I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

The standard semantics for counterfactuals ensures that any counterfactual with a true antecedent and true consequent is itself true. There have been many recent attempts to amend the standard semantics to avoid this result. I show that these proposals invalidate a number of further principles of the standard logic of counterfactuals. The case against the automatic truth of counterfactuals with true components does not extend to these further principles, however, so it is not clear that rejecting the latter should be (...) a consequence of rejecting the former. Instead I consider how one might defuse putative counterexamples to the truth of true-true counterfactuals. (shrink)

The human imagination remains one of the last uncharted terrains of the mind. People often imagine how events might have turned out something had been different. The of reality, those aspects more readily changed, indicate that counterfactual thoughts are guided by the same principles as rational thoughts. In the past, rationality and imagination have been viewed as opposites. But research has shown that rational thought is more imaginative than cognitive scientists had supposed. In The Rational Imagination, I argue that imaginative (...) thought is more rational than scientists have imagined. People exhibit remarkable similarities in the sorts of things they change in their mental representation of reality when they imagine how the facts could have turned out differently. For example, they tend to imagine alternatives to actions rather than inactions, events within their control rather than those beyond their control, and socially unacceptable events rather than acceptable ones. Their thoughts about how an event might have turned out differently lead them to judge that a strong causal relation exists between an antecedent event and the outcome, and their thoughts about how an event might have turned out the same lead them to judge that a weaker causal relation exists. In a simple temporal sequence, people tend to imagine alternatives to the most recent event. The central claim in the book is that counterfactual thoughts are organised along the same principles as rational thought. The idea that the counterfactual imagination is rational depends on three steps: (1) humans are capable of rational thought; (2) they make inferences by thinking about possibilities; and (3) their counterfactual thoughts rely on thinking about possibilities, just as rational thoughts do. The sorts of possibilities that people envisage explain the mutability of certain aspects of mental representations and the immutability of other aspects. (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)

Molinism is named after Luis de Molina (1535–1600). Molina and his fellow Jesuits became entangled in a fierce debate over issues involving the doctrine of divine providence, which is a picture of how God runs the world. Molinism reemerged in the 1970s after Alvin Plantinga unwittingly assumed it in his Free Will Defense against the ‘Logical’ Argument from Evil. Molinism has been the subject of vigorous debate in analytic philosophy of religion ever since. The main aim of this essay is (...) to survey the main contours of this debate. We will visit some ‘old’ battlefields and current hot spots in the ongoing Molinism Wars. (shrink)

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

I present a puzzle concerning counterfactual reasoning and argue that it should be solved by giving up the principle of substitution for logical equivalents.

Analyses are given of the concepts of absolute and prima facie obligation. The former is a maximizing analysis: roughly, one ought absolutely to perform those actions which are performed in the best worlds accessible to one. The latter analysis is roughly this: one ought prima facie to perform those actions which are such that those accessible worlds in which they are performed are better than the closest accessible worlds in which they are not performed. Accounts of conditional obligation, both absolute (...) and prima facie, are also given, and the issue of the detachment of unconditional from conditional obligation is addressed. (shrink)

Recently, Cohen and Timmerman, 1–18, 2016) argue that actualism has control issues. The view should be rejected, they claim, as it recognizes a morally irrelevant distinction between counterfactuals over which agents exercise the same kind of control. Here we reply on behalf of actualism.

This paper provides an update semantics for counterfactual conditionals. It does so by giving a dynamic twist to the ‘Premise Semantics’ for counterfactuals developed in Veltman (1976) and Kratzer (1981). It also offers an alternative solution to the problems with naive Premise Semantics discussed by Angelika Kratzer in ‘Lumps of Thought’ (Kratzer, 1989). Such an alternative is called for given the triviality results presented in Kanazawa et al. (2005, this issue).

Most relational theories assert both that spatial discourse is reducible to talk about physical objects and their spatial relations, and that the relation of congruence derives from a non-metrical relation which intervals bear or possibly bear to measuring instruments. We have shown that there are serious logical difficulties involved in maintaining both these positions and the thesis of the continuity of space. We have also shown that Grünbaum's motivating argument for the reduction of congruence is unsound, and, moreover, that the (...) prospects of formulating the kind of definition which this reduction requires seem to rest upon a wholly vague notion of physical possibility. Alternatively, if congruence is taken as primitive, it seems plausible that spatial discourse can be reconstructed so that there is no ontological commitment to spatial objects other than physical objects. Whether or not this relational thesis is ultimately defensible requires more elaboration of the relational theory, and investigation of its role in the formalizations of current physical theories. It is odd, considering the wide currency of relational theories, that this work has never been done. (shrink)

The aim of this paper is to identify what I take to be the main conceptual problem in Lewis’ semantics for counterfactuals when the Limit Assumption is not satisfied, what I call the Discrimination Problem , and to present and discuss a modification of Lewis’ semantics that aims at solving DP. First, I outline Lewis’ semantics, highlighting the aspects that will be relevant for our discussion. Second, I present DP and discuss it with a heuristic example. Third, I present the (...) new proposal and comment some formal consequences and the objections they give rise to. Fourth, I present an allegedly equivalent version of the proposal and discuss the difference between counterfactuals and strict conditionals. Finally, I defend that the two proposals are different and argue for the first one as the best way of capturing two intuitions that seem in conflict when the LA is not satisfied. I conclude with a dilemma: either the proposal here defended works or LA is inescapable. Thus, if the proposal doe.. (shrink)

Here’s a problem that any reliability theory must face, whether it’s one that holds that beliefs are justified just when they’re products of belief-forming mechanisms with the potential of having good records of yielding true beliefs, or one that holds that a belief meets the standards for knowledge if and only if its causal basis rules out any relevant chance of mistake. The problem is made evident when cast in probabilistic terms. Let r be S’s reason for tokening the true (...) belief that p under conditions c. Then, according to reliabilism, Sis justified in believing that p under c iff r makes it sufficiently probable that p, whileS knows that p iff the conditional probability that p on r and c is unity. But how do we specify the belief context c to be counted as epistemically relevant? As urged recently by John Pollock, on the face of it there seems to be no principled reason for excluding mention of the truth value of the proposition believed. As he says, ‘The only obvious way to construct an objective non-epistemic kind of definite probability is to make it conditional on everything that is true [at the belief’s tokening]’ ; and, as he notes, ‘one feature of the present circumstances is a characterization of the belief as a belief in [p ], and another feature is the truth value of [p]’. But if we allow both the belief token and its truth value membership in the relevant belief context, we then have the hopeless task of explaining how the probability of the token’s being true can be anything but one or zero, one if what is believed is true, and zero if it’s false. This in tum would commit reliabilism to the foolish doctrines that a belief’s truth is sufficient for knowledge, while no false belief is ever even justified. No wonder, then, that Pollock says ‘there is no way to construct an intelligible notion of reliability which does the job required by the reliabilist’. And he is surely right in this: Neither knowledge nor justification can be explained as the chance of a belief’s being true if the relevant belief context is required to mention both the belief tokened and its truth value. We would be engaged in a comparably pointless task were we to try to explain the likelihood of a wager’s being a good bet on a horse race when we had to include among the givens both which horse was picked and its finish, or were we to try to make sense of the assertion that a theory’s predictions have a good chance of being true when both what the theory predicts and its outcome had to be included among the givens. (shrink)

Let us call a statement of the form ‘If A was, is, or will be the case, then C was, is, or will be the case’ an indicative conditional. And let us call a statement of the form ‘If A had been, were, or were to be the case, then C would have been, would be, or would come to be the case’ a subjunctive, or counterfactual, conditional.