Indicative Conditionals, Misc

A plausible principle about the felicitous use of indicative conditionals says that there is something strange about asserting an indicative conditional when you know whether its antecedent is true. But in most contexts there is nothing strange at all about asserting indicative conditionals like ‘If Oswald didn’t shoot Kennedy, then someone else did’. This paper argues that the only compelling explanation of these facts requires the resources of contextualism about knowledge.

The material account claims that indicative conditionals are material. However, the conventional wisdom even among material account enthusiasts is that the material account cannot be extended to subjunctive conditionals. There are mainly three reasons that motivate this consensus: (1) the belief that if subjunctives were material, most subjunctive conditionals would be vacuously true, which is implausible; (2) its inconsistency with Adam pairs, which suggest that indicative and subjunctive conditionals have different truth conditions; and (3) the belief that it is an (...) inferior hypothesis compared to the possible world theories. I will argue against (1) that the counterintuitive aspects of vacuously true conditionals can be explained away in a uniform fashion, regardless of whether they are indicatives or subjunctives. I reinforce this assumption by showing that the positive arguments for the material account of indicatives are also intuitively valid for subjunctives. The point mentioned in (2) is resisted by explaining Adam pairs as logically equivalent conditionals that can be appropriate at different times, depending of the speaker’s epistemic situation. Finally, (3) is criticised by making the case that the possible world account faces insurmountable problems and that a full-blown material account of indicatives and subjunctives is overall a more elegant solution. (shrink)

Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey of basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted ‘if-then’ as a version of ‘implies’ and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of ‘if-then’ are used instead of being mentioned as the premise and (...) the conclusion of an implication relation. It was his opinion that the criticisms and alternatives to the material implication presented by C. I. Lewis and others would never be made in the first place if Russell simply called the Philonian construction ‘material conditional’ instead of ‘material implication’. Quine’s interpretation on the topic became hugely influential, if not universally accepted. This paper will present the following criticisms against this interpretation: (1) the notion of material implication does not involve a use-mention fallacy, since the components of ‘if-then’ are mentioned and not used; (2) Quine’s belief that the components of ‘if-then’ are used was motivated by a conditional-assertion view of conditionals that is widely controversial and faces numerous difficulties; (3) the Philonian construction remains paradoxical even if it is called ‘material conditional’; (4) the Philonian construction is more plausible when it is interpreted as a material implication. (shrink)

Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences in two circumstances: (1) when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a proposition she (...) accepts because she doesn’t know what the truth-values of its propositional contents; (2) when she accepts a proposition based on extensional evidence, but thinks that this evidence is insufficient to establish its logical consequences, which would require intensional evidence. It is argued that this tension is responsible for the counter-intuitive aspects of the material account of conditionals involving the negation of conditionals, hypothetical syllogism, contraposition and the inferential passage from disjunctions to conditionals (or-to-if). This tension is also behind some known puzzles involving conditionals, namely, conditional stand-offs, Adam pairs, the cheating partner example, jump-out conditionals, the problem of counterfactuals and the burglar’s puzzle. It is shown that this tension is always dissolved in favour of extensional evidence, since intensional evidence is defeasible, while extensional evidence is not. Thus, it is irrational to deny the logical consequences of an accepted proposition due to its reliance on intensional evidence and ignorance of its extensional evidence. (shrink)

The present dissertation investigates certain facets of the logical structure of oughts – where “ought” is used as a noun, roughly meaning obligation. I do so by following two lines of inquiry. The first part of the thesis places oughts in the context of practical rationality. The second part of the thesis concerns the inference rules governing arguments about oughts, and specifically the inference rule of Reasoning by Cases. These two lines of inquiry, together, aim to expound upon oughts in (...) rationality and reasoning. The methodology used in this dissertation is the one of philosophical logic, in which logical, qualitative models are developed to support and foster conceptual analysis. The dissertation consists of four main chapters. The first two chapters are devoted to the role of oughts in practical rationality. I focus on the so-called Enkratic principle of rationality, which – in its most general formulation – requires that if an agent believes sincerely and with conviction that she ought to do X, then she intends to X. I develop a logical framework to investigate the (static and dynamic) relation between those oughts believed by the agent and her intentions. It is shown that, under certain minimal assumptions, the Enkratic principle of rationality is a principle of limited validity. The following two chapters of the dissertation constitute a study of the classical inference rule of Reasoning by Cases, which – in its simplest form – moves from the premises “A or B”, “if A then C” and “if B then C” to the conclusion “C”. Recent literature has called the validity of Reasoning by Cases into question, with the most influential counterexample being the so-called Miners’ Puzzle – an instance of Reasoning by Cases where “C” involves oughts. I provide a unifying explanation of why the Miners’ Puzzle emerges. It is shown that, within specific boundaries, Reasoning by Cases is a valid inference rule. (shrink)

The standing tradition in theorizing about meaning, since at least Frege, identifies meaning with propositions, which are, or determine, the truth-conditions of a sentence in a context. But a recent trend has advocated a departure from this tradition: in particular, it has been argued that modal claims do not express standard propositional contents. This non-propositionalism has received different implementations in expressivist semantics and certain kinds of dynamic semantics. They maintain that the key aspect of interpretation of modal claims is the (...) characteristic dynamic effect they have on the context. I argue that pessimism about truth-conditions arises from an overly simplistic picture of content, context and their interaction. While I agree with the critics that an important aspect of modal meaning is the dynamic effect modals have on the context, I argue that they have mischaracterized the nature and the complexity of this effect. A more nuanced account of the interaction between modals and context shows that far from being incompatible with propositional meaning, the dynamic aspect of meaning is precisely what allows us to predict the correct propositional content of an utterance. (shrink)

Recently, there has been a shift away from traditional truth-conditional accounts of meaning towards non-truth-conditional ones, e.g., expressivism, relativism and certain forms of dynamic semantics. Fueling this trend is some puzzling behavior of modal discourse. One particularly surprising manifestation of such behavior is the alleged failure of some of the most entrenched classical rules of inference; viz., modus ponens and modus tollens. These revisionary, non-truth-conditional accounts tout these failures, and the alleged tension between the behavior of modal vocabulary and classical (...) logic, as data in support of their departure from tradition, since the revisionary semantics invalidate some of these patterns. I, instead, offer a semantics for modality with the resources to accommodate the puzzling data while preserving classical logic, thus affirming the tradition that modals express ordinary truth-conditional content. My account shows that the real lesson of the apparent counterexamples is not the one the critics draw, but rather one they missed: namely, that there are linguistic mechanisms, reflected in the logical form, that affect the interpretation of modal language in a context in a systematic and precise way, which have to be captured by any adequate semantic account of the interaction between discourse context and modal vocabulary. The semantic theory I develop specifies these mechanisms and captures precisely how they affect the interpretation of modals in a context, and do so in a way that both explains the appearance of the putative counterexamples and preserves classical logic. (shrink)

Chancy modus ponens is the following inference scheme: ‘probably φ’, ‘if φ, then ψ’, therefore, ‘probably ψ’. I argue that Chancy modus ponens is invalid in general. I further argue that the invalidity of Chancy modus ponens sheds new light on the alleged counterexample to modus ponens presented by McGee. I close by observing that, although Chancy modus ponens is invalid in general, we can recover a restricted sense in which this scheme of inference is valid.

We show that each of three natural sets of assumptions about the conditional entails necessitarianism: that anything possible is necessary.

Two experiments investigate two versions of Aristotle’s Thesis for the first time. Aristotle’s Thesis is a negated conditional, which consists of one propositional variable with a negation either in the antecedent or in the consequent. This task allows us to infer if people interpret indicative conditionals as material conditionals or as conditional events. In the first experiment I investigate between-participants the two versions of Aristotle’s Thesis crossed with abstract versus concrete task material. The modal response for all four groups is (...) consistent with the conditional event and inconsistentwith the material conditional interpretation. This observation is replicated in the second experiment. Moreover, the second experiment rules out scope ambiguities of the negation of conditionals. Both experiments provide new evidence against thematerial conditional interpretation of conditionals and support the conditional event interpretation. Finally, I discuss implications formodeling indicative conditionals and the relevance of this work for experimental philosophy. (shrink)

Decision theorists tend to treat indicative conditionals with reservation, because they can easily lead a deliberating agent astray. However, many indicatives can be very helpful in contexts of deliberation, so denying them all a role in such contexts seems to be overkill. We show that a recently revived inferential view on conditionals provides a straightforward explanation of why some indicatives are unassertable in contexts of deliberation and hints at a way of telling "deliberationally useless" and "deliberationally useful" conditionals apart.

ABSTRACTIf-thenism is a strategy of paraphrasing seemingly obvious claims in order to avoid their problematic commitments. The success of this strategy, says Yablo, depends on the possibility of reading everyday language conditionals incrementally. The incremental reading is to exclude that the supposition of the antecedent might interfere with the truth of the consequent, as in the standard or ‘interference’ reading. I argue that Yablo's main arguments for the incremental reading are question-begging.

This paper is a guide to the main ideas and innovations in Robert Stalnaker's "Indicative Conditionals". The paper is for a volume of essays on twenty-one classics of formal semantics edited by Louise McNally, Yael Sharvit and Zoltàn Gendler Szabò.

KK is the thesis that if you can know p, you can know that you can know p. Though it’s unpopular, a flurry of considerations has recently emerged in its favour. Here we add fuel to the fire: standard resources allow us to show that any failure of KK will lead to the knowability and assertability of abominable indicative conditionals of the form ‘If I don’t know it, p’. Such conditionals are manifestly not assertable—a fact that KK defenders can easily (...) explain. I survey a variety of KK-denying responses and find them wanting. Those who object to the knowability of such conditionals must either deny the possibility of harmony between knowledge and belief, or deny well-supported connections between conditional and unconditional attitudes. Meanwhile, those who grant knowability owe us an explanation of such conditionals’ unassertability—yet no successful explanations are on offer. Upshot: we have new evidence for KK. (shrink)

A few purported counterexamples to the Adams thesis have cropped up in the literature in the last few decades. I propose a theory that accounts for them, in a way that makes the connections between indicative conditionals and counterfactuals clearer.

This is a handbook article about conditionals.

This is a handbook article about indicative conditionals.

A part of Stalnaker (1968)’s influential theory of conditionals has been neglected, namely the role for an accessibility relation between worlds. I argue that the accessibility relation does not play the role intended for it in the theory as stated, and propose a minimal revision which solves the problem, and brings the theory in line with the formulation in Stalnaker & Thomason 1970.

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

Some left-nested indicative conditionals are hard to interpret while others seem fine. Some proponents of the view that indicative conditionals have No Truth Values (NTV) use their view to explain why some left-nestings are hard to interpret: the embedded conditional does not express the truth conditions needed by the embedding conditional. Left-nestings that seem fine are then explained away as cases of ad hoc, pragmatic interpretation. We challenge this explanation. The standard reasons for NTV about indicative conditionals (triviality results, Gibbardian (...) standoffs, etc.) extend naturally to NTV about biconditionals. So NTVers about conditionals should also be NTVers about biconditionals. But biconditionals embed much more freely than conditionals. If NTV explains why some left-nested conditionals are hard to interpret, why do biconditionals embed successfully in the very contexts where conditionals do not embed? (shrink)

When we discuss normative reasons, oughts, requirements of rationality, hypothetical imperatives (or “anankastic conditionals”), motivating reasons and so on, we often use verbs like “believe” and “want” to capture a relevant subject’s perspective. According to the received view about sentences involving these verbs, what they do is describe the subject’s mental states. Many puzzles concerning normative discourse have to do with the role that mental states consequently appear to play in this discourse. This book uses tools from formal semantics and (...) the philosophy of language to develop an alternative account of sentences involving these verbs. According to this view, which is called parentheticalism (in honour of J. O. Urmson), we very commonly use these verbs in a parenthetical sense. Used with this sense, these verbs themselves express backgrounded side-remarks on the contents they embed, and these latter, embedded contents constitute the at-issue contents of our utterances. This means that instead of speaking about the subject’s mental states, we often use sentences involving “believe” and “want” to speak about the world in a way that, in the conversational background, relates our utterances to her point of view. This idea is made precise, and it is used to solve various puzzles concerning normative discourse. The final result is a new, unified understanding of normative discourse, which gets by without postulating conceptual breaks between objective and subjective normative reasons, or normative reasons and rationality, or indeed between the reasons we ascribe to an agent and the reasons she herself can be expected to cite. Instead of being connected to either subjective mental states or objective facts, all of these normative statuses can be adequately articulated by citing worldly considerations from the subject’s point of view. (shrink)

The dominance conditional 'If I drink the contents of cup A, I will drink more than if drink the contents of cup B' is true if we know that the first cup contains more than the second. In the first part of the paper, I show that only one kind of theory of indicative conditionals can explain this fact — a Stalnaker-type semantics. In the second part of the paper, I show that dominance conditionals can help explain a long-standing mystery: (...) the question of how one-boxers and two-boxers are guided by conditionals to their respective answers to the Newcomb problem. I will suggest that both implicitly appeal to a decision theoretic principle I will call the Dominance Norm (DN), a principle that connects indicative dominance conditionals with rational courses of action. Finally, I show that DN in combination with a Stalnaker-type theory of indicatives commits us to the two-boxing answer in the Newcomb problem. (shrink)

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...) a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45. (shrink)

Here I present a new objection to the material or "hook" analysis of indicative conditionals - the thesis that an indicative conditional 'If A then C' has the truth-conditions of the so-called material conditional - based on Liar-like reasoning. This objection seems invulnerable to any Grice-Lewis-Jackson-inspired pragmatic rejoinder.

Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a universal theory (...) of Sobel sequences in terms of presuppositional anaphora. One relevant result is that the phenomenon neither counts against nor in favour of the simplified standard account of counterfactuals à la Stalnaker-Lewis. (shrink)

Brogaard and Salerno (2008) argued that counter-examples to contraposition, strengthening the antecedent, and hypothetical syllogism involving subjunctive conditionals only seem to work because they involve a contextual fallacy where the context assumed in the premise(s) is illicitly shifted in the conclusion. To avoid such counter-examples they have proposed that the context must remain fixed when evaluating an argument for validity. That is the Brogaard-Salerno Stricture. Tristan Haze (2016), however, has recently objected that intuitively valid argumentative forms such as conjunction introduction (...) do not satisfy this constraint. This paper has two goals. First, it argues that the Brogaard-Salerno Stricture is not violated in Haze’s putative counter-example. Second, it argues that since this stricture blocks the usual counter-examples to instances of classical argumentative forms that involve indicative or subjunctive conditionals, it is reasonable to infer that indicative and subjunctive conditionals are material. (shrink)

The truth-functional hypothesis states that indicative conditional sentences and the material implication have the same truth conditions. Haze (2011) has rejected this hypothesis. He claims that a self-referential conditional, coupled with a plausible assumption about its truth-values and the assumption that the truth-functional hypothesis is true, lead to a liar’s paradox. Given that neither the self-referential conditional nor the assumption about its truth-values are problematic, the culprit of the paradox must be the truth-functional hypothesis. Therefore, we should reject it. In (...) this paper I argue that, contrary to what Haze thinks, the truth-functional hypothesis is not to blame. In fact, no liar’s paradox emerges when the truth-functional hypothesis is true; it emerges only if it is false. (shrink)

It is generally agreed that there are two kinds of indicative conditionals that do not contain conditional 'then.' There are hypothetical conditionals such as 'If Mary has done the groceries, there is beer in the fridge' and there are biscuit conditionals such as 'If you are thirsty, there is beer in the fridge.' There is also broad consensus that we cannot find an analogous distinction between hypothetical and biscuit conditionals within indicative conditionals that do feature 'then.' Conditionals containing 'then,' it (...) is assumed, are uniformly read as hypothetical conditionals. In this article, I shall argue that there are biscuit conditionals featuring 'then.' This result, I take it, is not only interesting on its own. It also puts pressure on the popular view that conditional 'then' triggers the presupposition that in some situations in which the conditional's antecedent is not true, its consequent is not true either. (shrink)

U radu se navodi kontraprimer za Potkovicu (teoriju po kojoj indikativni kondicionali imaju iste istinosne uslove kao i materijalna implikacija), koji je modifikovana verzija “kondicionala sa igrališta” koje je konstruisao Džejson Deker. Pokazuje se zašto Dekerov primer nije dobar ako se prikaže u izvornoj formi, a zatim se, uz pomoć misaonog eksperimenta sa inverznim spektrom, nudi poboljšana verzija Dekerovog primera. Na kraju rada se ukazuje da modifikovani primer “kondicionala sa igrališta” ne predstavlja problem za epistemičku verziju dvodimenzionalne semantike (E2-D), i (...) da u tom smislu treba dati prednost E2-D u razumevanju semantike indikativnih kondicionala. (shrink)

I argue against the Ramsey test connecting indicative conditionals with conditional probability, by means of examples in which conditional probability is high but the conditional is intuitively implausible. At the end of the paper, I connect these issues to patterns of belief revision.

I give cases where the contrast between "if Shakespeare had not written Hamlet someone else would have" and "if Shakespeare did not write Hamlet and someone else did"is found in future tense sentences. This is often denied.

In this paper I look at indicative nested whether-conditionals, sentences like:If I pass the exam, I will pass whether I pray or not.The behavior of ‘if’ in these examples is to be contrasted with the behavior of ‘if’ in or-to-if conditionals:If Mary is at home or at work, then if she is not at home, she is at work.I argue that no currently available semantics for indicative conditionals can explain both the behavior of ‘if’ in nested whether-conditionals and the behavior (...) of ‘if’ in or-to-ifs. We need a theory that predicts both. While no currently available theory makes the right predictions, one theory comes close—Heim’s rendition of Stalnaker’s semantics :183–221, 1992). I show how to fix Heim’s view to get the right results for all cases. In sum, the paper argues for a particular development of Stalnaker’s semantics, and shows that whether-conditionals cannot be dealt with on other approaches. (shrink)

A dynamic semantics for iffy oughts offers an attractive alternative to the folklore that Chisholm's paradox enforces an unhappy choice between the intuitive inference rules of factual and deontic detachment. The first part of the story told here shows how a dynamic theory about ifs and oughts gives rise to a nonmonotonic perspective on deontic discourse and reasoning that elegantly removes the air of paradox from Chisholm's puzzle without sacrificing any of the two detachment principles. The second part of the (...) story showcases two bonus applications of the framework suggested here: it offers a response to Forrester's gentle murder paradox and avoids Kolodny and MacFarlane's miners paradox about deontic reasoning under epistemic uncertainty. A comparison between the dynamic semantic proposal made in this paper and a more conservative approach combining a static semantics with a dynamic pragmatics is provided. (shrink)

A proof by Allan Gibbard (Ifs: Conditionals, beliefs, decision, chance, time. Reidel, Dordrecht, 1981) seems to demonstrate that if indicative conditionals have truth conditions, they cannot be stronger than material implication. Angelika Kratzer's theory that conditionals do not denote two-place operators purports to escape this result [see Kratzer (Chic Linguist Soc 22(2):1–15, 1986, 2012)]. In this note, I raise some trouble for Kratzer’s proposed method of escape and then show that her semantics avoids this consequence of Gibbard’s proof by denying (...) modus ponens. I also show that the same holds for Anthony Gillies’ semantics (Philos Rev 118(3):325–349, 2009) and argue that this consequence of these theories is not obviously prohibitive—hence, both remain viable theories of indicative conditionals. (shrink)

Kratzer semantics for modals and conditionals generates the prediction that sentences of the form if p, ought p are trivially true. As Frank and Zvolenszky show, for certain flavors of modality, like deontic modality, this prediction is false. I explain some conservative solutions to the problem, and then argue that they are inadequate to account for puzzle cases involving self-frustrating oughts. These cases illustrate a general problem: there are two forms of information-sensitivity in deontic modals. Even generalizations of Kratzer semantics (...) that predict these two roles for information, e.g. Kolodny and MacFarlane, predict that they vary together. I propose a generalization of Kratzer semantics that allows the two roles for information to vary independently of each other. (shrink)

Many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to argue for an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on the evidential meaning of certain English and Dutch modal expressions.

At least many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to revive an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on two Dutch linguistic markers.

No existing conditional semantics captures the dual role of 'if' in embedded interrogatives — 'X wonders if p' — and conditionals. This paper presses the importance and extent of this challenge, linking it to cross-linguistic patterns and other phenomena involving conditionals. Among these other phenomena are conditionals with multiple 'if'-clauses in the antecedent — 'if p and if q, then r' — and relevance conditionals — 'if you are hungry, there is food in the cupboard'. Both phenomena are shown to (...) be problematic for existing analyses. Surprisingly, the decomposition of conditionals needed to capture the link with interrogatives provides a new analysis that captures all three phenomena. The model-theoretic semantics offered here relies on a dynamic conception of meaning and compositionality, a feature discussed throughout. (shrink)

We present an approach to combining three areas of research which we claim are all based on information theory: knowledge representation in Artificial Intelligence and Cognitive Science using prototypes, plans, or schemata; formal semantics in natural language, especially the semantics of the `if-then' conditional construct; and the logic of subjunctive conditionals first developed using a possible worlds semantics by Stalnaker and Lewis. The basic premise of the paper is that both schema-based inference and the semantics of conditionals are based on (...) Dretske's notion of information flow and Barwise and Perry's notion of a constraint in situation semantics. That is, the connection between antecedent and consequent of a conditional `if were the case then would be the case' is an informational relation holding with respect to a pragmatically determined utterance situation. The bridge between AI and conditional logic is that a prototype or planning schema represents a situation type, and the background assumptions underlying the application of a schema in a situation correspond to channel conditions on the flow of information. Adapting the work of Stalnaker and Lewis, the semantics of conditionals is modeled by a refinement ordering on situations: a conditional `if then ' holds with respect to a situation if all the minimal refinements of the situation that support also support . We present new logics of situations, information flow, and subjunctive conditionals based on three-valued partial logic that formalizes our approach, and conclude with a discussion of the resulting theory of conditionals, including the "paradoxes" of conditional implication, the difference between truth conditions and assertability conditions for subjunctive conditionals, and the relationship between subjunctive and indicative conditionals. (shrink)

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)

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.

Section 1 briefly examines three theories of indicative conditionals. The Suppositional Theory is defended, and shown to be incompatible with understanding conditionals in terms of truth conditions. Section 2 discusses the psychological evidence about conditionals reported by Over and Evans (this volume). Section 3 discusses the syntactic grounds offered by Haegeman (this volume) for distinguishing two sorts of conditional.

In "Against the Indicative," AUSTRALASIAN JOURNAL OF PHILOSOPHY 72 (1994): 17-26, and more recently in "Classifying `Conditionals': the Traditional Way is Wrong", ANALYSIS 60 (2000): 147, V.H. Dudman argues that (a) `If Oswald didn't shoot Kennedy then someone else did' and (b) `If Oswald doesn't shoot Kennedy then someone else will' should not be classified together as "indicative conditionals." Dudman relies on the assumption that (a) is entailed by (c) `Someone shot Kennedy', whereas (b) is not entailed by (d) `Someone (...) will shoot Kennedy'. I argue that the same reasoning which shows that (d) does not entail (b) also shows that (c) does not entail (a). One upshot is that Dudman's and Mellor's respective interpretations of so-called past indicative conditionals cannot be correct. (shrink)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B , and conditional bets, I bet you that if A then B . The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional— true , false , or void for indicative conditionals and win , lose (...) , or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgements in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis. (shrink)

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

In this article, I present a schema for generating counterexamples to the argument form known as Hypothetical Syllogism with indicative conditionals. If my schema for generating counterexamples to HS works as I think it does, then HS is invalid for indicative conditionals.

Lee Archie argued that if any truth values are consistently assigned to a natural language conditional to which Modus Ponens and Modus Tollens are valid argumentative forms, and affirming the consequent is an invalid argumentative form, this conditional would have the same truth conditions than a material implication. This argument is simple and it requires few assumptions that are relatively uncontroversial. We show that it is possible to extend Archie’s argument to three-valued logics and five-valued logics and vindicate a slightly (...) weaker conclusion, but that is still important: even if we would not believe in bivalence and in the classical negation operator, we would still have good reasons to accept that natural language conditionals and the material implication share truth conditions. (shrink)

This discussion note attempts to show that, pace Niko Kolodny and John MacFarlane, the Miners case intuitively speaks in favor of subjectivism. I argue that properly understood the intuitively correct judgements concerning the case are compatible with subjectivism. My argument is based, among other things, on a comparison between the Minders case and other cases as well as on considerations of blameworthiness.