A Probabilistic Semantics for Counterfactuals. Part A
Hannes Leitgeb2012, Review of Symbolic Logic
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Abstract
This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘if A then B’ to be true even in the presence of relevant ‘A and not B’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false.(Received August 10 2010)
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A Probabilistic Semantics for Counterfactuals. Part B
Review of Symbolic Logic, 2012
This is part B of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘if A then B’ to be true even in the presence of relevant ‘A and not B’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false.(Received August 10 2010)
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Since nothing is said to the contrary, the topic times of the two sub-clauses will be taken to coincide, in accordance with the principle of "topic consistency" (WK, sect. 5.2).
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The pattern of credences we are inclined to assign to counterfactuals challenges standard accounts of counterfactuals. In response to this prob- lem, the paper develops a semantics of counterfactuals in terms of the epsilon-operator. The proposed semantics stays close to the standard ac- count: 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 particu- lar, an explanation of how the puzzling credences in counterfactuals come about.
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On the received view, counterfactuals are analyzed using the concept of closeness between possible worlds: ‘if it had been that p, then it would have been the case that q’ is true at world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in the paper is which weights attach to different respects of similarity. I start by considering Lewis’s answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: If a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis’s to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details.
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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.
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According to the Counterfactual Comparative Account of harm and benefit (cca), an event is overall harmful (/beneficial) for a subject to the extent that this subject would have been better (/worse) off if it had not occurred. In this paper we present a challenge for cca. 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, problematic implications will emerge. For example, 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 cca in this respect, theorists of harm and benefit face a deadlock.
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The goal of this paper is to give an account of what it is for a proposition to be metaphysically necessary, and an explanation of the raison d'être of modal concepts. Both projects have their starting point in the idea that modal notions originate in our cognitive practice of counterfactual reasoning, i.e. of answering questions of the form ‘how would things be different if such-and-such were the case?’.
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In the preceding chapter, we explored the possibility of how serious criticism of the Hempel model of explanation might have been met by assuming that laws were representable as counterfactuals. That assumption only made matters worse. We now wish to look at a weaker claim that has had many advocates: It is the idea that laws are distinguished from true contingent generalizations in that they support their corresponding counterfactual conditionals, while mere contingent generalizations do not. We think that even this weaker connection is untenable. There are two widely endorsed criteria that have been used to distinguish those generalizations that are laws from the rest. One is that laws support their corresponding counterfactual conditionals,the counterfactual connection, and the other is that laws possess a special kind of necessity that non-laws don't have. These two criteria are closely connected, but neither one is intended to be both a necessary and sufficient condition. In this chapter we will consider only the counterfactual connection, and we will postpone modal considerations for a later chapter. The counterfactual connection for laws is simply that laws support their corresponding counterfactual conditionals. The notion of "support" needs some explanation. It cannot mean evidential support. There can be evidence for laws, but there are almost no cases where some laws are evidence for, or confirm other laws. I suggest, following the few leads in the literature, according to which "support" of the corresponding counterfactual means "logical implication". Thus we understand the counterfactual connection to be the claim that (C) Laws imply their corresponding counterfactuals. We will refer to (C) as The Counterfactual Connection. The immediate problem is that this formulation is ambiguous. There are at least two possible readings: (1) If A is a law, then A implies its corresponding counterfactual conditional. and (2) ℒ(A) implies the counterfactual corresponding to A, where "ℒ(A)" just states that it is a law that A.
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In a recent paper Lee Walters criticizes a number of philosophersincluding Gundersenfor committing a 'failure in the argumentative strategy' when they attempt to amend the standard Lewis semantics for counterfactuals in order to avoid the so-called principle of Conjunction Conditionalization. In this article we defend a Gundersen-style probability-based semantics against Walter's major misgivings: that it is not logically conservative, that it is committed to the Connection Hypothesis, and that it cannot deal satisfactory with irrelevant semi-factuals.
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Chapter hd: Counterfactuals and the second law1
rci.rutgers.edu
Chapter hd: Counterfactuals and the second law 1 Barry Loewer I will be discussing a kind of conditional (or counterfactual) typically expressed in English by subjunctive conditionals. Here are some examples: 'if I were to strike this match there would be an explosion', 'if there had been an explosion it is likely that I would have heard it', 'if the explosion had not occurred then the window would not have broken.' This kind of counterfactual is intimately connected with laws, explanation, causation, choice, knowledge, memory, measurement, chance, the asymmetry of past and future, etc; a veritable Who's Who of philosophically and scientifically significant concepts. Philosophers may disagree about the order of explanation among these items and counterfactuals but everyone ought to agree that we would make significant progress understanding them all if we had an account of what makes this kind of counterfactual statement true/false; what facts in our world (and worlds like ours) serve as the truth makers of these counterfactuals. One answer to the analogous question for certain regions of discourse is that their basic statements express fundamental facts that do not supervene on anything more basic. But whatever attractions this kind of view may have for some subject matters (e.g. spatial relations, values, consciousness, and modality) it is off the table here. More basic facts about laws, causation, probabilities, the distribution of fundamental properties, dispositions, our interests and beliefs, possible worlds or something else determine the truth-values of counterfactuals. 2
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