Zachary Goodsell

In classical modal logic possibility is definable in terms of necessity: to be possible is to be not necessarily false. However, this identification is intuitionistically dubious. This paper uses an intensionalist higher-order logic to analyse necessity and possibility from an intuitionistic point of view. Surprisingly, this higher-order point of view indicates that the orthodox principles of intuitionistic possibility, influentially articulated by Fischer Servi, are unjustified. In addition to forcing a reevaluation of the intuitionistic principles of modal logic, the results reveal an interesting landscape for intuitionistic modal metaphysics that can only be seen from a higher-order perspective.

Standard decision theory ranks risky prospects by their expected utility. This ranking does not change if the values of all possible outcomes are uniformly shifted or dilated. Similarly, if the values of the outcomes are negated, the ranking of prospects by their expected utility is reversed. In settings with unbounded levels of utility, the expected utility of prospects is not always defined, but it is still natural to accept the affine symmetry principles, which say that the true ranking of prospects is unchanged by shifts and dilations, and is reversed by negation—even in hard cases where expected utilities are undefined. This paper investigates the affine symmetry principles and their consequences. The principles are found to be surprisingly powerful. Combined with orthodox axioms, they assign precise utility values to previously problematic cases: for example, to the Pasadena prospect (Nover & Hájek, 2004) and to the alternating St Petersburg prospect. They also have important structural consequences, notably vindicating Colyvan's (2008) Relative Expectation Theory. The paper then establishes the consistency of the affine symmetry principles. In light of their fruitful consequences, this consistency result supports the adoption of the affine symmetry principles as fundamental axioms of decision theory.

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.

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.

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.

(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).

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.

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.

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.