David Grunberg

Our aim is to illuminate the interconnected notions of meaning and truth. For this purpose, we investigate the relationship between meaning theories based on commonsensical ‘means that’ and interpretive truth theories. The latter are Tarski–Davidson-style truth theories serving as meaning theories. We consider analytically true semantic principles containing ‘means’ and ‘means that’ side to side with ‘denotes’, ‘satisfies’, and ‘true’, which constitute the extensional semantic constants of interpretive truth theories. We show that these semantic constants are definable in terms of ‘means’ and ‘means that’ operators. The definitions themselves are semantic principles in the role of meaning postulates. We extend a meaning theory based on ‘means that’ by adjoining semantic principles to the axioms of the theory. Then, all axioms, hence all theorems, of a corresponding interpretive truth theory are provable in the extension of the meaning theory. Furthermore, every interpretive truth theory can be included in the extension of a corresponding meaning theory. Therefore, the extension of a meaning theory resulting from the adjunction of semantic principles constitutes a unified meaning-and-truth theory since it includes both a meaning theory and an interpretive truth theory.

Having drawn the distinction between logic as a discipline and logic as organon, this short paper focuses on the latter, the purpose of which is twofold. First, it highlights the importance of second-order logic and modal logic in ontology. To this aim, the role of second-order logic is illustrated in formalizing realist ontology committing to the existence of properties. It is also emphasized how quantified modal logic helps clarify de re/de dicto distinction that implicitly takes place in ordinary language. Secondly, the paper concentrates on the significance of modal logic in the philosophy of language. In pursuing this goal, we considered Kripke’s notions of rigid designator, necessary a posteriori and contingent a priori statements. Given the definition of rigid designator, it is possible to prove in quantified modal logic that an identity between proper names, like “Hesperus” and “Phosphorus”, if true, is necessarily true. But the truth of the identity statement “Hesperus = Phosphorus” is known a posteriori. Therefore, there are necessary a posteriori truths. There are also contingent a priori true statements like “The length of stick S at time t 0 = one meter”, as there exists a possible world in which this statement is false.

Previous work demonstrates that music with more surprising chords tends to be perceived as more enjoyable than music with more conventional harmonic structures. In that work, harmonic surprise was computed based upon a static distribution of chords. This would assume that harmonic surprise is constant over time, and the effect of harmonic surprise on music preference is similarly static. In this study we assess that assumption and establish that the relationship between harmonic surprise and music preference is not constant as time goes on. Analyses of harmonic surprise and preference from 1958 to 1991 showed increased harmonic surprise over time, and that this increase was significantly more pronounced in preferred songs. Separate analyses showed similar increases over the years from 2000 to 2019. As such, these findings provide evidence that the human perception of tonality is influenced by exposure. Baseline harmonic expectations that were developed through listening to the music of “yesterday” are violated in the music of “today,” leading to preference. Then, once the music of “today” provides the baseline expectations for the music of “tomorrow,” more pronounced violations—and with them, higher harmonic surprise values—become associated with preference formation. We call this phenomenon the “Inflationary-Surprise Hypothesis.” Support for this hypothesis could impact the understanding of how the perception of tonality, and other statistical regularities, are developed in the human brain.

Two alternative solutions to the problem of computing the values of theoretical quantities and of testing theoretical hypotheses are Sneed’s structuralist eliminationism and Glymour’s bootstrapping. Sneed attempts to solve the problem by eliminating theoretical quantities by means of the so-called Ramsey-Sneed sentence that represents the global empirical claim of the given theory. Glymour proposes to solve the problem by deducing the values of the theoretical quantities from the hypothesis to be tested. In those cases where the theoretical quantities are not strongly Ramsey-eliminable, eliminationism does not succeed in computing the values of theoretical quantities, and it is compelled to use bootstrapping in this task. On the other hand, we see that a general notion of bootstrapping provides a formally correct procedure for computing theoretical quantities, and thus contributes to the solution to the problem of testing theoretical hypotheses involving these quantities.