According to Augustine, abstract objects are ideas in the mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the mind of God. Call such a view the “Augustinian View of Numbers” (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that the theory in Studtmann’s paper can interpret the axioms of Peano Arithmetic minus the induction schema. This fact allows for the development of arithmetic in a natural way. The development eventuates in a theory that can interpret second-order arithmetic. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, self-cause that contains objects that not only serve as numbers but also encode information about each other.

I argue that modal terms have an epistemic interpretation on which concessive knowledge attributions are semantically contradictory. This is compatible with the fallibilist view that the basis on which we know something need not entail it, but not with the view that what is known need not be epistemically certain or necessary. The apparent contradictoriness of concessive knowledge attributions is not due to mere implicature, nor to assertion updating the modal base. And it is contextually invariant. Concessive knowledge attributions contrast markedly with concessive assertions and Moorean conjunctions, whose infelicity is plausibly due to norms of assertion. I briefly explain why the strict fallibilism I recommend is compatible with our ordinary use of ‘know,’ and with our knowing much on the basis of perception. Its contextual shiftiness closely parallels our variably strict use of temporal and other invariant terms with strict application conditions.

This work introduces a causal explanation of the passage of time, and contrasts it with rival explanations. In the causal explanation, laws of physics are shown to entail that events are in causal succession, and the passage of time is defined as their causal succession. The causal explanation is coupled with phenomenology of the passage of time, and contrasted with the project of making sense of the idea that time does not pass.

Stalnaker’s Thesis about indicative conditionals says, roughly, that the probability one ought to assign to an indicative conditional is equal to the probability that one ought to assign to its consequent conditional on its antecedent. Skyrms’s Thesis about counterfactual conditionals says, roughly, that the probability that one ought to assign to a counterfactual conditional equals one’s rational expectation of the chance, at a relevant past time, of its consequent conditional on its antecedent. In this article, I develop a new uniform theory of conditionals that allows us to derive a tenable version of Skyrms’s Thesis from a tenable version of Stalnaker’s Thesis, together with a chance-deference relating rational credence to beliefs about objective chance.

A growing number of epistemologists have endorsed the Ignorance Norm for Inquiry. Roughly, this norm says that one should not inquire into a question unless one is ignorant of its answer. I argue that, in addition to ignorance, proper inquiry requires a certain kind of knowledge. Roughly, one should not inquire into a question unless one knows it has a true answer. I call this the Knowledge Norm for Inquiry. Proper inquiry walks a fine line, holding knowledge that there is an answer in the left hand and ignorance of the answer in the right.

Why ought we to perform the actions that we ought to perform? We can categorize the various answers to this question depending on whether they hold that the oughts governing actions are explained by the oughts governing non-actions. In this essay, I show how a handful of plausible claims from normative ethics, moral psychology, and the philosophy of action entail the conclusion that what an agent ought to do is explained by the attitudes she ought to have.

Many theorists assume that a request is sincere if the speaker wants the addressee to perform the act requested. I argue that this assumption predicts an implausible mismatch between sincere assertions and sincere directives and needs to be revised. I present an alternative view, according to which directive utterances can only be sincere if they are self-directed. Other-directed directives, however, can be genuine or fake, depending on whether the speaker wants the addressee to perform the act in question. Finally, I argue that this new perspective opens the door to a satisfying theory of authentic expression, for both assertive and directive utterances. Authenticity consists in the combination of genuine and sincere speech, for example, in the case of assertion, when speakers assert something which they both believe (sincerity) and want the addressee to believe (genuineness).

Moral error theory has many troubling and counterintuitive consequences. It entails, for example, that actions we ordinarily think of as obviously wrong are not wrong at all. This simple observation is at the heart of much opposition to error theory. I provide a new defense against it. The defense is based on the impossibility of finding satisfying solutions to a wide range of puzzles and paradoxes in moral philosophy. It is a consequence of this that if any moral claims are true, then a lot of highly troubling and counterintuitive moral claims must be in their number. This means that troubling and counterintuitive moral claims are everybody’s problem—not just error theorists’, but also their opponents’. Indeed, there is a sense in which this shared problem is worse for the opponents of error theory than for error theorists themselves.

This is a critique of Hanks’s theory of propositions, which identifies propositions with predicative act types imbued with assertoric force. This identification turns propositions into assertoric contexts. Disjunctive propositions obey a fine-grained logic: b asserting A does not entail b asserting the disjunction A or B. Conjunctive propositions obey a coarser-grained logic: b asserting the conjunction A and B entails b asserting A and b asserting B. Distribution of assertion over conjunction inverts the scope distribution of the force operator and the logical operator, whereby the former can also take narrow scope with respect to the latter. Non-conjunctive molecular propositions, however, need to suspend the force of their constituent propositions, but then why identify propositions with assertoric contexts? I show that Hanks’s theory both fails to formally validate distribution over conjunction and to accommodate the divergent behavior of its disjunctive and conjunctive propositions. Also, I argue that distribution is philosophically a bad idea, anyway.

The wave function of quantum mechanics can be understood in terms of the dispositional role it plays in the dynamics of a distribution of matter in three-dimensional space (or four-dimensional spacetime). There is more than one way, however, of specifying its dispositional role. This paper considers Suárez’s theory of ‘Bohmian dispositionalism’, in which the particles are endowed with their own ‘Bohmian dispositions’, and Simpson’s theory of ‘Cosmic Hylomorphism’, in which the particle configuration comprises a hylomorphic substance which has an intrinsic power. I argue that Bohmian dispositionalism fails to capture intuitively correct counterfactuals about what would happen in Small Worlds which have only a small number of particles, but that this problem is avoided by Cosmic Hylomorphism, in which the cosmic power manifests a teleological process.

Uniqueness appears to enhance intrinsic value. A unique stamp sells for millions of dollars; Stradivarius violins are all the more precious because they are unlike any others. This observation has not gone overlooked in the value theory literature: uniqueness plays a starring role recalibrating the dominant Moorean understanding of the nature of intrinsic value. But the thesis that uniqueness enhances intrinsic value is in tension with another deeply plausible and widely held thesis, namely the thesis that there is a pro tanto reason to promote the good. It is argued that there is a second, distinct type of uniqueness that plays a more interesting and important axiological role: uniqueness imparts irreplaceable value. This gives occasion to develop the surprisingly undertheorized notion of irreplaceable value.

Suppose two players wish to divide a finite set of indivisible items, over which each distributes a specified number of points. Assuming the utility of a player’s bundle is the sum of the points it assigns to the items it contains, we analyze what divisions are fair. We show that if there is an envy-free (EF) allocation of the items, two other desirable properties—Pareto-optimality (PO) and Maximinality (MM)—can also be satisfied, rendering these three properties compatible. But there may be no EF division, in which case some division must satisfy a modification of Bentham’s (1789/2017) “greatest satisfaction of the greatest number” property, called maximum Nash welfare (MNW), that satisfies PO. However, an MNF division may be neither MM nor EFX, which is a weaker form of EF. We conjecture that there is always an EFX allocation that satisfies MM, ensuring that an allocation is maximin, precisely the property that Rawls (1971/1999) championed. We discuss four broader philosophical implications of our more technical analysis.

This paper examines whether certain workers have a moral claim to decent wages for work that contributes to the social surplus in a fundamental way. This "fundamental" way refers to work whose fruits other members of society need to live acceptably good lives (not maximally good ones). The paper argues that what is due to this type of worker is based on the nature of the benefit that her labor produces for others in society and on the returned value that such labor should, by virtue of fair play considerations, command. The core of the argument in the paper is that such benefit is connected to an important dimension of human freedom, which is enabled by the absence of necessity to toil to secure subsistence in society. The paper also dwells on questions related to whose responsibility it should be to guarantee decent pay for contributions to society.

What explains why we are subjects for whom objects can have value, and what explains which objects have value for us? Axiologicians say that the value of humanity is the answer. I argue that our value, no matter what it is like, cannot perform this task. We are animals among others. An explanation of the value of objects for us must fit into an explanation of the value of objects for animals generally. Different objects have value for different animals. Those differences depend on differences in animal natures and, in particular, on the diverse characteristic capacities of different animals. Once we invoke animal natures, there is nothing for the value of animality, including the value of humanity, to explain.

In his article "Against Schmought" (The Journal of Philosophy, CXVIII 2021), Matthew Vermaire discusses the central problems I focus on in my book Choosing Normative Concepts (2017). Vermaire defends an attempted solution, or dissolution, of these problems. While there is much in Vermaire’s discussion to admire, I do not think Vermaire’s solution works, and here I explain why. Key to my response is the distinction between employing a concept and reasoning about the concept.