Talk (Work in Progress): Bruno Jacinto (MCMP/LMU)
Variables as Punctuation Marks
According to Frege variables are punctuation marks. They have no meaning. In particular, variables neither refer arbitrarily nor have as their semantic values objects with the property of being arbitrary.
The Fregean development of the view that variables are meaningless into a semantic theory for first-order languages is known to be inconsistent with the compositionality of these languages. Recently, Wehmeier (2018) proposed an alternative semantic theory that is both compositional and consistent with the view that variables have no meaning. Yet, as observed by Pickel and Rabern (unpublished), Wehmeier's theory has implausible commitments. These ultimately result from the fact that Wehmeier's account of the semantics of individual constants is akin to the Tarskian account of the semantics of variables.
A plausible compositional semantic theory for first-order languages on which variables are meaningless thus remains to be developed. The main aim of this talk is to propose and defend such a semantic theory, the VPM theory. Three main aspects characterise the VPM theory: 1) in general, expressions of first-order languages are context-dependent; 2) there is no one semantic operation that corresponds to the formation rule for atomic formulae; 3) formulae have as their semantic values entities of a kind that constitutes a generalisation of the Russellian notion of a propositional function. The VPM theory will be shown to be compositional and consistent with further data on the semantics of first-order languages.