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In On Empirically Equivalent Systems of the World from 1975, Quine formulated a thesis of underdetermination roughly to the effect that every scientific theory has an empirically equivalent but logically incompatible rival, one that cannot be discarded merely as a terminological variant of the former. For Quine, the truth of this thesis was an open question. If true, some would argue that it undermines any belief in scientific theories that is based purely on their empirical success. But despite its potential significance, surprisingly little has been done by way of establishing or refuting it. My aim is to establish the thesis for as large a class of theories as possible. Under various precisifications of the concepts involved, I show that it holds for all consistent and recursively axiomatizable theories that postulate infinitely many theoretical entities.

In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can (in some suitable sense of the word) agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief (credence) in a null hypothesis after he has rejected it than before, then (in certain situations) he has to either have trivial or incoherent credences to begin with or fail to update his credences by conditionalization.

Some realists claim that theoretical entities like numbers and electrons are indispensable for describing the empirical world. Motivated by the meta-ontology of Quine, I take this claim to imply that, for some first-order theory T and formula $$\delta (x)$$ δ ( x ) such that $$T \vdash \exists x \delta \wedge \exists x \lnot \delta $$ T ⊢ ∃ x δ ∧ ∃ x ¬ δ , where $$\delta (x)$$ δ ( x ) is intended to apply to all and only empirical entities, there is no first-order theory $$T'$$ T ′ such that (a) T and $$T'$$ T ′ describe the $$\delta $$ δ :s in the same way, (b) $$T' \vdash \forall x \delta $$ T ′ ⊢ ∀ x δ , and (c) $$T'$$ T ′ is at least as attractive as T in terms of other theoretical virtues. In an attempt to refute the realist claim, I try to solve the general problem of nominalizingT (with respect to $$\delta $$ δ ), namely to find a theory $$T'$$ T ′ satisfying conditions (a)–(c) under various precisifications thereof. In particular, I note that condition (a) can be understood either in terms of syntactic or semantic equivalence, where the latter is strictly stronger than the former. The results are somewhat mixed. On the positive side, even under the stronger precisification of (a), I establish that (1) if the vocabulary of T is finite, a nominalizing theory can always be found that is recursive if T is, and (2) if T postulates infinitely many $$\delta $$ δ :s, a nominalizing theory can always be found that is no more computationally complex than T. On the negative side, even under the weaker precisification of (a), I establish that (3) certain finite theories cannot be nominalized by a finite theory.

Arguably, the proposition that Mark Twain is Samuel Clemens and the proposition that water is H2O are both a posteriori. Nevertheless, they both seem to be necessary. Ever since Davies and Humberstone (Philos Stud 38(1):1–31, 1980), it has been known that two-dimensional semantics can account for this fact. But two-dimensionalism isn’t the only theory on the market that purports to do so. In this paper, I will look at two alternatives, one by Scott Soames and one by Kathrin Glüer-Pagin and Peter Pagin, and argue that both of them fail. Regarding the former, I argue that the conceptually possible but metaphysically impossible worlds one is required to postulate are hard to conceive of on closer inspection. As for the latter, the proposal doesn’t work for certain modal sentences, and I show that it cannot be easily amended.

Many expressions intuitively have different epistemic andmodal profiles. For example, co-referring proper names are substitutable salva veritate in modal contexts but not in belief-contexts. Two-dimensional semantics, according to which terms have both a so-called primary and a secondary intension, is a framework that promises to accommodate and explain these diverging intuitions. The framework can be applied to indexicals, proper names or predicates. Graeme Forbes (2011) argues that the two-dimensional semantics of David Chalmers (2011) fails to account for so-called nested contexts. These are linguistic contexts where a sentence is embedded under both epistemic and modal operators. Chalmers and Rabern (2014) suggest a two-dimensional solution to the problem. Their semantics solves the nesting-problem, but at the cost of invalidating certain plausible principles.We suggest a solution that is both simpler and avoids this cost.