Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think that (...) there is some sense in which arithmetic is true and determinate. (shrink)

The principle of Anteriority says that prospects that are identical from the perspective of every possible person’s welfare are equally good overall. The principle enjoys prima facie plausibility, and has been employed for various theoretical purposes. Here it is shown using an analogue of the St Petersburg Paradox that Anteriority is inconsistent with central principles of axiology.

(Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized to extensions of the language of arithmetic, and are applied to answer a (...) question posed by Bacon and Dorr (2024). (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of (...) LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

The notion of an extended simple region (henceforth ESR) has recently been marshalled in the service of arguments for a variety of conclusions. Exactly how to understand the idea of extendedness as it applies to simple regions, however, has been largely ignored, or, perhaps better, assumed. In this paper we first (§1) outline what we take to be the standard way that philosophers are thinking about extendedness, namely as an intrinsic property of regions. We then introduce an alternative picture (§2), (...) according to which extendedness is extrinsic. In §3 we argue that it matters which way of thinking about extendedness is the right one, since how ESRs behave is sensitive to what extendedness consists in, and various arguments that appeal to ESRs turn out to be unsound if extendedness is extrinsic rather than intrinsic. (shrink)

Moral encroachment is the thesis that morality has an effect---unrecognized by traditional epistemology---on which doxastic states are epistemically appropriate. The thesis is increasingly popular among those who, in opposition to Gendler (2011), desire harmony between epistemic and moral demands on belief. This paper has three main goals. First, drawing on attractive structural principles concerning belief and justification, it is shown that a thoroughgoing harmony between moral and epistemic demands is implausible. This weakens the motivation for positing moral encroachment, but a (...) proponent might still hope that moral encroachment can have a significant effect, so that many of the central cases of apparent disharmony can be avoided. The next goal of the paper is to argue that any significant effect of moral encroachment would manifest itself in the credences which are most epistemically appropriate. Finally, it is shown that even a small effect of moral encroachment on credence is in tension with widely accepted basic constraints on epistemically appropriate credence. (shrink)

Morgenbesser's Coin is a thought experiment that exemplifies a widespread disposition to infer counterfactual independence from causal independence. I argue that this disposition is mistaken by analysing a closely related thought experiment.

Moral encroachment is the thesis that morality has an effect---unrecognized by traditional epistemology---on which doxastic states are epistemically appropriate. The thesis is increasingly popular among those who, in opposition to Gendler (2011), desire harmony between epistemic and moral demands on belief. This paper has three main goals. First, drawing on attractive structural principles concerning belief and justification, it is shown that a thoroughgoing harmony between moral and epistemic demands is implausible. This weakens the motivation for positing moral encroachment, but a (...) proponent might still hope that moral encroachment can have a significant effect, so that many of the central cases of apparent disharmony can be avoided. The next goal of the paper is to argue that any significant effect of moral encroachment would manifest itself in the credences which are most epistemically appropriate. Finally, it is shown that even a small effect of moral encroachment on credence is in tension with widely accepted basic constraints on epistemically appropriate credence. (shrink)

This essay analyzes the implications of the performative aspects of Julia Kristeva 's Powers of Horror by situating this work in the context of similar aspects of her previous work. This construction and its relationship to abjection are integral components of Kristeva 's notion of practice and as such are fundamental to her critique of Hegel and Freud.

Various decision theories share a troubling implication. They imply that, for any finite amount of value, it would be better to wager it all for a vanishingly small probability of some greater value. Counterintuitive as it might be, this fanaticism has seemingly compelling independent arguments in its favour. In this paper, I consider perhaps the most prima facie compelling such argument: an Egyptology argument (an analogue of the Egyptology argument from population ethics). I show that, despite recent objections from Russell (...) (2023) and Goodsell (2021), the argument’s premises can be justified and defended, and the argument itself remains compelling. (shrink)