Counterfactual Research Articles

Conjunctions, Disjunctions and Lewisian Semantics for Counterfactuals

Consider the reasonable axioms of subjunctive conditionals (1) if p q 1 and p q 2 at some world, then p (q 1 & q 2) at that world, and (2) if p 1 q and p 2 q at some world, then (p 1 ∨ p 2) q at that world, where p q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably false. I will then show how Lewisian semantics can be modified so as to assure (1) and (2) even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then.

Comments on Vogel

Subjunctivitis is a condition afflicting epistemologists, a tendency to employ subjunctive conditionals in their accounts of knowledge. Jonathan Vogel identifies two common strains of subjunctivitis one featuring the subjunctive conditional, sensitivity, and the other, safety and he offers families of counterexamples to each. His cases are ingeniously crafted and highly intuitive. They demonstrate that modalizing in epistemology is not a painless ordeal. But my goal here is damage control; subjunctivitis, I think, may prove to be worth its side effects. I will argue that, for reasons both thematic and specific, the counterexamples are not so compelling as to force the abandonment of modal epistemology. First, while the intuitive force of Vogel's examples is especially acute, much of that force derives not specifically from modal nature of the analyses, but from the familiar and perfectly general paradoxes of skepticism and of the lottery. Thus, one should draw broader lessons from the counterexamples only if an independent and more satisfying solution to the paradoxes is available. Second, under scrutiny the cases reveal certain ambiguities, the resolution of which opens up space for subjunctive conditional accounts to form responses. Third, the extension of Vogel's case against sensitivity to contextualist theories relies partly upon a confusion of use and mention. In what follows, I will briefly review the notions of sensitivity and safety as well as their applications to some epistemic problems, then present Vogel's counterexamples with my rejoinders.

PHILOSOPHICAL KNOWLEDGE AND KNOWLEDGE OF COUNTERFACTUALS

Metaphysical modalities are definable from counterfactual conditionals, and the epistemology of the former is a special case of the epistemology of the latter. In particular, the role of conceivability and inconceivability in assessing claims of possibility and impossibility can be explained as a special case of the pervasive role of the imagination in assessing counterfactual conditionals, an account of which is sketched. Thus scepticism about metaphysical modality entails a more far-reaching scepticism about counterfactuals. The account is used to question the significance of the distinction between a priori and a posteriori knowledge.

Semantic Composition and Presupposition Projection in Subjunctive Conditionals

The goal of this paper is to offer a compositional semantics for sub- junctive and indicative will conditionals, and to derive the projection properties of the types of conditionals we consider and in particular those of counterfactual conditionals. It is argued that subjunctive conditionals are ''bare'' conditional embedded under temporal and aspectural operators, which constrain the inter- pretation of the modal operators in the embedded conditional. Furthermore, it is argued that a theory of presupposition projection a la Heim together with the present proposal about their logical form explains the projection facts.

Tense and Time in Counterfactual Conditionals

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Ceteris Paribus Conditionals and Comparative Normalcy

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species of variably strict conditional I hope to shed new light upon their content and their logic.

Impossible worlds

Richard Brian Davis offers several criticisms of a semantics I once proposed for subjunctive conditionals with impossible antecedents. I reply to these.

Counterfactuals and Epistemic Probability

Philosophers have often attempted to use counterfactual conditionals to analyze probability. This article focuses on counterfactual analyzes of epistemic probability by Alvin Plantinga and Peter van Inwagen. I argue that a certain type of counterfactual situation creates problems for these analyses. I then argue that Plantinga’s intuition about the role of warrant in epistemic probability is mistaken. Both van Inwagen’s and Plantinga’s intuitions about epistemic probability are flawed.

Causal Pluralism versus Epistemic Causality

It is tempting to analyse causality in terms of just one of the indicators of causal relationships, e.g., mechanisms, probabilistic dependencies or independencies, counterfactual conditionals or agency considerations. While such an analysis will surely shed light on some aspect of our concept of cause, it will fail to capture the whole, rather multifarious, notion. So one might instead plump for pluralism: a different analysis for a different occasion. But we do not seem to have lots of different concepts of cause - just one eclectic notion. The resolution of this conundrum, I think, requires us to accept that our causal beliefs are generated by a wide variety of indicators, but to deny that this variety of indicators yields a variety of concepts of cause. This focus on the relation between evidence and causal beliefs leads to what I call *epistemic* causality. Under this view, certain causal beliefs are appropriate or rational on the basis of observed evidence; our notion of cause can be understood purely in terms of these rational beliefs. Causality, then, is a feature of our epistemic representation of the world, rather than of the world itself. This yields one, multifaceted notion of cause.

An Analysis of Stapp’s “A Bell-Type Theorem without Hidden Variables”

H.P. Stapp has proposed a number of demonstrations of a Bell-type theorem which dispensed with an assumption of hidden variables, but relied only upon locality together with an assumption that experimenters can choose freely which of several incompatible observables to measure. In recent papers his strategy has centered upon counterfactual conditionals. Stapp’s paper in American Journal of Physics, 2004, replies to objections raised against earlier expositions of this strategy and proposes a simplified demonstration. The new demonstration is criticized, several subtleties in the logic of counterfactuals are pointed out, and the proofs of J.S. Bell and his followers are advocated.

A Counterfactual Analysis of the Concepts of Logical Truth and Necessity

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 counterfactual conditionals in an unfamiliar foundational role.

Morgenbesser's coin, counterfactuals and independence

Morgenbesser's coin, counterfactuals and independence

I *-ARMCHAIR PHILOSOPHY, METAPHYSICAL MODALITY AND COUNTERFACTUAL THINKING

A striking feature of the traditional armchair method of philosophy is the use of imaginary examples: for instance, of Gettier cases as counterexamples to the justified true belief analysis of knowledge. The use of such examples is often thought to involve some sort of a priori rational intuition, which crude rationalists regard as a virtue and crude empiricists as a vice. It is argued here that, on the contrary, what is involved is simply an application of our general cognitive capacity to handle counterfactual conditionals, which is not exclusively a priori and is not usefully conceived as a form of rational intuition. It is explained how questions of metaphysical possibility and necessity are equivalent to questions about counterfactuals, and the epistemology of the former (in particular, the role of conceiving or imagining) is a special case of the epistemology of the latter. A non-imaginary Gettier case is presented in order to show how little difference it makes.

Making Counterfactual Assumptions

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).

On the Lumping Semantics of Counterfactuals

Kratzer (1981) discussed a naïve premise semantics of counterfactual conditionals, pointed to an empirical inadequacy of this interpretation, and presented a modification—partition semantics—which Lewis (1981) proved equivalent to Pollock's (1976) version of his ordering semantics. Subsequently, Kratzer (1989) proposed lumping semantics, a different modification of premise semantics, and argued it remedies empirical failings of ordering semantics as well as of naïve premise semantics. We show that lumping semantics yields truth conditions for counterfactuals that are not only different from what she claims they are, but also inferior to those of the earlier versions of premise semantics.

Proper names in twin worlds: Monophyly, paraphyly, and the world around us

This paper addresses the theoretical relevance of monophyletic, paraphyletic and polyphyletic groups under the paradigm of sophisticated scientific realism. The doctrine of metaphysical realism is introduced using the philosophy of Karl Popper as an example, which is then contrasted with scientific realism. A discussion of the nature of causal relations presents an account of counterfactual conditionals. The current state of art casts the theory of phylogenetic systematics in a stark contrast of classes (universals) and individuals (particulars). In practice, however, individuals piggyback on classes, or sets. Natural kinds are introduced in order to overcome this deep dichotomy. The theoretical relevance of natural kinds lies in their explanatory value, and that may change with changing context. It is for this reason that non-monophyletic groups can have explanatory value (their members can function as tokens of causally relevant kinds) within certain domains of evolutionary biology. Explanatory value is maximized by integration of the genealogical hierarchy of species and monophyletic taxa with other areas of evolutionary biology.

What is a disposition?

Attempts to capture the distinction between categorical and dispositional states in terms of more primitive modal notions – subjunctive conditionals, causal roles, or combinatorial principles – are bound to fail. Such failure is ensured by a deep symmetry in the ways dispositional and categorical states alike carry modal import. But the categorical/dispositional distinction should not be abandoned; it underpins important metaphysical disputes. Rather, it should be taken as a primitive, after which the doomed attempts at reductive explanation can be transformed into circular but interesting accounts.

Conditional Predictions

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I first outline the motivation for the probabilistic turn and Lewis' triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey's 'random-variable' approach, which circumvents these problems by giving up the notion that conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey's conditional, but also opens up the possibility of a unified probabilistic account of indicative and counterfactual conditionals.

The Deep Black Sea: Observability and Modality Afloat

In the spirit of B. C. van Fraassen's view of science called Constructive Empiricism, we propose a scientific criterion to decide whether a concrete object is observable, as well as a coextensive scientific-philosophical definition of observability, and we sketch a rigorous account of modal language occurring in science. We claim that our account of observability solves three problems to which current accounts of observability, notably van Fraassen's own accounts, give rise. We further claim that our account of modal propositions (subjunctive conditionals included), which proceeds wholly within the framework of the semantic view on scientific theories, grounds his claim that such an account is possible without relying on 'inflationary metaphysics', notably without postulating an infinitude of different universes besides the universe we inhabit. We thus claim to solve a fourth problem: how to give a precise nominalist account of modal language in science tailor-made for Constructive Empiricism.

Counterfactual and Semifactual Conditionals Prime Alternative Possibilities.

The authors examined in 3 experiments the comprehension of counterfactuals, such as "If it had rained, the plants would have bloomed," and semifactuals, such as "Even if it had rained, the plants would have bloomed," compared with indicative conditionals, "If it rained, the plants bloomed." The first experiment showed that people read the negative conjunction, "not p and not q" faster when it was primed by a counterfactual than when it was primed by an indicative conditional. They read the affirmative conjunction, "p and q" equally quickly when it was primed by either conditional. The 2nd experiment showed that people read the negated-antecedent conjunction, "not p and q" faster when it was primed by a semifactual conditional. The 3rd experiment corroborated these results in a direct comparison of counterfactuals and semifactuals. The authors discuss the implications of the results for the mental representations of different conditionals.