(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)

It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a (...) related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision- theoretic implications. -/- The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgments about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to nonmeasurable regions. (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.

In an anonymous referee report written in 1945, Church suggested a sweeping argument against verificiationism, the thesis that every truth is knowable. The argument, which was published with due acknowledgement by Fitch almost two decades later, has generated significant attention as well as some interesting successor arguments. In this paper, we present the most important episodes in this intellectual history using the logic that Church himself favoured, and we give reasons for thinking that the arguments are less than decisive. However, (...) we present some new arguments against verificationism that we believe to be dialectically effective. (shrink)

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 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.

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)

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 (...) (Noûs, 2023) and Goodsell (Analysis 81(3):420–426, 2021), the argument’s premises can be justified and defended, and the argument itself remains compelling. (shrink)

The dóxa is a major aspect of Parmenides’ “scientific” commitment, as evidenced by studies of its discoveries in various fields of knowledge. Among them in astronomy. However, these studies have ended up identifying a scientific plan separate from the mythicalreligious and philosophical one of the first part. This survey explores the possibility of reconsidering the presence in the Parmenides’ dóxa of ontology and theology. It does so by proposing the hypothesis that the proem contains among the multiple semantic-linguistic layers the (...) mythopoeic presentation of the astronomical theorem of the identity of Eos and Hesperus, with the intent of showing, from the very beginning and in the most authoritative language for his audience, the alḗtheia of «being» on the divine stage of the celestial sphere. In our reading, therefore, the deities that enter the scene give life to a firmament that interconnects every cosmic dimension with each other and leads the one who knows (the εἰδότα φῶτα; B1, 3) – he knows that πᾶν πλέον ἐστὶν ὁμοῦ φάεος καὶ νυκτὸς because ἐπεὶ οὐδετέρωι μέτα μηδέν (B9, 3-4) – on the other side of the sky, in the presence of the theá that will reveal to him the meaning of everything. (shrink)

In this paper I will investigate the identity of the daímōn introduced by Parmenides in B12, 3 DK, the deity “who steers all things”. The importance of this deity is not adequately reflected in ancient doxography but in recent decades many scholars have reconsidered its role. I argue that in Parmenides’ poem this daímōn may play a relevant role in connecting the theological, ontological and cosmological planes. My purpose is to provide enough arguments for the hypothesis that the daímōn may (...) be the same goddess, Themis, who in the proem (B1, 28) is paired with Dike as a guide for Parmenides to the theá who will reveal to him the truth of tò eón, and in the part of the poem called alḗtheia (B8, 32) is echoed as the divine personification of the thémis of tò eón itself. I will examine the different identities and attributes found in the accounts on Parmenides’ daímōn and will compare them with the identities and attributes that the mythological tradition assigns to the goddess Themis. (shrink)