– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (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)

The material account of indicative conditionals faces a legion of counterexamples that are the bread and butter in any entry about the subject. For this reason, the material account is widely unpopular among conditional experts. I will argue that this consensus was not built on solid foundations, since these counterexamples are contextual fallacies. They ignore a basic tenet of semantics according to which when evaluating arguments for validity we need to maintain the context constant, otherwise any argumentative form can be (...) rendered invalid. If we maintain the context fixed, the counterexamples to the material account are disarmed. Throughout the paper I also consider the ramifications of this defence, make suggestions to prevent contextual fallacies, and anticipate some possible misunderstandings and objections. (shrink)

In non‐literal uses of language, the content an utterance communicates differs from its literal truth conditions. Loose talk is one example of non‐literal language use (amongst many others). For example, what a loose utterance of (1) communicates differs from what it literally expresses: (1) Lena arrived at 9 o'clock. Loose talk is interesting (or so I will argue). It has certain distinctive features which raise important questions about the connection between literal and non‐literal language use. This paper aims to (i.) (...) introduce a range of novel data demonstrating certain overlooked features of loose talk, and (ii.) develop a new theory of the phenomenon which accounts for these data. In particular, this theory is motivated by the need to explain minimal pairs such as (2)-(3): (2) Lena arrived at 9 o'clock, but she did not arrive at 9 o'clock exactly. (3) ?? Lena did not arrive at 9 o'clock exactly, but she arrived at 9 o'clock. (2) and (3) agree in their truth conditions. Yet they differ in felicity. As such, they constitute a problem for any account which hopes to predict the acceptability of the loose use of a sentence from its truth conditions and the context of utterance alone. Instead, it will be argued, to explain loose talk phenomena we must posit an additional layer of meaning outstripping truth conditions. This layer of meaning is shown to exhibit a range of properties, all of which point to its being semantically encoded. Thus, if correct, the theory provides a new example of how semantic meaning must extend beyond literal, truth‐conditional content. (shrink)

Many have accepted that ordinary counterfactuals and might counterfactuals are duals. In this paper, I show that this thesis leads to paradoxical results when combined with a few different unorthodox yet increasingly popular theses, including the thesis that counterfactuals are strict conditionals. Given Duality and several other theses, we can quickly infer the validity of another paradoxical principle, ‘The Counterfactual Direct Argument’, which says that ‘A> ’ entails ‘A> ’. First, I provide a collapse theorem for the ‘counterfactual direct argument’. (...) The counterfactual direct argument entails the logical equivalence of the subjunctive and material conditional, given a variety of assumptions. Second, I provide a semantics that validates the counterfactual direct argument without collapse. This theory further develops extant dynamic accounts of conditionals. I give a new semantics for disjunction, on which A or B is only true in a context when A and B are both unsettled. The resulting framework validates CDA while invalidating other commonly accepted principles concerning the conditional and disjunction. (shrink)

I show that Kavka's toxin puzzle raises a problem for the “Responsibility Theodicy,” which holds that the reason God typically does not intervene to stop the evil effects of our actions is that such intervention would undermine the possibility of our being significantly responsible for overcoming and averting evil. This prominent theodicy seems to require that God be able to do what the agent in Kavka's toxin story cannot do: stick by a plan to do some action at a future (...) time even though when that time comes, there will be no good reason for performing that action. I assess various approaches to solving this problem. Along the way, I develop an iterated variant of Kavka's toxin case and argue that the case is not adequately handled by standard causal decision theory. (shrink)

There are at least two traditional conceptions of numerical degree of similarity. According to the first, the degree of dissimilarity between two particulars is their distance apart in a metric space. According to the second, the degree of similarity between two particulars is a function of the number of (sparse) properties they have in common and not in common. This paper argues that these two conceptions are logically independent, but philosophically inconsonant.

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have something to say on the (...) matter. (shrink)

Can I will that my maxim becomes a universal law? . . .It would be easy to show how common human reason, with this compass, knows well how to distinguish . . . what is consistent or inconsistent with duty. (Kant, Foundations, 403–4)How exactly is this compass to work? Cases bring out connected difficulties to do, (1), with whether ''social contexts'' are to be in or out of descriptions of actions maxims would have agents do – for example, ''disarming alone'' (...) and ''voting when enough others would even if one did not'', or ''disarming'' and ''voting'' simply; and, (2), with a seldom noticed ambiguity of ''everyone''s acting in accordance with a maxim'' and ''a maxim''s becoming universal law''. The paper argues dilemmatically for the inadequacy of Kant''s test for maxims consistent with duty whatever policy for social contexts and manner of maxims becoming universal laws it is said to invoke. (shrink)

According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics "lose" the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive interpretations. To (...) solve it I stress that implications for ordinary imperfect players are limited. (shrink)

The paper describes a new way of thinking about conditionals, in terms of information transfer between worlds. This way of looking at things provides an answer to some of the standard problems concerning conditionals, and undercuts the claim that indicative and subjunctive conditionals are distinct.

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)

Act teleological theories are theories that judge an action permissible just in case its outcome is maximally good.[1] It is usually assumed that act teleological theories cannot be @i, i.e., make the permissibility of actions depend on what the past was like (e.g., on what promises were made, what wrong doings were done, and more generally on what actions were performed).[2] I shall argue that this is not so. Although @u act teleological theories, such as classical act utilitarianism, are not (...) past-regarding, there are other types of act teleological theories that are past-regarding. (shrink)

Folklore has it that Sobel sequences favor a variably strict analysis of conditionals over its plainly strict alternative. While recent discussions for or against the lore have focussed on Sobel sequences involving counterfactuals, this paper draws attention to the fact that indicative Sobel sequences are just as felicitous as are their counterfactual cousins. The fact, or so I shall argue here, disrupts the folklore: given minimal assumptions about the semantics and pragmatics of indicative conditionals, a textbook variably strict analysis fails (...) to predict that indicative Sobel sequences are felicitous. The correct lesson to draw from Sobel sequences is that their felicity challenges classical implementations of the variably strict and of the plainly strict analysis alike. In response to this challenge I develop a dynamic strict analysis of conditionals that handles indicative Sobel sequences with grace while preserving intuitive constraints on the semantics and pragmatics of their members. A discussion of how such an analysis may handle the challenge from reverse Sobel sequences is provided. (shrink)

This paper is about Sobel sequences, which are sequences of counterfactuals that supposedly display two interesting properties: first, they are consistent, as accounted for by the famous Lewis-Stalnaker analysis; but second, they are not consistent in the reverse order, which is not accounted for by Lewis-Stalnaker. I argue that there has been an empirical oversight in the literature on these sequences: there are consistent sequences, and there are irreversible sequences, but no sequence is both. The Lewis-Stalnaker theory neatly captures Sobel (...) sequences, and also captures the inconsistency of Lewis sequences. But there is still a dynamic asymmetry at work with Lewis sequences, which I account for by appeal to the pragmatic phenomenon of imprecision. Lewis sequences seem consistent because they do not belie factual disagreements, but rather metalinguistic disagreements about how precise to be. This also accounts for their irreversibility—such metalinguistic disagreements about the standard of precision are only possible in one direction, as famously observed by Lewis, who observed them in discourses not containing counterfactuals. (shrink)

A theory of right action is implicit in Hume's delineation of the virtues. It gives qualified priority to 'rules of justice' as Hume's remarks on 'that species of utility which attends this virtue' require. It is a useful actual-rule, not an ideal possible-rule, purely utilitarian theory that discounts rules of justice in 'extraordinary cases', has a problem when rules conflict and invites the question 'Why not hark directly to the supreme law of utility in every case?'. It does not reflect (...) contractarian considerations of mutuality of interests evident in Hume's texts, which while sometimes relevant to what is reasonable, are in his view never also relevant to what is moral.(publisher). (shrink)