I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.

The author's motivation for constructing the calculi of this paper\nis so that time and tense can be "discussed together in the same\nlanguage" (p. 282). Two types of enriched propositional caluli for\ntense logic are considered, both containing ordinary propositional\nvariables for which any proposition may be substituted. One type\nalso contains "clock-propositional" variables, a,b,c, etc., for\nwhich only clock-propositional variables may be substituted and that\ncorrespond to instants or moments in the semantics. The other type\nalso contains "history-propositional" variables, u,v,w, etc., for\nwhich only history-propositional variables may (...) be substituted and\nthat correspond to maximally linearly ordered subsets of instants.\nThis second type is for tense logics in which time is not linear\nand where at any moment there may exist alternative future courses\nof events. Quantifiers are included in both types but only for clock-\nand history-propositional variables. However, these quantifiers are\ngiven an essentially substitutional interpretation. In addition,\nbesides each clock-propositional variable being true at exactly one\ninstant, the semantics requires that for each instant there be at\nleast one clock-propositional variable true at that instant, which\nin effect amounts to having each instant of the model "denoted" in\nthe formalism by some clock-propositional variable. Thus it is not\nsurprising that quantification over clock-propositional variables\nturns out to have a "well behaved first-order semantics" (p. 284).\n{One axiom relating history- with clock-propositions seems to need\nrevision: CKTauTbuAUabUba. Since the clock-propositional variables\nmight be true at the same instant the consequent should include an\nalternative, namely, LCab.} Besides the standard truth-functional\nand tense operators G,H,F,P, the author includes L for "it is\nalways the case that". The model-theoretic earlier-than relation\nordering instants and the semantic truth-at (an instant) relation\nare formalized by Uab and Taα (for a wff α) which\nare defined respectively as LCbPa (whenever the clock-proposition\nb is the case the clock-proposition a was the case) and LCaα\n(α is the case whenever the clock-proposition a is the case).\nBecause the future tense operators are definable in terms of U\nand T and the latter are definable in terms of L and P, the\ndual of H, the author notes that his completeness proofs can be\nrestricted to L and H as primitive and with the future tense\noperators used for other interpretations, especially Prior, A.'s\nindeterminist "it will be the case that", where time is not linear.\nThe author concludes with some rather technical observations showing\nthat "in ordinary tense logics the instants are nonstandard elements\nof the models. This provides", according to the author, "a semantic\npressure to build the instants into tense logic, so that they will\nappear as standard elements in the models" (p. 283). (shrink)

Epistemic decision theorists aim to justify Bayesian norms by arguing that these norms further the goal of epistemic accuracy—having beliefs that are as close as possible to the truth. The standard defense of Probabilism appeals to accuracy dominance: for every belief state that violates the probability calculus, there is some probabilistic belief state that is more accurate, come what may. The standard defense of Conditionalization, on the other hand, appeals to expected accuracy: before the evidence is in, one should expect (...) to do better by conditionalizing than by following any other rule. We present a new argument for Conditionalization that appeals to accuracy‐dominance, rather than expected accuracy. Our argument suggests that Conditionalization is a rule of coherence: plans that conflict with Conditionalization don't just prescribe bad responses to the evidence; they also give rise to inconsistent attitudes. (shrink)

Part of the Studies in Crime and Public Policy series, this book, written by one of the top philosophers of punishment, examines the main trends in penal theorizing over the past three decades. Duff asks what can justify criminal punishment, and then explores the legitimacy of actual practices by examining what would count as adequate justification for them. Duff argues that a "communicative conception of punishment," which he presents as a third way between consequentialist and retributive theories, offers the most (...) fruitful way of understanding punishment's meaning and justification. Duff addresses such questions as how much sentences should be constrained by proportionality requirements; what modalities of punishment best communicate their intended meaning; and what decisionmaking procedures he envisions. This book will appeal to criminologists, philosophers, and others interested in theories of punishment. (shrink)

In [1, §4], my ‘proof’ that GH1 has the finite model property is incorrect; there are considerable obscurities towards the end of §1, particularly on p. 33; and I should have exhibited the finite models for GH1. In §1 of this paper I expand the analysis of the sub-directly irreducible models for GH1 which I give in §1 of [1]. In §2 I give a correct proof that GH1 has the finite model property. In §3 I exhibit these finite models (...) as models on certain ordered sets. (shrink)

Gender discrimination and sexual harassment of female police officers by their male counterparts remain areas of liability where police departments appeared to have failed to effectively confront the nagging issues. However, the appreciable level of research conducted on these issues in the global North has not been matched by the South, where issues bordering on sexual violence have cultural underpinnings. Drawing from the case of the Nigeria Police Force, feminist analysis was used to explore the lived reality of 43 female (...) officers in a qualitative study. Participants expressed distress in abiding by structural discriminatory regulations against female officers which include non-admittance of married women into the force, forbidding unmarried officers from getting pregnant, and a stipulated minimum of three-year work period before a female officer can marry. Findings also indicated that participants suffer a variety of sexual harassment, intimidation, and, violence from their male colleagues, while they feel constrained in reporting their victimization. Important policy and practical implications requiring the Nigerian police to address hegemonic masculinity and promote gender equality were provided. (shrink)

Marcia Baron has offered an illuminating and fruitful discussion of extra-legal excuses. What is particularly useful, and particularly important, is her focus on our excusatory practices—on the ways and contexts in which we make, offer, accept, bestow and reject excuses: if we are to reach an adequate understanding of excuses, their implications and their grounds, we must attend to the roles that they can play in our human activities and relationships—and to the complexities and particularities of those roles. However, I (...) want to focus my comments less on the details of Baron’s discussions of excuses in extra-legal contexts than on the implications of her discussion for our understanding of excuses in the criminal law. What light (if any, a sceptic might add) can such analyses of our extra-legal concepts and practices throw on legal concepts and doctrines? (shrink)

The discovery of the microworld presented a serious trial for many systems of views held by mankind, including its logic. This world was found to lack the familiar solid bodies, the unchanging particles and interrelations between them, the reflection of which, in one way or another, is the logic of the macroscopic world. What elementary particle physics encountered in the microscopic world seemed illogical: the rest-mass of a particle equals zero; a part that is not smaller than the whole; a (...) particle that in diffraction experiments moved like a wave; and much else that was unusual and strange in the properties of elementary particles. One of these properties was actually so named by physicists — "strangeness.". (shrink)

In response to Lawrence Solum's advocacy of a ‘virtue–centred theory of judging’, I argue that there is indeed important work to be done in identifying and characterising those qualities of character that constitute judicial virtues – those qualities that a person needs if she is to judge well (though I criticise Solum's account of one of the five pairs of judicial vices and virtues that he identifies – avarice and temperance). However, Solum's more ambitious claims – that a judge's vice (...) necessarily corrupts her decisions, and that in at least some contexts we must define a legally correct decision as one that would be reached by a virtuous judge – should be rejected: we can undermine the former by attending to the requirements of due process, and the latter by attending to the ways in which a judge would try to justify her decision. (shrink)

In this article, we consider two independently appealing theories—the Growing-Block view and Humean Supervenience—and argue that at least one is false. The Growing-Block view is a theory about the nature of time. It says that past and present things exist, while future things do not, and the passage of time consists in new things coming into existence. Humean Supervenience is a theory about the nature of entities like laws, nomological possibility, counterfactuals, dispositions, causation, and chance. It says that none of (...) these entities are fundamental, since if they were, this would entail the existence of irreducible necessary connections between matters of fact. Instead, these entities supervene on a fundamental, non-nomological ‘Humean mosaic’ of property instances at spacetime points. We will further explain and motivate the Growing-Block view and Humean Supervenience in Sects. 2 and 3, but first, we turn to our master argument. (shrink)