Epistemic Accounts of Indicative Conditionals

Numerous triviality results have been directed at a collection of views that tie the probability of a conditional sentence to the conditional probability of the consequent on its antecedent. -/- In this paper I argue that this identification makes little sense if conditional sentences are context sensitive. The best alternative, I argue, is a version of the thesis which states that if your total evidence is E then the evidential probability of a conditional evaluated in a context where E is (...) salient is the probability of the consequent given the antecedent. The biggest challenge to this thesis comes from the 'static' triviality arguments developed by Stalnaker, Hajek and Hall. It is argued that these arguments rely on invalid principles of conditional logic and that the thesis is consistent with a reasonably strong logic that does not include the principles in question. (shrink)

This note relates the Lewis/Kratzer view of conditionals as restrictors to the philosophical debate over the meaning of conditionals.

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)

The prevailing viewpoint concerning conditionals asserts two claims: (1) conditionals featuring non-assertive acts in their consequents, such as commands and promises, cannot plausibly be construed as assertions of material implication; (2) the most promising hypothesis for such sentences is conditional-assertion theory, which defines a conditional as a conditional speech act, i.e., the performance of a speech act given the assumption of the antecedent. This hypothesis carries significant and far-reaching implications, as conditional speech acts are not synonymous with a proposition possessing (...) truth conditions. This paper opposes such a view in two steps. Firstly, it presents a battery of objections against conditional-assertion theory. Secondly, it advances the argument that such examples can indeed be convincingly construed as assertions of 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, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences 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 are the truth-values of its propositional contents. This tension motivates counterexamples to the negation of conditionals, the propositional analysis of conditionals, hypothetical syllogism, contraposition and or-to-if. It is argued that these counterexamples are non-starters because they rely on a mix of intensionally based premises and extensionally based conclusions. Instead, a genuine counterexample to classical argumentative forms should present circumstances where an intuitively true and extensionally based premise leads to an intuitively false conclusion that is also extensionally based. The other point is that evidentiary concerns about intensionally based beliefs should be constrained by the truth conditions of propositions presented by classical logic, which are nothing more than requirements of coherence in distributions of truth value. It is argued that this restriction also dissolves some known puzzles such as conditional stand-offs, the Adams pair, the opt-out property and the burglar’s puzzle. (shrink)

*This is a project I hope to come back to one day. It stalled, a bit, on the absence of a positive theory of update I could be satisfied with* When should we believe a indicative conditional, and how much confidence in it should we have? Here’s one proposal: one supposes actual the antecedent; and sees under that supposition what credence attaches to the consequent. Thus we suppose that Oswald did not shot Kennedy; and note that under this assumption, Kennedy (...) was assassinated by someone other than Oswald. Thus we are highly confident in the indicative: if Oswald did not kill Kennedy, someone else did. (shrink)

Indicative and subjunctive conditionals are in non-complimentary distribution: there are conversational contexts at which both are licensed (Stalnaker (1975), Karttunen & Peters (1979), von Fintel (1998)). This means we can ask an important, but under-explored, question: in contexts which license both, what relations hold between the two? -/- In this paper, I’ll argue for an initially surprising conclusion: when attention is restricted to the relevant contexts, indicatives and subjunctives are co-entailing. §1 introduces the indicative/subjunctive distinction, along with a discussion of (...) the relevant notion of entailment; §2 presents the main argument of the paper, and §3 considers some of the philosophical implications the argument in §2. Finally, §4 argues that we can reconcile the equivalence of indicatives and subjunctives with apparently conflicting judgments. (shrink)

The chapter is devoted to the probability and acceptability of indicative conditionals. Focusing on three influential theses, the Equation, Adams’ thesis, and the qualitative version of Adams’ thesis, Sikorski argues that none of them is well supported by the available empirical evidence. In the most controversial case of the Equation, the results of many studies which support it are, at least to some degree, undermined by some recent experimental findings. Sikorski discusses the Ramsey Test, and Lewis’s triviality proof, with special (...) attention dedicated to the popular ways of blocking it. Sikorski concludes that the role of the three theses in future studies of conditionals should be re-thought, and he presents alternative proposals. (shrink)

If modus ponens is valid, then you should take up smoking.

Timothy Williamson has defended the claim that the semantics of the indicative ‘if’ is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by a fallible cognitive heuristic, called the Suppositional Procedure. Williamson’s Suppositional Conjecture has it that the Suppositional Procedure is humans’ primary way of prospectively assessing conditionals. This paper raises some doubts on the Suppositional Procedure and Conjecture.

This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation built on the principle that the antecedent of a conditional is probabilistically independent of the conditional and a more transparent method of constructing such measures is provided. McGee's Dutch book argument is restructured to more clearly reveal that it introduces a (...) novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee's analysis|generating a rather wide consensus that it yields `unintuitive' or `wrong' probabilities for compounds |fail to strike at their intended target; for to honour the intuitions of the counterexamples one must either give up the Ramsey Test or the standard laws of probability. It will be argued that we need to give up neither if we take the counterexamples as further evidence that the indicative conditional sometimes allows for a non-epistemic `causal' interpretation alongside its usual epistemic interpretation. (shrink)

This paper outlines an account of concessive conditionals that rests on two main ideas. One is that the logical form of a sentence as used in a given context is determined by the content expressed by the sentence in that context. The other is that a coherent distinction can be drawn between a reading of ‘if’ according to which a conditional is true when its consequent holds on the supposition that its antecedent holds, and a stronger reading according to which (...) a conditional is true when its antecedent supports its consequent. As we will suggest, the logical form of concessive conditionals can be elucidated by relying on this distinction. (shrink)

Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in (...) the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (shrink)

This article explores conditionals expressing that the antecedent makes a difference for the consequent. A ‘relevantised’ version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case the consequent is accepted if the belief state is revised by the antecedent and the consequent fails to be accepted if (...) the belief state is revised by the antecedent’s negation. The connective thus defined violates almost all of the traditional principles of conditional logic, but it obeys an interesting logic of its own. The article also gives the logic of an alternative version, the ‘Dependent Ramsey Test,’ according to which a conditional is accepted just in case the consequent is accepted if the belief state is revised by the antecedent and the consequent is rejected if the belief state is revised by the antecedent’s negation. This conditional is closely related to David Lewis’s counterfactual analysis of causation. (shrink)

In my article, I present a new version of a probabilistic truth prescribing semantics for natural language indicative conditionals. The proposed truth conditions can be paraphrased as follows: an indicative conditional is true if the corresponding conditional probability is high and the antecedent is positively probabilistically relevant for the consequent or the probability of the antecedent of the conditional equals 0. In the paper, the truth conditions are defended and some of the logical properties of the proposed semantics are described.

The Ramsey Test is considered to be the default test for the acceptability of indicative conditionals. I will argue that it is incompatible with some of the recent developments in conceptualizing conditionals, namely the growing empirical evidence for the _Relevance Hypothesis_. According to the hypothesis, one of the necessary conditions of acceptability for an indicative conditional is its antecedent being positively probabilistically relevant for the consequent. The source of the idea is _Evidential Support Theory_ presented in Douven (2008). I will (...) defend the hypothesis against alleged counterexamples, and show that it is supported by growing empirical evidence. Finally, I will present a version of the Ramsey test which incorporates the relevance condition and therefore is consistent with growing empirical evidence for the relevance hypothesis. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

.This paper discusses Aristotle’s thesis and Boethius’ thesis, the most distinctive theorems of connexive logic. Its aim is to show that, although there is something plausible in Aristotle’s thesis and Boethius’ thesis, the intuitions that may be invoked to motivate them are consistent with any account of indicative conditionals that validates a suitably restricted version of them. In particular, these intuitions are consistent with the view that indicative conditionals are adequately formalized as strict conditionals.

I generalize the notion of a conditional attitude by bringing together two topics of inquiry. One is the ordinary inquiry into conditional attitudes. The other topic is the inquiry into the attitude of thinking that a proposition is likely, or having a high credence in a proposition. For instance, what is it to intend to go to the game if it is likely that Kershaw pitches? Being likely that Kershaw pitches is the condition of the attitude. Given a natural position (...) about statements like “It is likely that Kershaw pitches,” the target attitude looks different from ordinary conditional attitudes. (shrink)

The Identity principle says that conditionals with the form 'If p, then p' are logical truths. Identity is overwhelmingly plausible, and has rarely been explicitly challenged. But a wide range of conditionals nonetheless invalidate it. I explain the problem, and argue that the culprit is the principle known as Import-Export, which we must thus reject. I then explore how we can reject Import-Export in a way that still makes sense of the intuitions that support it, arguing that the differences between (...) indicative and subjunctive conditionals play a key role in solving this puzzle. (shrink)

This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...) hinge on the Ramsey Test, advocated by Adams, Stalnaker, Lewis, and others. (shrink)

A conversation can be conceived as aiming to circumscribe a set of possibilities that are relevant to the goals of the conversation. This set of possibilities may be conceived as determined by the goals and objective circumstances of the interlocutors and not by their propositional attitudes. An indicative conditional can be conceived as circumscribing a set of possibilities that have a certain property: If the set of relevant possibilities is subsequently restricted to one in which the antecedent holds, then it (...) will be restricted as well to one in which the consequent holds. We will identify a number of desiderata concerning the validity of arguments; we will develop a formally precise semantics for conditionals conceived in this way that satisfies the desiderata, and we will present a deductive calculus that is sound and complete with respect to the semantics. Finally, we will argue that the semantics compares well, both formally and foundationally, with two other semantic theories of indicative conditionals that satisfy the desiderata, namely, those of Gillies and Bledin. (shrink)

Bradley offers a quick and convincing argument that no Boolean semantic theory for conditionals can validate a very natural principle concerning the relationship between credences and conditionals. We argue that Bradley’s principle, Preservation, is, in fact, invalid; its appeal arises from the validity of a nearby, but distinct, principle, which we call Local Preservation, and which Boolean semantic theories can non-trivially validate.

This thesis is about indicative conditionals and apparent counterexamples to classically valid argument forms. Specifically, it applies the following four theories: - material (inspired by Grice (1961, 1975 and 1989)); - possible-worlds (inspired by Stalnaker (1981); Lewis (1976); and Kratzer (2012)), - suppositional (inspired by Adams (1975) and Edgington (1995 and 2014)); and - hybrid (inspired by Jackson (1987)) to try and solve the following two counterexamples: - Vann McGee’s to modus ponens (1985); and - Lewis Carroll’s to modus tollens (...) (1894). I argue that none of the theories I consider can explain – without facing any problems – the three individually plausible but jointly inconsistent theses that give rise to the apparent counterexamples. The three theses of the trilemma are the following: (1) the argument is invalid; (2) the argument is an instance of modus ponens or modus tollens; and (3) modus ponens or modus tollens is valid. (shrink)

Vann McGee has proposed a counterexample to the Ramsey Test. In the counterexample, a seemingly trustworthy source has testified that p and that if not-p, then q. If one subsequently learns not-p, then one has reason to doubt the trustworthiness of the source and so, the argument goes, one has reason to doubt the conditional asserted by the source. Since what one learns is that the antecedent of the conditional holds, these doubts are contrary to the Ramsey Test. We argue (...) that the counterexample fails. It rests on a principle of testimonial dependence that is not applicable when a source hedges his or her claims. (shrink)

In a recent pair of publications, Richard Bradley has offered two novel no-go theorems involving the principle of Preservation for conditionals, which guarantees that one’s prior conditional beliefs will exhibit a certain degree of inertia in the face of a change in one’s non-conditional beliefs. We first note that Bradley’s original discussions of these results—in which he finds motivation for rejecting Preservation, first in a principle of Commutativity, then in a doxastic analogue of the rule of modus ponens —are problematic (...) in a significant number of respects. We then turn to a recent U-turn on his part, in which he winds up rescinding his commitment to modus ponens, on the grounds of a tension with the rule of Import-Export for conditionals. Here we offer an important positive contribution to the literature, settling the following crucial question that Bradley leaves unanswered: assuming that one gives up on full-blown modus ponens on the grounds of its incompatibility with Import-Export, what weakened version of the principle should one be settling for instead? Our discussion of the issue turns out to unearth an interesting connection between epistemic undermining and the apparent failures of modus ponens in McGee’s famous counterexamples. (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)

Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramsey test for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that was applied (...) in the new debate, and instead base my arguments on explicit representations of belief states and canonical constructions of belief state revisions. (shrink)

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

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)

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)

A paper by Schulz (Philos Stud 149:367–386, 2010) describes how the suppositional view of indicative conditionals can be supplemented with a derived view of epistemic modals. In a recent criticism of this paper, Willer (Philos Stud 153:365–375, 2011) argues that the resulting account of conditionals and epistemic modals cannot do justice to the validity of certain inference patterns involving modalised conditionals. In the present response, I analyse Willer’s argument, identify an implicit presupposition which can plausibly be denied and show that (...) accepting it would blur the difference between plain assumptions and their epistemic necessitations. (shrink)

This is a handbook article about indicative conditionals.

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)

Chalmers and Hájek argue that on an epistemic reading of Ramsey’s test for the rational acceptability of conditionals, it is faulty. They claim that applying the test to each of a certain pair of conditionals requires one to think that one is omniscient or infallible, unless one forms irrational Moore-paradoxical beliefs. I show that this claim is false. The epistemic Ramsey test is indeed faulty. Applying it requires that one think of anyone as all-believing and if one is rational, to (...) think of anyone as infallible-if-rational. But this is not because of Moore-paradoxical beliefs. Rather it is because applying the test requires a certain supposition about conscious belief. It is important to understand the nature of this supposition. (shrink)

This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with 'knows', and we call into question the thesis that all knowledge ascriptions have truth-conditions.

Test for the rational acceptance of conditionals and it still incites much of the interest in conditional reasoning. For instance, the test has been considered as a good starting point for several formal semantics for conditionals. Furthermore, its ramifications have important implications for several disciplines, from logic and artificial intelligence to decision theory and psychology. This volume presents a small but fine sample of the state of the art of such multifarious area of research.

Abstract I analyse the relationship between the Ramsey Test (RT) for the acceptance of indicative conditionals and the so-called problem of decision-instability. In particular, I argue that the situations which allegedly bring about this problem are troublesome just in case the relevant conditionals are evaluated by non-suppositional versions, e.g. causal/evidential, of the test. In contrast, a suppositional RT, by highlighting the metacognitive nature of the evaluation of indicative conditionals, allows an agent to run a simulation of such evaluation, without yet (...) committing her to the acceptance of such conditionals. I conclude that a suppositional interpretation of RT is superior to its nonsuppositional counterparts and by briefly showing that a suppositional RT is compatible with a deliberational decision theory. (shrink)

Conditional information can be equally asserted in the forms if p, then q (e.g., ?if I am ill, I will miss work tomorrow?) and q, if p (e.g., ?I will miss work tomorrow, if I am ill?). While this type of clause order manipulation has previously been found to have no influence on the ultimate conclusions participants draw from conditional rules, we used self-paced reading to examine how it affects the real time incremental processing of everyday conditional statements. Experiment 1 (...) revealed that clause order interacts with presuppositional congruency as readers hypothetically represent counterfactual statements. When if p, then q counterfactuals contained a presupposition that was incongruent with prior context, these statements took longer to read than when the presupposition was congruent, but for q, if p conditionals there was no such congruency effect. Experiment 2 revealed that reading times were influenced by the subjective probability of an indicative conditional regardless of clause order, with a penalty observed for low-probability statements relative to high-probability statements in both conditional clause orders. These data reveal a dissociation whereby clause order mediates the effect of suppositional congruency on reading times, but does not mediate the effect of subjective probability. (shrink)

According to operator theories, "if" denotes a two-place operator. According to restrictor theories, "if" doesn't contribute an operator of its own but instead merely restricts the domain of some co-occurring quantifier. The standard arguments (Lewis 1975, Kratzer 1986) for restrictor theories have it that operator theories (but not restrictor theories) struggle to predict the truth conditions of quantified conditionals like -/- (1) a. If John didn't work at home, he usually worked in his office. b. If John didn't work at (...) home, he must have worked in his office. -/- Gillies (2010) offers a context-shifty conditional operator theory that predicts the right truth conditions for epistemically modalized conditionals like (1b), thus undercutting one standard argument for restrictor theories. I explore how we might generalize Gillies' theory to adverbially quantified conditionals like (1a) and deontic conditionals, and argue that a natural generalization of Gillies' theory -- following his strategy for handling epistemically modalized conditionals -- won't work for these other conditionals because a crucial assumption that epistemic modal bases are closed (used to neutralize the epistemic quantification contributed by "if") doesn't have plausible analogs in these other domains. (shrink)

Adams famously suggested that the acceptability of any indicative conditional whose antecedent and consequent are both factive sentences amounts to the subjective conditional probability of the consequent given the antecedent. The received view has it that this thesis offers an adequate partial explication of Ramsey’s test, which characterizes graded acceptability for conditionals in terms of hypothetical updates on the antecedent. Some results in van Fraassen may raise hope that this explicatory approach to Ramsey’s test is extendible to left-nested conditionals, that (...) is, conditionals whose antecedent is itself conditional in form. We argue that this interpretation of van Fraassen’s results is to be rejected. Specifically, we provide an argument from material inadequacy against a generalization of Adams’ thesis for left-nested conditionals. (shrink)

We present a way of classifying the logically possible ways out of Gärdenfors' inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramsey test—we determine which of the assumptions in three different versions of Gärdenfors' theorem turn out to be false. This is done by constructing ranked models in which such Ramsey-test conditionals are evaluated and which are subject to (...) natural postulates on belief revision and acceptability sets for conditionals. Along the way we show that in contrast with what Gärdenfors himself proposed, there is no dichotomy of the form: either the Ramsey test has to be given up or the Preservation condition. Instead, both of them follow from our postulates. (shrink)

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes these two results (...) into account while doing justice to the key intuitions underlying the Ramsey Test. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore's Paradox. (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.

The paper presents a non-monotonic inference relation on a language containing a conditional that satisfies the Ramsey Test. The logic is a weakening of classical logic and preserves many of the ‘paradoxes of implication’ associated with the material implication. It is argued, however, that once one makes the proper distinction between supposing that something is the case and accepting that it is the case, these ‘paradoxes’ cease to be counterintuitive. A representation theorem is provided where conditionals are given a non-bivalent (...) semantics and epistemic states are represented via preferential models. (shrink)

I set out and defend a view on indicative conditionals that I call “indexical relativism ”. The core of the view is that which proposition is expressed by an utterance of a conditional is a function of the speaker’s context and the assessor’s context. This implies a kind of relativism, namely that a single utterance may be correctly assessed as true by one assessor and false by another.

It is argued that indicative conditionals are best viewed as having truth conditions (and so they are in part factual) but that these truth conditions are ‘gappy’ which leaves an explanatory gap that can only be filled by epistemic considerations (and so indicative conditionals are in part epistemic). This dual nature of indicative conditionals gives reason to rethink the relationship between logic viewed as a descriptive discipline (focusing on semantics) and logic viewed as a discipline with a normative import (focusing (...) on epistemic notions such as ‘reasoning’, ‘beliefs’ and ‘assumptions’). In particular, it is argued that the development of formal models for epistemic states can serve as a starting point for exploring logic when viewed as a normative discipline. (shrink)