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.

With his new riddle of induction, Goodman raised a problem for enumerative induction which many have taken to show that only some ‘natural’ properties can be used for making inductive inferences. Arguably, however, (i) enumerative induction is not a method that scientists use for making inductive inferences in the first place. Moreover, it seems at first sight that (ii) Goodman’s problem does not affect the method that scientists actually use for making such inferences—namely, classical statistics. Taken together, this would indicate that (iii) ‘naturalness’ is not such a relevant concept for the problem of induction, after all. I have no objections against (i) and (iii). But, contrary to (ii), I argue that classical statistics does face a version of Goodman’s problem, which I call the statistical riddle of induction. Given that his problem merely is an instance of the more general problem of underdetermination, this is hardly surprising. Perhaps more importantly, I also show how my riddle can be used for exposing a common fallacy in probabilistic reasoning, without relying on Bayesian assumptions.

In what sense, and to what extent, do rules of inference determine the meaning of logical constants? Motivated by the principle of charity, a natural constraint on the interpretation of logical constants is to make the rules of inference come out sound. But, as Carnap observed, although this constraint does rule out some non-standard interpretations, it does not rule them all out. This is known as Carnap’s problem. I suggest that a charitable interpretation of the logical constants should, as far as possible, make the rules of inference both sound and complete, and I show how this idea can be brought to bear on a successful solution to Carnap’s problem in the case of classical propositional logic, as well as classical first-order logic. In fact, the solution generalizes to any logic whose rules of inference are sound and complete with respect to a bivalent semantics that is classical with respect to negation.

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 δ(x)δ(x) such that T⊢∃xδ∧∃x¬δT⊢∃xδ∧∃x¬δ, where δ(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 δδ:s in the same way, (b) T′⊢∀xδT′⊢∀xδ, 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 nominalizing T (with respect to δδ), 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 δδ: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 Gluer-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.

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.

The main purpose of this paper is to investigate various notions of empirical equivalence in relation to the two main arguments for realism in the philosophy of science, namely the no-miracles argument and the indispensability argument. According to realism, one should believe in the existence of the theoretical entities (such as numbers and electrons) postulated by empirically adequate theories. According to the no-miracles argument, one should do so because truth is the the best explanation of empirical adequacy. According to the indispensability argument, one should do so because the theoretical terms employed in the formulation of an empirically adequate theory are practically indispensable for the formulation of its empirical content. The no-miracles argument might be refuted if one can establish an underdetermination thesis to the effect that every theory has empirically equivalent rivals that are incompatible with each other. Insofar as truth cannot explain the empirical adequacy of two incompatible theories, there is an obvious conflict between the underdetermination thesis and the no-miracles argument. I show that, under certain assumptions, some but not all notions of empirical equivalence support the underdetermination thesis. The indispensability argument might be refuted if one can establish a dispensability thesis to the effect that, for any theory with a practical formulation (e.g. for any axiomatizable theory), there is an empirically equivalent theory with a practical formulation in purely empirical terms. I show that (using axiomatizability as the measure of practicality) some but not all notions of empirical equivalence support this thesis.

When it comes to Kripke-style semantics for quantified modal logic, there’s a choice to be made concerning the interpretation of the quantifiers. The simple approach is to let quantifiers range over all possible objects, not just objects existing in the world of evaluation, and use a special predicate to make claims about existence (an existence predicate). This is the constant domain approach. The more complicated approach is to assign a domain of objects to each world. This is the varying domain approach. Assuming that all terms denote, the semantics of predication on the constant domain approach is obvious: either the denoted object has the denoted property in the world of evaluation, or it hasn’t. On the varying domain approach, there’s a third possibility: the object in question doesn’t exist. Terms may denote objects not included in the domain of the world of evaluation. The question is whether an atomic formula then should be evaluated as true or false, or if its truth value should be undefined. This question, however, cannot be answered in isolation. The consequences of one’s choice depends on the interpretation of molecular formulas. Should the negation of a formula whose truth value is undefined also be undefined? What about conjunction, universal quantification and necessitation? The main contribution of this paper is to identify two partial semantics for logical operators, a weak and a strong one, which uniquely satisfy a list of reasonable constraints (Theorem 2.1). I also show that, provided that the point of using varying domains is to be able to make certain true claims about existence without using any existence predicate, this result yields two possible partial semantics for quantified modal logic with varying domains.

A glass couldn't contain water unless it contained H2O-molecules. Likewise, a man couldn't be a bachelor unless he was unmarried. Now, the latter is what we would call a conceptual or analytical truth. It's also what we would call a priori. But it's hardly a conceptual or analytical truth that if a glass contains water, then it contains H2O-molecules. Neither is it a priori. The fact that water is composed of H2O-molecules was an empirical discovery made in the eighteenth century. The fact that all bachelors are unmarried was not. But neither is a logical truth, so how do we explain the difference? Two-dimensional semantics is a framework that promises to shed light on these issues. The main purpose of this thesis is to understand and evaluate this framework in relation to various alternatives, to see whether some version of it can be defended. I argue that it fares better than the alternatives. However, much criticism of two-dimensionalism has focused on its alleged inability to provide a proper semantics for certain epistemic operators, in particular the belief operator and the a priori operator. In response to this criticism, a two-dimensional semantics for belief ascriptions is developed using structured propositions. In connection with this, a number of other issues in the semantics of belief ascriptions are addressed, concerning indexicals, beliefs de se, beliefs de re, and the problem of logical omniscience.