I investigate syntactic notions of theoretical equivalence between logical theories and a recent objection thereto. I show that this recent criticism of syntactic accounts, as extensionally inadequate, is unwarranted by developing an account which is plausibly extensionally adequate and more philosophically motivated. This is important for recent anti-exceptionalist treatments of logic since syntactic accounts require less theoretical baggage than semantic accounts.

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...) accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic. (shrink)

This book presents a critical analysis of the semantic incommensurability thesis of Thomas Kuhn and Paul Feyerabend. In putting forward the thesis of incommensurability, Kuhn and Feyerabend drew attention to complex issues concerning the phenomenon of conceptual change in science. They raised serious problems about the semantic and logical relations between the content of theories which deploy unlike systems of concepts. Yet few of the more extreme claims associated with incommensurability stand scrutiny. The argument of this book is as follows. (...) The terms of theories with different concepts diverge semantically and the vocabularies of such theories may not be fully intertranslatable. Given the possibility of referential overlap between the terms of conceptually divergent theories, it does not follow that the content of such theories is incomparable. Nor, given the distinction between understanding a language and translation from one language into another, does it follow that the proponents of mutually untranslatable theories are unable to communicate. Neither is it the case that the shift between conceptually divergent theories involves a discontinuous transition between theories which have no common reference or that refer to distinct worlds of their own making. The semantic differences resulting from conceptual variance may be embraced within a thoroughly realist framework on which they are construed as diverse linguistic relations to a fixed and independent reality. -/- The book, which was originally published in 1994, has now been re-issued in the Routledge Revivals series. -/- . (shrink)

One of the objections against the thesis of underdetermination of theories by observations is that it is unintelligible. Any two empirically equivalent theories — so the argument goes—are in principle intertranslatable, hence cannot count as rivals in any non-trivial sense. Against that objection, this paper shows that empirically equivalent theories may contain theoretical sentences that are not intertranslatable. Examples are drawn from a related discussion about incommensurability that shows that theoretical non-intertranslatability is possible.

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants Kripke-Feferman truth. The first, KF+CONS, features a consistent but partial truth predicate. The second, KF+COMP, an inconsistent but complete truth predicate. It is well-known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability under natural assumptions coincides with (...) definitional equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of KF+CONS and KF+COMP raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)

(First paragraph.) Ontology is often described as the inquiry into what exists, but there is some disagreement among (meta-) ontologists about what “existence” means and whether there are different kinds or senses of “existence” or just one; that is, whether “existence” is equivocal or univocal. Furthermore, there is a growing number of philosophers (many of whom take inspiration from Aristotle’s metaphysical writings) who argue that ontology should not be concerned so much with what exists, but with what is fundamental or (...) real (or something similar). Each of the positions in this debate is centered on a concept or small class of concepts that is intended to capture what ontology is about. Examples of such ontological core concepts are: existence, subsistence, Dasein, being, independent being, being real, being fundamental, being a fundamental constituent of reality, being irreducible. This paper intends to answer the twofold question of what (kind of notions) these ontological core concepts are, and how (and how much) they (can) differ. I will argue that there can be no difference between such concepts other than differing domains, and that any domain is a restriction in a maximally expanded universe, and therefore, equivalent to a (restricting) property. Furthermore, such differences between domains (or restricting properties) are intertranslatable, and consequently, there is not much room for substantial difference. Whatever difference remains is largely due to differences in focus or differences in the (phrasing of) questions ontologists try to answer. (shrink)