Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossible worlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossible worlds and argues that commitment to them can and should be had without great metaphysical or logical cost. The paper then provides an (...) account of reasoning with impossible worlds, by treating such reasoning as reasoning employing counterpossible conditionals, and provides a semantics for the proposed treatment. (shrink)

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.

What does 'if' mean? Timothy Williamson presents a controversial new approach to understanding conditional thinking, which is central to human cognitive life. He argues that in using 'if' we rely on psychological heuristics, fast and frugal methods which can lead us to trust faulty data and prematurely reject simple theories.

The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) (...) to solve the problems associated with propositional attitude contexts, intentional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphysical theory of such atypical worlds tend to move too quickly from philosophical characterizations to formal semantics. (shrink)

Conditionals has at its center an extended essay on this problematic and much-debated subject in the philosophy of language and logic, which the widely respected Oxford philosopher Michael Woods had been preparing for publication at the time of his death in 1993. It appears here edited by his eminent colleague David Wiggins, and is accompanied by a commentary specially written by a leading expert on the topic, Dorothy Edgington. This masterly and original treatment of conditionals will demand the attention of (...) all philosophers working in this area. (shrink)

Given his hostility to intensional locutions, it is not surprising that Quine was suspicious of the subjunctive conditional. Although he admitted its usefulness as a heuristic device, in order to introduce dispositional terms, he held that it had no place in a finished scientific theory. In this paper I argue in support of something like Quine’s position. Many contemporary philosophers are unreflectively realist about subjunctives, regarding them as having objective truth values. I contest this. “Moderate realist” theorists, such as Lewis (...) and Stalnaker, admit that subjunctives are context-relative and often indeterminate; I argue, using some examples from the contemporary literature on conditionals, that these features are deeper and more widespread than they think. “Ultra-realist” theories, which deny any indeterminacy, are not credible. Hence subjunctives are unsuitable for certain purposes, in particular the description of mind-independent reality. (shrink)

A number of papers have argued in favour of the material account of indicative conditionals, but typically they either concentrate on defending the account from the charge that it has counterintuitive consequences, or else focus on some particular positive argument in favour of the theory. In this paper, I survey the various positive arguments that can be given, presenting simple versions where possible and showing the connections between them. I conclude with some methodological considerations.

Peirce's example puts another nail in the coffin of the truth-functionality thesis. Conditionals are not truth-functional.

Classic work by one of the most brilliant figures in post-war analytic philosophy.

E. J. Lowe; Indicative and counterfactual conditionals, Analysis, Volume 39, Issue 3, 1 June 1979, Pages 139–141, https://doi.org/10.1093/analys/39.3.139.

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.

In his 1987 book _Conditionals, Frank Jackson presents an argument to the effect that the indicative conditionals of natural language have the same truth conditions as the material conditional of truth-functional logic. This Jackson refers to as the "paradox of indicative conditionals." I offer a solution to this paradox by arguing that some conditionals that appear to be in the indicative mood are actually subjunctives, to which the paradox does not apply. I support this proposed solution with some historical observations (...) on the evolution of the English verb phrase. (edited). (shrink)

This collection introduces the reader to some of the most interesting current work on conditionals. Particular attention is paid to possible world semantics for conditionals, the role of conditional probability in helping us to understand conditionals, implicature and the material conditional, and subjunctive versus indicative conditionals. Contributors include V.H. Dudman, Dorothy Edgington, Nelson Goodman, H.P. Grice, David Lewis, and Robert Stalnaker.

This paper is obsolete. It is superseded by the book, Conditionals in Context, MIT Press, 2005.

"If you turn left at the next corner, you will see a blue house at the end of the street." That sentence -- a conditional -- might be true even though it is possible that you will not see a blue house at the end of the street when you turn left at the next corner. A moving van may block your view; the house may have been painted pink; a crow might swoop down and peck out your eyes. Still, (...) in some contexts, we might ignore these possibilities and correctly assert the conditional. In this book, Christopher Gauker argues that such context-relativity is the key to understanding the semantics of conditionals. Contexts are defined as objective features of the situation in which a conversation takes place, and the semantic properties of sentences -- conditionals included -- are defined in terms of assertibility in a context. One of the primary goals of a theory of conditionals has to be to distinguish correctly between valid and invalid arguments containing conditionals. According to Gauker, an argument is valid if the conclusion is assertible in every context in which the premises are assertible. This runs counter to what Gauker sees as a systematic misreading of the data by other authors, who judge arguments to be invalid if they can think of a context in which the premises are judged true and some other context in which the conclusion is judged false. Different schools of thought on conditionals reflect fundamentally different approaches to semantics. Gauker offers his theory as a motive and test case for a distinctive kind of semantics that dispenses with reference relations and possible worlds. (shrink)

In "Truth and the Past, " Dummett, best known as a proponent of antirealism, clarifies his current positions on the metaphysical issue of realism and the ...

Michael Dummett's three John Dewey Lectures--"The Concept of Truth," "Statements About the Past," and "The Metaphysics of Time"--were delivered at Columbia University in the spring of 2002. Revised and expanded, the lectures are presented here along with two new essays by Dummett, "Truth: Deniers and Defenders" and "The Indispensability of the Concept of Truth." In _Truth and the Past,_ Dummett clarifies his current positions on the metaphysical issue of realism and the philosophy of language. He is best known as a (...) proponent of antirealism, which loosely characterizes truth as what we are capable of knowing. The events of the past and statements about them are critical tests of an antirealist position. These essays continue and significantly contribute to Dummett's work. (shrink)

The score was tied in the bottom of the ninth, I was on third base, and there was only one out when Bubba hit a towering fly ball to deep left-center. Although I’m no speed-demon, the ball was hammered so far that I easily could have scored the winning run if I had tagged up. But I didn’t. I got caught up in the excitement and stupidly played it half way, standing between third and home until I saw the center (...) fielder make his spectacular catch, after which I had to return sheepishly to third. The next batter grounded out, and we lost the game in extra innings. (shrink)

kind of joke to ask what is the case if the antecedent is false—“And where are the biscuits if I don’t want any?”, “And what’s on PBS if I’m not interested?”, “And who shot Kennedy if that’s not what I’m asking?”. With normal indicative conditionals like.

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)

It is widely agreed that contraposition, strengthening the antecedent and hypothetical syllogism fail for subjunctive conditionals. The following putative counter-examples are frequently cited, respectively.

This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten, provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – assumed to (...) be merely (p⊃q) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q. (shrink)

The author maintains that there is no special problem about the verification or analysis of counterfactual or unfulfilled conditional statements. there is no special problem about the verification or analysis of subjunctive conditionals. it exhausts the peculiar philosophical interest of these two classes of statement to explain why no philosopher ought to think them peculiarly interesting, and to explain why so many do. the author states that it should not be supposed that if he achieves his aim, all the difficulties (...) and disputes which have occurred in discussions supposed to be about counterfactual or subjunctive conditionals will be settled in his article. this is because many of these difficulties have arisen, not out of features peculiar to either of these classes of statement, but out of features common to all conditional statements. (staff). (shrink)

Reasoning with conditionals is often thought to be non-monotonic, but there is no incompatibility with classical logic, and no need to formalise inference itself as probabilistic. When the addition of a new premise leads to abandonment of a previously compelling conclusion reached by modus ponens, for example, this is generally because it is hard to think of a model in which the conditional and the new premise are true.