This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical truth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach places the (...) class='Hi'>counterfactual conditionals in an unfamiliar foundational role. (shrink)

I propose a counterfactual theory of infinite regress arguments. Most theories of infinite regress arguments present infinite regresses in terms of indicative conditionals. These theories direct us to seek conditions under which an infinite regress generates an infinite inadmissible set. Since in ordinary language infinite regresses are usually expressed by means of infinite sequences of counterfactuals, it is natural to expect that an analysis of infinite regress arguments should be based on a theory of counterfactuals. The Stalnaker–Lewis theory (...) of counterfactuals, augmented with some fundamental notions from metric-spaces, provides a basis for such an analysis of infinite regress arguments. Since the technique involved in the analysis is easily adaptable to various analyses, it facilitates a rigorous comparison among conflicting philosophical analyses of any given infinite regress. (shrink)

David Lewis’s counterfactual analysis of cause consisted of the counterfactual conditional closed under transitivity.2 Namely, a sufficient condition for A’s being a cause of C is that ∼A > ∼C be true; and a necessary as well as sufficient condition is that there be a series of true counterfactuals ∼A > ∼E1, ∼E1 > ∼E2, . . . , ∼En >∼C (n > 0).

Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a new form of analysis for counterfactuals: analysis by algorithmic complexity. Inspired by Lewis-Stalnaker's Possible Worlds Semantics, the proposed method allows for a new interpretation of the debate between David Lewis and Robert Stalnaker regarding the Limit and Singularity assumptions. Besides other results, we offer a new way to answer (...) the problems raised by Goodman and Quine regarding vagueness, context-dependence, and the non- monotonicity of counterfactuals. Engaging in a dialogue with literature, this study will seek to bring new insights and tools to this debate. We hope our method of analysis can make counterfactuals more understandable in an intuitively plausible way, and a philosophically justifiable manner, aligned with the way we usually think about counterfactual propositions and our imaginative reasoning. (shrink)

There is a traditional view, maintained by Aquinas and others, which holds that there is a mutual entailment between the power to Create Ex Nihilo and the property of omnipotence. In his Metaphysical Disputations, however, Suarez attacks the traditional view by pointing out a seriousflaw in Aquinas’s argument. Suarez claims that there is no reason in principle why God cannot miraculously bestow CEN-power to creatures––albeit in a limitedform––even on the assumption that God cannot make creatures omnipotent. In this paper the (...) authors argue that the debate can be resolved in favor of Aquinas;that CEN-power does indeed strictly imply omnipotence. After clarifying a sufficient condition for the property of omnipotence, the authors argue that attention to amodest possible worlds semantics and some interesting properties of counterfactuals are together sufficient to show that beings with CEN-power are in every case beings that are omnipotent. (shrink)

On David Lewis's original analysis of causation, c causes e only if c is linked to e by a chain of distinct events such that each event in the chain (counter-factually) depends on the former one. But this requirement precludes the possibility of late pre-emptive causation, of causation by fragile events, and of indeterministic causation. Lewis proposes three different strategies for accommodating these three kinds of cases, but none of these turn out to be satisfactory. I offer a single (...) analysis of causation that resolves these problems in one go but which respects Lewis's initial insights. One distinctive feature of my account is that it accommodates indeterministic causation without resorting to probabilities. (shrink)

The counterfactual analysis of causation has focused on one particular counterfactual conditional, taking as its starting-point the suggestion that C causes E iff (C E). In this paper, some consequences are explored of reversing this counterfactual, and developing an account starting with the idea that C causes E iff (E C). This suggestion is discussed in relation to the problem of pre-emption. It is found that the 'reversed' counterfactual analysis can handle even the most (...) difficult cases of pre-emption with only minimal complications. The paper closes with a discussion of the wider philosophical implications of developing a reversed counterfactual analysis, especially concerning the differentiation of causes from causal conditions, causation by absences, and the extent to which causes suffice for their effects. (shrink)

Causal overdetermination – i.e. instances in which x, y, and z all occur and intuitively the occurrence of x alone is sufficient for the occurrence of z and the occurrence of y alone is sufficient for the occurrence of z – has long been considered a problem for counterfactual analyses of causation. Intuitively, we want to say both x and y caused z, but standard Lewisian counterfactual analysis yields the result that neither x nor y caused z. (...) David Lewis, himself, suggested that overdetermination ought to be left as “spoils to the victor”. I show how, if we modify Lewis’ account of events slightly, we can bring counterfactual analysis in line with our intuitions about overdetermination. (shrink)

This paper evaluates the recent trend to renounce the similarity approach to counterfactuals in favor of the older metalinguistic theory. I try to show, first, that the metalinguistic theory cannot work in anything like its present form (the form described by many in the last decade who claim to be able to solve Goodman''s old problem of cotenability). This is so, I argue, because the metalinguistic theory requires laws of nature of a sort that we (apparently) do not have: current (...) physical theory cannot underwrite the metalinguistic theory. Second, I draw from the first point a motivation for the similarity approach, a motivation based on theoretical considerations apart from the standard ones of pretheoretical intuition. (shrink)

This paper aims to outline a counterfactual theory of divine atemporal causation that avoids problems of preemption. As a result, the presentation of the analysis is structured such that my counterfactual analysis directly addresses preemption issues. If these problems can be avoided, the theist is well on her way to proposing a usable metaphysical concept of atemporal divine causation. In the first section, I outline Lewis’ original counterfactual analysis as well as how these cases (...) of preemption cause problems for his analysis. In particular, two cases of preemption have proven problematic for counterfactual analyses: late preemption and trumping preemption. In the second section, I propose a counterfactual analysis of divine causation that is not subject to these problems of preemption. I present a counterfactual analysis of timeless divine causation, supplemented by a definition of what it means for God to allow an event to happen. In the third section, I argue this analysis is not prey to problems of preemption. (shrink)

If we seek to analyse causation in terms of counterfactual conditionals then we must assume that there is a class of counterfactuals whose members (i) are all and only those we need to support our judgements of causation, (ii) have truth-conditions specifiable without any irreducible appeal to causation. I argue that (i) and (ii) are unlikely to be met by any counterfactual analysis of causation. I demonstrate this by isolating a class of counterfactuals called non-projective counterfactuals, or (...) NP-counterfactuals, and indicate how counterfactual analyses of causation must appeal to them to account for the correct causal judgements we make. I show that the truth-conditions of NP-counterfactuals are specifiable only by irreducible appeal to causation. A dilemma then holds: if counterfactual analyses of causation eschew appeal to NP-counterfactuals they are empirically inadequate, but if they appeal to NP-counterfactuals they are circular and thus conceptually inadequate. (shrink)

May assumes that if moral beliefs are counterfactually dependent on irrelevant factors, then those moral beliefs are based on defective belief-forming processes. This assumption is false. Whether influence by irrelevant factors is debunking depends on the mechanisms through which this influence occurs. This raises the empirical bar for debunkers and helps May avoid an objection to his Debunker’s Dilemma.

Counterfactual analyses of causation can provide elegant analyses of many cases of causation. However, they fail to give intuitively correct analyses of cases involving a commonplace variety of late preemptive causation. I argue that a small emendation can solve the problem.

In a recent paper Causal Asymmetry, Douglas Ehring has proposed an intriguing solution to the vexing problem of causal asymmetry. The aim of this paper is to show that his theory is not satisfactory. Moreover, the examples that I use in showing the defect of Ehring's theory also indicate that the counterfactual analysis of causation has a problem that cannot be remedied by Marshall Swain's suggested refinement of the counterfactual analysis of causation in Causation and Distinct (...) Events. (shrink)

In this paper, I raise a problem for standard precisifications of the Relational Analysis of attitude reports. The problem I raise involves counterfactual attitude verbs. such as ‘wish’. In short, the trouble is this: there are true attitude reports ‘ S wishes that P ’ but there is no suitable referent for the term ‘that P ’. The problematic reports illustrate that the content of a subject’s wish is intimately related to the content of their beliefs. I capture (...) this fact by moving to a framework in which ‘wish’ relates subjects to sets of pairs of worlds, or paired propositions, rather than—as is standardly assumed—sets of worlds. Although other types of counterfactual attitude reports, for example those involving ‘imagine’, may be similarly problematic, at this stage it is unclear whether they can be handled the same way. (shrink)

Ordinarily counterfactuals are seen as making statements about states of affairs, albeit ones that hold in merely possible or alternative worlds. Thus analyzed, nearly all counterfactuals turn out to be incoherent. Any counterfactual, thus analyzed, requires that there be a metaphysically (not just epistemically) possible world w where the laws are the same as here, and where almost all of the facts are the same as here. (The factual differences relate to the antecedent and consequent of the counter-factual.) But, (...) as I show, this requirement typically involves the positing of worlds whose necessary non-existence can be shown by fairly elementary deductions. Further, the possible-worlds analysis of counterfactuals is guilty of covert circularity. For, thus analyzed, counterfactuals can only be understood in terms of laws of nature (the laws that apply here are assumed in the hypothetical world - except in the atypical case where the counterfactual is also a counter-nomic). But the concept of a law cannot itself be defined except in terms of the notion of a counterfactual (a law is given by a counterfactual-supporting proposition). I give a purely epistemic analysis of counterfactuals, arguing that they are crypto-probability propositions. I also argue that the relevant kind of probability can be defined wholly in terms of what has happened (not what would happen and not even what must happen in a nomic sense). So my analysis isn’t guilty of any kind of circularity. (shrink)

Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social psychology contain at least one mediation test (Rucker, Preacher, Tormala, & Petty, 2011). Standard parametric approaches to mediation analysis employ regression models, and either the “difference method” (Judd & Kenny, 1981), more common in epidemiology, or the “product method” (Baron & Kenny, 1986), more common (...) in the social sciences. In this article, we first discuss a known, but perhaps often unappreciated, fact that these parametric approaches are a special case of a general counterfactual framework for reasoning about causality first described by Neyman (1923) and Rubin (1924) and linked to causal graphical models by Robins (1986) and Pearl (2006). We then show a number of advantages of this framework. First, it makes the strong assumptions underlying mediation analysis explicit. Second, it avoids a number of problems present in the product and difference methods, such as biased estimates of effects in certain cases. Finally, we show the generality of this framework by proving a novel result which allows mediation analysis to be applied to longitudinal settings with unobserved confounders. (shrink)

Thought experiments are ubiquitous in science and especially prominent in domains in which experimental and observational evidence is scarce. One such domain is the causal analysis of singular events in history. A long‐standing tradition that goes back to Max Weber addresses the issue by means of ‘what‐if’ counterfactuals. In this paper I give a descriptive account of this widely used method and argue that historians following it examine difference makers rather than causes in the philosopher’s sense. While difference making (...) is neither necessary nor sufficient for causation, to establish difference makers is more consistent with the historians’ more ultimate purposes. †To contact the author, please write to: Department of Philosophy, Erasmus University, 3000 DR Rotterdam, The Netherlands; e‐mail: [email protected]. (shrink)

This paper discusses a puzzle raised by Sharon Berry, published in Analysis. The question in the background of this puzzle is how we should deal with seemingly plausible possibility judgements that commit us to counterfactual truths that find no basis in reality. Three answers to this question and their corresponding solutions to the puzzle will be discussed. The last answer provides a way to make sense of the claim that it is in some cases indeterminate whether a proposition (...) is possible and offers an account of indeterminate modal status. (shrink)

Cohen and Meskin 2006 recently offered a counterfactual theory of information to replace the standard probabilistic theory of information. They claim that the counterfactual theory fares better than the standard account on three grounds: first, it provides a better framework for explaining information flow properties; second, it requires a less expensive ontology; and third, because it does not refer to doxastic states of the information-receiving organism, it provides an objective basis. In this paper, I show that none of (...) these is really an advantage. Moreover, the counterfactual theory fails to satisfy one of the basic properties of information flow, namely the Conjunction principle. Thus, I conclude, there is no reason to give up the standard probabilistic theory for the counterfactual theory of information. (shrink)

This chapter contains sections titled: The Counterfactual Character of Historiography Understanding Metaphysical Preliminaries Causal Counterfactual Analysis in Historiography Counterfactuals and Practical Reasoning Science and Counterfactuals References Further Reading.

Counterfactual analysis is an interesting feature of thought experiments, because it requires the imagination of alternative states of the world (see also publications by Fearon, Lebow and Stein, Reiss, and Tetlock and Belkin, who suggest the same). In historical analysis, the use of imagination is often the focus of criticisms of such counterfactual analysis. In this article, I consider three strategies for constraining imagination: making limited counterfactual changes, limiting counterfactual changes to the decisions (...) of important figures, and using evidence to restrict the scope for imagination. Given the focus of this special issue, I will relate this discussion to Lewis’s and Woodward’s analyses of counterfactuals in the philosophy of science. I show that counterfactual analysis in historical cases has some resemblance to Lewis’s and Woodward’s analyses, but that what Lewis calls “transition periods” cannot be left entirely vague, as Lewis suggests, nor can counterfactual changes be seen simply as interventions, as Woodward suggests. I propose that efforts to limit imagination in historical counterfactuals are ultimately problematic, but that imagination can nevertheless play a useful role in counterfactual analysis. (shrink)

Kit Fine (1994. “Essence and Modality”, Philosophical Perspectives 8: 1-16) argues that the standard modal account of essence as de re modality is ‘fundamentally misguided’ (p. 3). We agree with his critique and suggest an alternative counterfactual analysis of essence. As a corollary, our counterfactual account lends support to non-vacuism the thesis that counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are not always vacuously true.

The basic idea of counterfactual theories of causation is that the meaning of causal claims can be explained in terms of counterfactual conditionals of the form “If A had not occurred, C would not have occurred”. While counterfactual analyses have been given of type-causal concepts, most counterfactual analyses have focused on singular causal or token-causal claims of the form “event c caused event e”. Analyses of token-causation have become popular in the last thirty years, especially since (...) the development in the 1970's of possible world semantics for counterfactuals. The best known counterfactual analysis of causation is David Lewis's (1973b) theory. However, intense discussion over thirty years has cast doubt on the adequacy of any simple analysis of singular causation in terms of counterfactuals. Recent years have seen a proliferation of different refinements of the basic idea to achieve a closer match with commonsense judgements about causation. (shrink)

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

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)

Among the many philosophers who hold that causal facts1 are to be explained in terms of—or more ambitiously, shown to reduce to—facts about what happens, together with facts about the fundamental laws that govern what happens, the clear favorite is an approach that sees counterfactual dependence as the key to such explanation or reduction. The paradigm examples of causation, so advocates of this approach tell us, are examples in which events c and e— the cause and its effect— both (...) occur, but: had c not occurred, e would not have occurred either. From this starting point ideas proliferate in a vast profusion. But the remarkable disparity among these ideas should not obscure their common foundation. Neither should the diversity of opinion about the prospects for a philosophical analysis of causation obscure their importance. For even those philosophers who see these prospects as dim—perhaps because they suffer post-Quinean queasiness at the thought of any analysis of any concept of interest—can often be heard to say such things as that causal relations among events are somehow “a matter of” the patterns of counterfactual dependence to be found in them. (shrink)

Expanding on a discussion by Hansson, this paper treats of Goodman's and Lewis' accounts of counterfactual conditionals, comparing the senses in which these theories may be accused of circularity. While I do maintain that in this respect Lewis has an edge over Goodman, the paper's aim is not so much to reach a firm conclusion as to disentangle some previously conflated aspects of the issue. It is also suggested that the importance of avoiding circularity may vary depending on the (...) philosophical purpose of one's analysis. (shrink)

The conditional analysis of ability statements has many versions. In this paper I will deal with the version which claims that ‘x can do y’ is equivalent to ‘if x were to choose to do y, then x would do y.’ However, my comments should be equally applicable to any analysis of ability statements that can properly be called a version of the conditional analysis. The intuition behind the conditional analysis is that what it is for (...) one to be able to do something is for one's choice to be effective. To have an ability to do y is for it to be true that one's choosing to do y would be effective - one's choosing to do y would result in one's doing y. But this intuition is not captured by the conditional analysis in its standard form, and a restriction is needed to mend this defect. This restriction is based on a distinction among counterfactual conditionals. (shrink)

En temps normal, les contrefactuels sont conçus comme produisant des énoncés portant sur des états de choses, mais des états de choses se trouvant dans des mondes simplement possibles ou alternes. Analysés ainsi, il s’avère que presque tous les contrefactuels sont incohérents. Tout contrefactuel analysé de la sorte exige qu’il y ait un monde métaphysiquement (et pas épistémiquement seulement) possible w où les lois sont les mêmes qu’ici, et où la quasi-totalité des faits sont les mêmes qu’ici. (Les différences factuelles (...) sont liées à l’antécédent et au conséquent du contrefactuel.) Mais comme je vais le montrer, cette exigence implique de manière typique la postulation de mondes dont on peut démontrer la nécessaire non-existence au moyen de déductions assez élémentaires. De plus, l’analyse des contrefactuels en termes de mondes possibles est coupable de circularité cachée. Analysés ainsi, les contrefactuels ne peuvent effectivement être compris qu’en termes de lois de la nature (les lois qui s’appliquent ici sont présupposées dans le monde hypothétique — excepté dans le cas atypique où le contrefactuel est également un contre-nomique). Mais il y a un argument répandu voulant que le concept de loi ne puisse pas être défini lui-même, sinon dans les termes de la notion de contrefactuel (une loi est, entre autres, quelque chose qui vient à l’appui des contrefactuels). Je donnerai une analyse purement épistémique des contrefactuels, déclarant que ce sont des propositions pseudo-probabilistes. Je déclarerai également que le type de probabilité en question peut être défini intégralement en termes de ce qui a été le cas (non pas de ce qui aurait été le cas, ni même de ce qui doit être le cas en un sens nomique.) Mon analyse n’est donc coupable d’aucune sorte de circularité. (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)

This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback-less) models are considered. Composition and effectiveness also hold in Lewis's closest-world semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but (...) not in Lewis's closest-world semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models. (shrink)