A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

Conventional wisdom has it that truth is always evaluated using our actual linguistic conventions, even when considering counterfactual scenarios in which different conventions are adopted. This principle has been invoked in a number of philosophical arguments, including Kripke’s defense of the necessity of identity and Lewy’s objection to modal conventionalism. But it is false. It fails in the presence of what Einheuser (2006) calls c-monsters, or convention-shifting expressions (on analogy with Kaplan’s monsters, or context-shifting expressions). We show that c-monsters naturally (...) arise in contexts, such as metalinguistic negotiations, where speakers entertain alternative conventions. We develop an expressivist theory—inspired by Barker (2002) and MacFarlane (2016) on vague predications and Einheuser (2006) on counterconventionals—to model these shifts in convention. Using this framework, we reassess the philosophical arguments that invoked the conventional wisdom. (shrink)

We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...) can be extended to counterpossibles more generally. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

"Aristotle was a systematic writer who often cross-referred to the definitions of terms given elsewhere in his work. Book 5 of the Metaphysics is important because it consists of definitions of the main uses of key terms in Aristotle's philosophy, and it is extremely valuable to have a commentary on this important text by Alexander of Aphrodisias, the leading commentator of his school. Alexander provides a detailed commentary on all of the thirty terms analysed in Book 5, weighing (...) alternative interpretations of what Aristotle says one against another, defending Peripatetic views against actual and possible criticisms, and attempting to integrate what is said in Book 5 into the context of the Metaphysics as a whole."--Bloomsbury Publishing. (shrink)

Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...) connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. (shrink)

I develop an expressivist account of verbal disagreements as practical disagreements over how to use words rather than factual disagreements over what words actually mean. This account enjoys several advantages over others in the literature: it can be implemented in a neo-Stalnakerian possible worlds framework; it accounts for cases where speakers are undecided on how exactly to interpret an expression; it avoids appeals to fraught notions like subject matter, charitable interpretation, and joint-carving; and it naturally extends to an analysis of (...) metalinguistic negotiations. (shrink)

These suggestions for the betterment and elucidation of the text of the De Beneficiis are additional to those already published in the Classical Quarterly in January, 1934. They are based on a conviction much deepened since that time that Buck1 is right when he says: N allein, und zwar ohne seine Ueberarbeitungen von späteren Händen, darf die Grundlage des Textes von de beneficiis bilden. Préchac3, the latest critical editor in this field, substantially confirms Buck's sweeping conclusion by an independent survey (...) of the evidence. The readings designated in the Teubner text3 as N2 and N3 are themselves conjectures, not readings drawn from independent sources of testimony, and as conjectures they must be judged. Gertz4 had long before discerned the truth even if he seemed somewhat cavalier in his attitude toward other manuscripts than N. (shrink)

A common objection to the very idea of conceptual engineering is the topic continuity problem: whenever one tries to “reengineer” a concept, one only shifts attention away from one concept to another. Put differently, there is no such thing as conceptual revision: there’s only conceptual replacement. Here, I show that topic continuity is compatible with conceptual replacement. Whether the topic is preserved in an act of conceptual replacement simply depends on what is being replaced (a conceptual tool or a conceptual (...) role) and what the topic under discussion is. Thus, the topic continuity problem only arises from a failure to specify these two things. (shrink)

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals (...) with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...) interpretation of the logical connectives. I argue this semantics compares favorably to the more common impossible worlds semantics, which faces difficulties interpreting propositionally quantified logic talk. (shrink)

The development of natural theology in the Middle Ages was driven by the rebirth experienced by Western Europe beginning in the 1000s owing to the emergence of stable monarchies and reconquest of the Iberian Peninsula. This expansion gave scholars access to the vast libraries of scientific and philosophical literature held in Arabic cultural centres – libraries that contained Aristotelian works on natural, ethical, and metaphysical sciences, which had for centuries been lost to the Latin West. The new texts fed the (...) growth of universities, where secular interests helped shape the curriculum, as the centre of intellectual gravity shifted from the monastery to the town. This chapter examines the figures that represent various moments in the medieval tradition, during and after these developments. Anselm and Abelard immediately predate the universities and recovery of Aristotle. Aquinas and John Duns Scotus write on either side of the Condemnations of 1277. Raymonde of Sabunde's work first applies the expression ‘natural theology’ to Christian practice, and Yves of Paris seeks late into the seventeenth century to revitalize this project. The chapter begins with a brief discussion of Aquinas' thought and influence. (shrink)

This commentary argues that the observed heterogeneity in fairness views, documented in many economic experiments, poses a challenge to the partner choice theory developed by Baumard et al. It also discusses the extent to which their theory can explain how people consider inequalities due to pure luck.

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...) with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

It is shown that one common formulation of Stalnaker's semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason 1967; Stalnaker 1970 and Lewis 1973, ch. 6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the Limit Assumption is (...) stated. I close with some remarks about what this means for the logic of conditionals. (shrink)

Counterfactual scepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had ϕ obtained, then ϕ □→ ψ is false. This principle seems to follow from two fairly weak principles, namely, that ‘chance ensures could’ and that ϕ □→ ψ and ϕ ⋄→ ¬ ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: given some modest (...) closure principles, they entail absurdities. Moreover, on the most promising strategy for saving these principles, they do not, in the relevant sense, entail the chance-undermines-would principle. Instead, they entail a principle that only supports counterfactual indeterminism, the view that most ordinary counterfactuals are chancy, that is, not settled true. I demonstrate this by developing an indeterminist semantics that vindicates the clash and chance-ensures-could principles but not the chance-undermines-would principle. This view, I argue, offers a better account of our credal and linguistic judgements than counterfactual scepticism. (shrink)

While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of cross-world predication, whereby objects in one world are related to objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts (...) of cross-world predication all leave something to be desired. I then propose an account of cross-world predication based on quantified hybrid logic and show how it overcomes the limitations of these previous accounts. I will conclude by discussing various philosophical consequences and applications of such an account. (shrink)

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...) accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic. (shrink)

Recently, Yudkowsky and Soares (2018) and Levinstein and Soares (2020) have developed a novel decision theory, Functional Decision Theory (FDT). They claim FDT outperforms both Evidential Decision Theory (EDT) and Causal Decision Theory (CDT). Yet FDT faces several challenges. First, it yields some very counterintuitive results (Schwarz 2018; MacAskill 2019). Second, it requires a theory of counterpossibles, for which even Yudkowsky and Soares (2018) and Levinstein and Soares (2020) admit we lack a “full” or “satisfactory” account. Here, I focus on (...) the latter problem of counterpossibles. My aim is to establish two claims. First, the problem of counterpossibles does not even arise without a fairly strong assumptionone that rarely applies to human agents, but may apply to artificial agents. And second, even given this assumption, the problem is solvable, though how best to solve it remains an open question. (shrink)

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often justified (...) only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

A supplemental document for "Metalinguistic Gradability".

Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with propositional quantifiers, which (...) are necessary for regimenting some logic talk. Second, it develops an alternative framework based on logical expressivism, which explains logic talk using shifting conventions. When combined with the standard S5π+ semantics for propositional quantifiers, this framework results in a well-behaved system that does not face the problems of the impossible worlds semantics. It can also be naturally extended with hybrid operators to regiment a broader range of logic talk, e.g., claims about what laws hold according to other logics. The resulting system, called hyperlogic, is therefore a better framework for modeling logic talk than previous accounts. (shrink)

Alexander W. Hall - Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio - Journal of the History of Philosophy 46:1 Journal of the History of Philosophy 46.1 170-172 Muse Search Journals This Journal Contents Reviewed by Alexander W. Hall Clayton State University John Lee Longeway, translator. Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III–II: De Syllogismo (...) Demonstrativo, and Selections from the Prologue to the Ordinatio. Notre Dame, IN: University of Notre Dame Press, 2007. Pp. xx + 432. Cloth, $58.00. William of Ockham never delivered his promised exposition of Posterior Analytics. In its place, we have Summa Logicae III–II, and the Prologue to his Ordinatio... (shrink)

Norwegian School of Economics and Business Administration and Chr. Michelsen Institute, Norway, bertil.tungodden{at}nhh.no ' + u + '@' + d + ' '//--> Liberal egalitarian theories of justice argue that inequalities arising from non-responsibility factors should be eliminated, but that inequalities arising from responsibility factors should be accepted. This article discusses how the fairness argument for redistribution within a liberal egalitarian framework is affected by a relocation of the cut between responsibility and non-responsibility factors. The article also discusses the claim (...) that equalization of some non-responsibility factors will reduce the ideal level of redistribution. Key Words: responsibility • liberal egalitarianism • redistribution. (shrink)

It is a central political goal to secure disabled individuals the same opportunities as others to pursue their conception of a good life. This goal reflects an ambition to combine an egalitarian and a liberal moral intuition. In this article, we analyse how disabled individuals who take part in economic activity should be compensated in order to respect these two intuitions. The article asks how a system of disability compensation should be structured and what the level of such compensation should (...) be. It also analyses how the answers to these questions depend on whether the disabled individuals are held responsible for their choice of work effort. (shrink)

A supplemental document for "The Logic of Hyperlogic. Part A: Foundations".

THE PROBLEM OF THE INTERPRETATION OF HAMANN Johann Georg Hamann is an intriguing but poorly known figure in the contemporary intellectual world. Yet this is the man whom Kierkegaard saluted as "Emperor!", whose writings were to have been arranged for publication by none other than Goethe himself, and whom Dilthey numbered among the primordial figures in the rise of modern historical consciousness. There are reasons for the persistence of this general ignorance. Hamann is deep. And, in addition, there is his (...) forbidding style. The readers of Kierkegaard and Dilthey, two other giants who them selves achieved late recognition, have not had to face this kind of imposing obstacle. Not only does Hamann expect his readers to handle themselves in deep water, but to intuit their way between his ideas which bob up like islands with no visible connection between them. Like Kierkegaard too, Hamann has had his troubles with the public. He himself referred to the hope that he would be understood by a "better posterity". In fact only the last few years have seen the printing of some of his more controversial writings, in particular his theories on the nature of human sexuality. (shrink)

A country's right to levy taxes is a fundamental aspect of its sovereignty. Without the power to tax, a government would be unable to redistribute resources among its citizens and provide public goods. The question of how tax rights should be distributed is therefore one of the oldest and most important problems of tax theory. Increased international economic integration has made this question even more important, as a larger share of economic transactions take place across national borders, giving rise to (...) situations in which more than one country is able to tax the same base.How such conflicts are resolved affects both the ability of countries to redistribute resources domestically and the international distribution of tax revenues. The allocation of tax rights therefore raises important questions of distributive justice, questions that require a normative theory of the right to tax. This essay seeks to evaluate the current distribution of tax rights by examining whether it can in fact be justified within the main approaches to distributive justice. (shrink)

Distance and morality. I argue that in "Faminine Ethics: the Problem of Distance in Morality and Singer's Ethical Theory" Frances Kamm fails to produce a pair of cases in which a moral difference is present that is not attributable to factors other than distance. I also point out that Kamm's attempts at explaining why distance could possibly matter in morality fall far short. I conclude that there is no reason for us to believe that distance matters in morality and offer (...) an explanation for why it might nevertheless appear to us that it does---there are numerous factors, normally correlated with distance, that are of great moral significance. In the process I offer a few methodological remarks. ;The problem of numbers. I argue that John Taurek's conclusion in "Should the Numbers Count?" remains a viable alternative to the standard view of the role of numbers in morality. I claim that Taurek brings up valid concerns regarding the standard view, and that the objections that have so far been raised against Taurek's position are by far insufficient to remove it from contention. I then point out and try to address several problems, including the problem of very large numbers, which should be a concern to anyone who is sympathetic to Taurek's views. I do not claim to have the answers, but I suggest a direction in which one may look for a solution. ;The return of the trolley. I examine several purported solutions to the Trolley Problem and find them all severely deficient. In light of the systematic failure of efforts to solve the Trolley Problem, I suggest that perhaps no solution has been found because there is no solution to find. I proceed to give a positive argument for the claim that diverting the trolley is not morally permissible and try to give an explanation of how the intuitions of the majority could have been so deeply mistaken. Since my proposed "solution" relies heavily on the making/allowing distinction, I conclude with a discussion of that distinction and a defense of its moral significance. (shrink)