract

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these terms are introduced through the axioms of a theory.

A choice-semantical approach to theoretical truth

“…1 The second account originates from the Ramsey sentence and makes use of Hilbert's epsilon operator, thereby aiming at an explicit definition of theoretical terms ( [9,29]). 2 Whereas the former account is couched in semantic terms, the latter is purely syntactic. Neither approach, however,…”

New account of empirical claims in structuralism

“…What follows is an attempt to outline the basic ideas of an emendation of the linguistic approach to scientific theories which has been developed in Andreas (2007Andreas ( , 2009). This emendation is deeply inspired by Carnap's work on theoretical terms in Carnap (1939Carnap ( , 1956Carnap ( , 1958 as well as his Logical Syntax of Language (1937).…”

The Epsilon-Reconstruction of Theories and Scientific Structuralism

“…The objective in the first part of the paper will be to give a modernized presentation of the logic underlying Carnap's approach, in particular his use of Hilbert's epsilon-operator in the definition of theoretical terms. As we will see, a closer study of this logical framework and its standard choice-functional semantics will allow us to 2 For a discussion of this indefinite character of theoretical terms see, in particular, [2], [18], [25], and [43]. Carnap's work on the so-called "partial" or "indirect interpretation" of theoretical terms in [13] and [14] can be considered as an early systematic attempt to deal with this indefinite character of such terms.…”

“…1 Questions of this sort are usually referred to as "the problem of theoretical terms" (e.g. [28,37,2,25]). …”

“…Put differently, it is often the case that the reference of theoretical terms is not specified uniquely by the theory in which they occur. 2 A central topic in the literature is thus the question how to accommodate for this indefinite character of the theoretical vocabulary in the logical reconstruction of scientific theories. The second issue under discussion concerns the philosophical interpretation of different forms of theory reconstruction with respect to their ontological underpinnings.…”