At the center of the literature on conditionals lies the division between indicative and subjunctive conditionals, and Ernest Adams’ famous minimal pair: If Oswald didn’t shoot Kennedy, someone else did. If Oswald hadn’t shot Kennedy, someone else would have. While a lot of attention is paid to figuring out what these different kinds of conditionals mean, significantly less attention has been paid to the question of why their grammatical differences give rise to their semantic differences. In this paper, I articulate (...) and defend an answer to this question that illuminates and unifies the meanings of both kinds of conditionals. The basic idea is that epistemic and metaphysical possibilities differ with respect to their interaction with time, such that there can be present epistemic possibilities with different pasts, while present metaphysical possibilities share the same past. The interpretation of conditionals is subject to a pragmatic constraint that rules out interpretations in which their consequents are directly settled by information used to build their domains. The past + future morphology on subjunctives, but not indicatives, is what allows them to receive a metaphysical interpretation in light of this pragmatic constraint. The resulting theory predicts several surprising features of indicatives and subjunctives, which I argue are correct. (shrink)

The purpose of this note is to dispute Michael Ayers' claim that "there is no special problem of subjunctive conditionals".

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and (...) an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals. (shrink)

Book synopsis: Philosophers have long been fascinated by the connection between cause and effect: are 'causes' things we can experience, or are they concepts provided by our minds? The study of causation goes back to Aristotle, but resurged with David Hume and Immanuel Kant, and is now one of the most important topics in metaphysics. Most of the recent work done in this area has attempted to place causation in a deterministic, scientific, worldview. But what about the unpredictable and chancey (...) world we actually live in: can one theory of causation cover all instances of cause and effect? (shrink)

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

I develop an account of counterfactual conditionals using “causal models”, and argue that this account is preferable to the currently standard account in terms of “similarity of possible worlds” due to David Lewis and Robert Stalnaker. I diagnose the attraction of counterfactual theories of causation, and argue that it is illusory.

The abstract structure of inquiry - the process of acquiring and changing beliefs about the world - is the focus of this book which takes the position that the "pragmatic" rather than the "linguistic" approach better solves the philosophical problems about the nature of mental representation, and better accounts for the phenomena of thought and speech. It discusses propositions and propositional attitudes (the cluster of activities that constitute inquiry) in general and takes up the way beliefs change in response to (...) potential new information, suggesting that conditional propositions should be understood as projections of epistemic policies onto the world.Robert C. Stalnaker is a professor in the Sage School of Philosophy at Cornell University. A Bradford Book. (shrink)

Some cases show that counterfactual conditionals (‘counterfactuals’ for short) are inherently ambiguous, equivocating between forward-tracking and backtracking counterfactu- als. Elsewhere, I have proposed a causal modeling semantics, which takes this phenomenon to be generated by two kinds of causal manipulations. (Lee 2015; Lee 2016) In an important paper (Hiddleston 2005), Eric Hiddleston offers a different causal modeling semantics, which he claims to be able to explain away the inherent ambiguity of counterfactuals. In this paper, I discuss these two semantic treatments (...) and argue that my (bifurcated) semantics is theoretically more promising than Hiddleston’s (unified) semantics. (shrink)

Counterfactuals are inherently ambiguous in the sense that the same counterfactual may be true under one mode of counterfactualization but false under the other. Many have regarded the ambiguity of counterfactuals as consisting in the distinction between forward-tracking and backtracking counterfactuals. This is incorrect since the ambiguity persists even in cases not involving backtracking counterfactualization. In this paper, I argue that causal modeling semantics has the resources enough for accounting for the ambiguity of counterfactuals. Specifically, we need to distinguish two (...) types of causal manipulation, which I call “intervention” and “extrapolation” respectively. To intervene in a causal model M is to change M’s structural equations in some specific ways, while to extrapolate M is to change the value assignment of M’s variables in some specific ways. I argue that intervention and extrapolation offer a natural explanation for the ambiguity of counterfactuals. (shrink)

This book contends that insufficient attention has been paid to the syntax of conditionals, as investigated by linguists.

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. (...) Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence. (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)

Philosophers have long analyzed the truth-condition of counterfactual conditionals in terms of the possible-worlds semantics advanced by Lewis [13] and Stalnaker [23]. In this paper, I argue that, from the perspective of philosophical semantics, the causal modeling semantics proposed by Pearl [17] and others (e.g., Briggs [3]) is more plausible than the Lewis-Stalnaker possible-worlds semantics. I offer two reasons. First, the possible-worlds semantics has suffered from a specific type of counterexamples. While the causal modeling semantics can handle such examples with (...) ease, the only way for the possible-worlds semantics to do so seems to cost it its distinctive status as a philosophical semantics. Second, the causal modeling semantics, but not the possible-worlds semantics, has the resources enough for accounting for both forward-tracking and backtracking counterfactual conditionals. (shrink)

Conditional sentences are among the most intriguing and puzzling features of language, and analysis of their meaning and function has important implications for, and uses in, many areas of philosophy. Jonathan Bennett, one of the world's leading experts, distils many years' work and teaching into this book, making it the fullest and most authoritative treatment of the subject.

The idea that english has more than one declarative "mood" has been dismissed as superstitious by empirically-minded grammarians of english for centuries--with such spectacular unsuccess, however, that the indicative/subjunctive dichotomy stands today as a cornerstone for philosophical and logical speculation about "conditionals." let me be next into the breach. i shall urge that there is no grammatical basis for any such distinction. and as for the particular adjudications of mood logicians and philosophers actually propose, there is neither rhyme nor reason (...) to them. my bent, then, is basically destructive. but i shall also be outlining a better taxonomy. (shrink)