In this paper, we propose a unified account of conditionals inspired by Frank Ramsey. Most contemporary philosophers agree that Ramsey’s account applies to indicative conditionals only. We observe against this orthodoxy that his account covers subjunctive conditionals as well—including counterfactuals. In light of this observation, we argue that Ramsey’s account of conditionals resembles Robert Stalnaker’s possible worlds semantics supplemented by a model of belief. The resemblance suggests to reinterpret the notion of conditional degree of belief in order to overcome a (...) tension in Ramsey’s account. The result of the reinterpretation is a tenable account of conditionals that covers indicative and subjunctive as well as qualitative and probabilistic conditionals. (shrink)

The current special issue focuses on logical and probabilistic approaches to reasoning in uncertain environments, both from a formal, conceptual and argumentative perspective as well as an empirical point of view. In the present introduction we give an overview of the types of problems addressed by the individual contributions of the special issue, based on fundamental distinctions employed in this area. We furthermore describe some of the general features of the special issue.

Normality judgements are frequently used in everyday communication as well as in biological and social science. Moreover they became increasingly relevant to formal logic as part of defeasible reasoning. This paper distinguishes different kinds of normality statements. It is argued that normality laws like “Birds can normally fly” should be understood essentially in a statistical way. The argument has basically two parts: firstly, a statistical semantic core is mandatory for a descriptive reading of normality in order to explain the logical (...) features of normality laws. Secondly, a statistical justification of normality statements can be derived by game theoretic considerations if the normality law is understood as communication convention. (shrink)

What distinguishes indicative conditionals from subjunctive conditionals, according to one popular view, is that the so-called Adams’ thesis holds for the former kind of conditionals but the so-called Skyrms’ thesis for the latter. According to a plausible metaphysical view, both conditionals and chances supervene on non-modal facts. But since chances do not supervene on facts about particular events but facts about event-types, the past as well as the future is chancy. Some philosophers have worried that this metaphysical view is incompatible (...) with the aforementioned view on the probability of conditionals. This paper however shows that there is no need to worry, as these views can all be simultaneously satisfied within the so-called Multidimensional Possible World Semantics for conditionals. (shrink)

This paper develops a Multidimensional Decision Theory and argues that it better captures ordinary intuitions about fair distribution of chances than classical decision theory. The theory is an extension of Richard Jeffrey’s decision theory to counterfactual prospects and is a form of Modal Consequentialism, according to which the value of actual outcomes often depends on what could have been. Unlike existing versions of modal consequentialism, the multidimensional decision theory allows us to explicitly model the desirabilistic dependencies between actual and counterfactual (...) outcomes that, I contend, are at the heart of common intuitions about fair distribution of chances. (shrink)

It has recently been argued that indeterminacy and indeterminism make most ordinary counterfactuals false. I argue that a plausible way to avoid such counterfactual skepticism is to postulate the existence of primitive modal facts that serve as truth-makers for counterfactual claims. Moreover, I defend a new theory of ‘might’ counterfactuals, and develop assertability and knowledge criteria to suit such unobservable ‘counterfacts’.

In contemporary works on conditionals, the Ramsey test is a procedure for the evaluation of conditional sentences. There are several versions of the test, all inspired by a footnote by the British philosopher and mathematician Frank Ramsey, in his General Propositions and Causality. However, no study on Ramsey's own account of conditionals has been put forth so far. Furthermore, the footnote seems to cover indicative conditionals only, and this has led to the belief that no account of counterfactuals can be (...) found in Ramsey's work. In this paper, I recover Ramsey's account of counterfactuals and show that it is sketched in the footnote too. The result is a well-developed account of counterfactuals that resembles many contemporary ones. But Ramsey uses the same approach also for other types of conditionals, and this casts doubts on the current criteria for the classification of this type of sentences. (shrink)

There seem to be two ways of supposing a proposition: supposing “indicatively” that Shakespeare didn’t write Hamlet, it is likely that someone else did; supposing “subjunctively” that Shakespeare hadn’t written Hamlet, it is likely that nobody would have written the play. Let P be the probability of B on the subjunctive supposition that A. Is P equal to the probability of the corresponding counterfactual, A □→B? I review recent triviality arguments against this hypothesis and argue that they do not succeed. (...) On the other hand, I argue that even if we can equate P with P, we still need an account of how subjunctive conditional probabilities are related to unconditional probabilities. The triviality arguments reveal that the connection is not as straightforward as one might have hoped. (shrink)

The pattern of credences we are inclined to assign to counterfactuals challenges standard accounts of counterfactuals. In response to this problem, the paper develops a semantics of counterfactuals in terms of the epsilon-operator. The proposed semantics stays close to the standard account: the epsilon-operator substitutes the universal quantifier present in standard semantics by arbitrarily binding the open world-variable. Various applications of the suggested semantics are explored including, in particular, an explanation of how the puzzling credences in counterfactuals come about.

According to James Woodward’s influential interventionist account of causation, X is a cause of Y iff, roughly, there is a possible intervention on X that changes Y. Woodward requires that interventions be merely logically possible. I will argue for two claims against this modal character of interventions: First, merely logically possible interventions are dispensable for the semantic project of providing an account of the meaning of causal statements. If interventions are indeed dispensable, the interventionist theory collapses into a counterfactual theory (...) of causation. Thus, the interventionist theory is not tenable as a theory of causation in its own right. Second, if one maintains that merely logically possible interventions are indispensable, then interventions with this modal character lead to the fatal result that interventionist counterfactuals are evaluated inadequately. Consequently, interventionists offer an inadequate theory of causation. I suggest that if we are concerned with explicating causal concepts and stating the truth-conditions of causal claims we best get rid of Woodwardian interventions. (shrink)

This paper examines a neglected puzzle about conditionals: namely, the fact that each of a pair of conditionals with incompatible consequents, [A > C] and [B > C*], may be properly affirmable in circumstances when one does not believe, and is not entitled to infer, the denial of the conjunction of the antecedents, i.e. ~(A & B). The puzzle is why this should be so, since the conditionals entail the conjunction on the popular accounts of conditionals. I present a pragmatic (...) solution which distinguishes between two levels of affirmability. (shrink)

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$ ¬ ◊ (...) ( p ∧ ¬ q ) ∧ ◊ p ∧ ◊ ¬ q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. (shrink)

The variably strict analysis of conditionals does not only largely dominate the philosophical literature, since its invention by Stalnaker and Lewis, it also found its way into linguistics and psychology. Yet, the shortcomings of Lewis–Stalnaker’s account initiated a plethora of modifications, such as non-vacuist conditionals, presuppositional indicatives, perfect conditionals, or other conditional constructions, for example: reason relations, difference-making conditionals, counterfactual dependency, or probabilistic relevance. Many of these new connectives can be treated as strengthened or weakened conditionals. They are definable conditionals. (...) This article develops a technique to infer the logic for such definable conditionals from the known logic of the underlying defining conditional. The technique is applied to central examples. The results show that a large part of the zoo of conditionals arises from a basic conditional—a constant nucleus of the different contextual and conceptual variations of variably strict conditionals. (shrink)

According to the Counterfactual Comparative Account of harm and benefit, an event is overall harmful for a subject to the extent that this subject would have been better off if it had not occurred. In this paper we present a challenge for the Counterfactual Comparative Account. We argue that if physical processes are chancy in the manner suggested by our best physical theories, then CCA faces a dilemma: If it is developed in line with the standard approach to counterfactuals, then (...) it delivers that the value of any event for a subject is indeterminate to the extreme, ranging from terribly harmful to highly beneficial. This problem can only be avoided by developing CCA in line with theories of counterfactuals that allow us to ignore a-typical scenarios. Doing this generates a different problem: when the actual world is itself a-typical we will sometimes get the result that the counterfactual nonoccurrence of an actual benefit is itself a benefit. An account of overall harm bearing either of these two implications is deficient. Given the general aspiration to account for deprivational harms and the dominance of the Counterfactual Comparative Account in this respect, theorists of harm and benefit face a deadlock. (shrink)

In this paper, I propose and defend a pair of necessary conditions on evidence-based knowledge which bear resemblance to the troubled sensitivity principles defended in the philosophical literature. We can think of the traditional principles as simple but inaccurate approximations of the new proposals. Insofar as the old principles are intuitive and used in scientific and philosophical contexts, but are plausibly false, there’s a real need to develop precise and correct formulations. These new renditions turned out to be more cautious, (...) so they won’t be able to do everything the old principled promised they could. For example, they respect closure for knowledge. But these sober formulations, or something like them, might be the best that we can do with respect to sensitivity. And there’s value in understanding the limits to these types of principles. (shrink)

Just as knowledge contextualism offers a way out of knowledge skepticism in the face of powerful skeptical arguments, counterfactual contextualism purports to answer the many compelling arguments for the skeptical thesis that most ordinary counterfactuals of the form ‘if A had happened, C would have happened’, are false. In this article I review a few of the arguments for counterfactual skepticism, before surveying the various types of contextualist responses. I then discuss some of the recent objections to counterfactual contextualism, with (...) an eye toward weighing contextualism's costs with the costs of accepting skepticism. I conclude by remarking on some of the implications that skepticism and contextualism each has for many disputes in metaphysics. (shrink)

ABSTRACT The apparent consistency of Sobel sequences famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if is asserted prior to —the second counterfactual asserted no longer rings true. This (...) is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this cost is acceptable. (shrink)

We will present a new lottery-style paradox on counterfactuals and chance. The upshot will be: combining natural assumptions on the truth values of ordinary counterfactuals, the conditional chances of possible but non-actual events, the manner in which and relate to each other, and a fragment of the logic of counterfactuals leads to disaster. In contrast with the usual lottery-style paradoxes, logical closure under conjunction—that is, in this case, the rule of Agglomeration of counterfactuals—will not play a role in the derivation (...) and will not be entailed by our premises either. We will sketch four obvious but problematic ways out of the dilemma, and we will end up with a new resolution strategy that is non-obvious but less problematic: contextualism about what counts as a proposition. This proposal will not just save us from the paradox, it will also save each premise in at least some context, and it will be motivated by independent considerations from measure theory and probability theory. (shrink)

Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in (...) philosophy”—to adapt Wigner’s phrase—is analogous to that of mathematical explanations in science. As success-criteria for mathematical philosophy, we propose that it should be correct, responsive, illuminating, promising, relevant, and adequate. (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)

Weak ontic necessity is the ontic necessity expressed by “should/ought to” in English. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds at the present world is irrelevant to whether its prejacent holds at the present world. In this paper, by combining premise semantics and update semantics for conditionals, we present a logical theory for conditional weak ontic necessity based on context update. A context is a set of (...) ordered defaults, determining expected possible states of the present world. Sentences are evaluated with respect to contexts. When evaluating the conditional weak ontic necessity with respect to a context, we first update the context with the antecedent, then check whether the consequent holds with respect to the updated context. We compare this theory to some related works. The logic’s expressivity is studied. (shrink)

The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...) absolute and relative frequencies, two empirical notions, are used to empirically test, or confirm, hypotheses about objective chances, a metaphysical notion, as a role-model. Specifically, I want to use this probabilistic account of the testing of chance hypotheses as a role-model for the account of the testing of counterfactuals, another metaphysical notion, that I will present in Sections 4 to 8. I will conclude by comparing my proposal to one non-probabilistic and one probabilistic alternative in Section 9. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the (...) counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals. (shrink)

Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, counterfactuals have truth conditions-roughly, a counterfactual is true (...) when the corresponding conditional chance is sufficiently high. I argue that problems arise from the disparity between truth and high chance, between approximate truth and high chance, and from counterfactuals for which the corresponding conditional chances are undefined. However, Edgington, Leitgeb and I can unite in opposition to Stalnaker and Lewis-style ‘similarity’ accounts of counterfactuals. (shrink)

Are counterfactuals with true antecedents and consequents trivially true? The principle of Conjunction Conditionalization →) is highly controversial. Many philosophers view it as an attractive feature of Lewis’s semantics for counterfactuals that it can easily be modified to avoid this principle. However, Walters and Williams beg to differ. They argue that Conjunction Conditionalization is an indispensable ingredient of any Lewisian semantics, since CC is entailed by standard Lewisian theorems and a plausible semantic claim about irrelevant semifactuals. If this is true, (...) the entire tradition of revisionist counterfactual semantics is misguided, and so are many philosophical theories in which counterfactuals play a role. We argue, in defense of the revisionist tradition, that Walters and Williams’ ‘plausible semantic claim’ is in fact anything but plausible. It turns out to entail semantic principles far more controversial than Conjunction Conditionalization. (shrink)

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...) to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this. (shrink)

Thought experiments invite us to evaluate philosophical theses by making judgements about hypothetical cases. When the judgements and the theses conflict, it is often the latter that are rejected. But what is the nature of the judgements such that they are able to play this role? I answer this question by arguing that typical judgements about thought experiments are in fact judgements of normal counterfactual sufficiency. I begin by focusing on Anna-Sara Malmgren’s defence of the claim that typical judgements about (...) thought experiments are mere possibility judgements. This view is shown to fail for two closely related reasons: it cannot account for the incorrectness of certain misjudgements, and it cannot account for the inconsistency of certain pairs of conflicting judgements. This prompts a reconsideration of Timothy Williamson’s alternative proposal, according to which typical judgements about thought experiments are counterfactual in nature. I show that taking such judgements to concern what would normally hold in instances of the relevant hypothetical scenarios avoids the objections that have been pressed against this kind of view. I then consider some other potential objections, but argue that they provide no grounds for doubt. (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

The present paper investigates the first step of rational belief acquisition. It, thus, focuses on justificatory relations between perceptual experiences and perceptual beliefs, and between their contents, respectively. In particular, the paper aims at outlining how it is possible to reason from the content of perceptual experiences to the content of perceptual beliefs. The paper thereby approaches this aim by combining a formal epistemology perspective with an eye towards recent advances in philosophy of cognition. Furthermore the paper restricts its focus, (...) it concentrates on the case of color perception and perceptual beliefs about color. (shrink)

We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.

We show that five important elements of the ‘nomological package’— laws, counterfactuals, chances, dispositions, and counterfactuals—needn’t be a problem for the Growing-Block view. We begin with the framework given in Briggs and Forbes (in The real truth about the unreal future. Oxford studies in metaphysics. Oxford University Press, Oxford, 2012 ), and, taking laws as primitive, we show that the Growing-Block view has the resources to provide an account of possibility, and a natural semantics for non-backtracking causal counterfactuals. We show (...) how objective chances might ground a more fine-grained concept of feasibility, and furnished a places in the structure where causation and dispositions might fit. The Growing-Block view, thus understood, provides the resources to explain the close link between modality and tense, so that it predicts modal change as time passes. This account lets us capture not only what the future might hold for us, and also what might have been. (shrink)

This article presents an extension of Lewis’ analysis of counterfactuals to a graded framework. Unlike standard graded approaches, which use the probabilistic framework, we employ that of many-valued logics. Our principal goal is to provide an adequate analysis of the main background notion of Lewis’ approach—the one of the similarity of possible worlds. We discuss the requirements imposed on the analysis of counterfactuals by the imprecise character of similarity and concentrate in particular on robustness, i.e., the requirement that small changes (...) in the similarity relation should not significantly change the truth value of the counterfactual in question. Our second motivation is related to the logical analysis of natural language: analyzing counterfactuals in the framework of many-valued logics allows us to extend the analysis to counterfactuals that include vague statements. Unlike previous proposals of this kind in the literature, our approach makes it possible to apply gradedness at various levels of the analysis and hence provide a more detailed account of the phenomenon of vagueness in the context of counterfactuals. Finally, our framework admits a novel way of avoiding the Limit Assumption, keeping the core of Lewis’ truth condition for counterfactuals unchanged. (shrink)

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) (...) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP (...) _3.4_ Infinite sums _3.5_ Definition of NAP functions via infinite sums _3.6_ Relation to numerosity theory _4_ Objections and Replies _4.1_ Cantor and the Archimedean property _4.2_ Ticket missing from an infinite lottery _4.3_ Williamson’s infinite sequence of coin tosses _4.4_ Point sets on a circle _4.5_ Easwaran and Pruss _5_ Dividends _5.1_ Measure and utility _5.2_ Regularity and uniformity _5.3_ Credence and chance _5.4_ Conditional probability _6_ General Considerations _6.1_ Non-uniqueness _6.2_ Invariance Appendix. (shrink)

Ordinary Language Philosophy has largely fallen out of favour, and with it the belief in the primary importance of analyses of ordinary language for philosophical purposes. Still, in their various endeavours, philosophers not only from analytic but also from other backgrounds refer to the use and meaning of terms of interest in ordinary parlance. In doing so, they most commonly appeal to their own linguistic intuitions. Often, the appeal to individual intuitions is supplemented by reference to dictionaries. In recent times, (...) Internet search engine queries for expressions of interest have become quite popular. Apparently, philosophers attempt to surpass the limits of their own linguistic intuitions by appealing to experts or to factual uses of language. I argue that this attempt is commendable but that its execution is wanting. Instead of appealing to dictionaries or Internet queries, philosophers should employ computer-based linguistic corpora in order to confirm or falsify hypotheses about the factual use of language. This approach also has some advantages over methods employed by experimental philosophers. If the importance of ordinary language is stressed, the use of linguistic corpora is hardly avoidable. (shrink)

Distributive egalitarians believe that distributive justice is to be explained by the idea of distributive equality (DE) and that DE is of intrinsic value. The socio-relational critique argues that distributive egalitarianism does not account for the “true” value of equality, which rather lies in the idea of “equality as a substantive social value” (ESV). This paper examines the socio-relational critique and argues that it fails because – contrary to what the critique presupposes –, first, ESV is not conceptually distinct from (...) DE, and second, the idea of ESV cannot serve as a “foundation” or “root” of distributive egalitarianism. (shrink)

We investigate the semantics of historical counterfactuals in indeterministic contexts. We claim that "plain" and "necessitated" counterfactuals differ in meaning. To substantiate this claim, we propose a new semantic treatment of historical counterfactuals in the Branching Time framework. We supplement our semantics with supervaluationist postsemantics, thanks to which we can explain away the intuitions which seem to talk in favor of the identification of "would" with "would necessarily".

Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...) then, but bounded. This paper presents a surprising paradox: If counterfactuals are tolerant and bounded, then we can prove a flat contradiction using natural rules of inference. Something has to go then. But what? (shrink)