We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.
It is generally agreed that constructions of the form “if P, Q” are capable of conveying a number of different relations between antecedent and consequent, with pragmatics playing a central role in determining these relations. Controversy concerns what the conventional contribution of the if-clause is, how it constrains the pragmatic processes, and what those processes are. In this essay, I begin to argue that the conventional contribution of if-clauses to semantics is exhausted by the fact that these clauses introduce a (...) proposition without presenting it as true so that the consequent can be understood in relation to it. Given our cognitive interests in such non-truth-presentational introductions, conditionals will make salient the wide but nevertheless disciplined variety of contents that we naturally attribute to them; no further substantial constraints of the sorts proposed by standard theories of conditionals are needed to explain the phenomena. If this is correct, it provides prima facie evidence for a radically contextualist account of conditionals according to which conditionals have no truth-evaluable or intuitively complete content absent some contextually provided, sufficiently salient relation between antecedent and consequent. (shrink)
We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.
Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are (...) explored. (shrink)
In this paper the informativeness account of assertion (Pagin in Assertion. Oxford University Press, Oxford, 2011) is extended to account for inference. I characterize the conclusion of an inference as asserted conditionally on the assertion of the premises. This gives a notion of conditional assertion (distinct from the standard notion related to the affirmation of conditionals). Validity and logical validity of an inference is characterized in terms of the application of method that preserves informativeness, and contrasted with consequence (...) and logical consequence, that is defined in terms of truth preservation. The proposed account is compared with that of Prawitz (Logica yearbook 2008, pp. 175-192. College Publications, London, 2009). (shrink)
The interest of epistemic comparative conditionals comes from the fact that they represent genuine ‘comparative epistemic relations’ between propositions, situations, evidences, abilities, interests, etc. This paper argues that various types of epistemic comparative conditionals uniformly represent comparative epistemic relations via the comparison of epistemic positions rather than the comparison of epistemic standards. This consequence is considered as a general constraint on a theory of knowledge attribution, and then further used to argue against the contextualist thesis that, in (...) some cases, considering a new counter- possibility can raise the epistemic standard of knowledge attribution. Instead, the paper shows that considering a new counter-possibility can only lower the epistemic position of a putative knower. Moreover, since the comparison, by the nature of conditionals, is free from any commitment to the truth-values of specific knowledge attributions, my conclusion is free from the debate between contextualism and invariantism on whether the truth-value of a knowledge attribution can actually vary with context. (shrink)
This book looks at the ways in which conditionals, an integral part of philosophy and logic, can be of practical use in computer programming. It analyzes the different types of conditionals, including their applications and potential problems. Other topics include defeasible logics, the Ramsey test, and a unified view of consequence relation and belief revision. Its implications will be of interest to researchers in logic, philosophy, and computer science, particularly artificial intelligence.
I’ll describe a range of systems for nonmonotonic conditionals that behave like conditional probabilities above a threshold. The rules that govern each system are probabilistically sound in that each rule holds when the conditionals are interpreted as conditional probabilities above a threshold level specific to that system. The well-known preferential and rational consequence relations turn out to be special cases in which the threshold level is 1. I’ll describe systems that employ weaker rules appropriate to thresholds lower (...) than 1, and compare them to these two standard systems. (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  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  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)
It is commonly agreed that logic studies the form of arguments and that the concept of a consequence relation is based on the idea of truth-preservation in all models. Based on some observations about arguments involving conditionals, Brogaard and Salerno argue that the consequence relation should be defined in terms of truth-preservation within one fixed context. I will argue that Ichikawa’s contextualism for counterfactuals can be treated as an elucidation of what they have in mind. Instead of (...) standing for or against Stalnaker’s or Lewis’s semantics of counterfactuals, I will argue that the key to explaining the phenomena in question is the concept of a consequence relation. To support the point above, logical contextualism or relativism will be introduced and defended. I thus suggest that the concept of a consequence relation is sensitive to the context in which a certain argument is asserted. (shrink)
This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl to formalize a causal (...) notion of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman and Kratzer will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)
In this paper I explore a version of standard (expected utility) decision theory in which the probability parameter is interpreted as an objective chance believed by agents to obtain and values of this parameter are fixed by indicative conditionals linking possible actions with possible outcomes. After reviewing some recent developments centering on the common-cause counterexamples to the standard approach, I introduce and briefly discuss the key notions in my own approach. (This approach has essentially the same results as the (...) causal approach in common-cause cases.) I then discuss the Rule of Dominance and find, in the context of the present proposal, that it cannot serve as an independent source of action justification. Turning next to Newcomb''s Problem, I argue that the much discussed issue of back-tracking counterfactuals is something of a red herring for decision theory. Once the twin distractions of back-tracking counterfactuals and Dominance Reasoning are set aside the 1-box solution emerges as a natural consequence of the present proposal. It is of interest that this proposal agrees with the causal approach in the standard common-cause examples and the expected-utility approach in the Newcomb case: one can be smart and rich and keep on smoking. (shrink)
This Critical Notice is about aboutness in logic and language. In a first part, I discuss the origin of the issue and the philosophical background to Yablo's book Aboutness (PUP 2014), which is itself the subject of the second and main part of my paper.
According to traditional logical expressivism, logical operators allow speakers to explicitly endorse claims that are already implicitly endorsed in their discursive practice — endorsed in virtue of that practice’s having instituted certain logical relations. Here, I propose a different version of logical expressivism, according to which the expressive role of logical operators is explained without invoking logical relations at all, but instead in terms of the expression of discursive-practical attitudes. In defense of this alternative, I present a deflationary account of (...) the expressive role of vocabulary by which we ascribe logical relations. (shrink)
Recently, John Bell has proposed that a specific conditional logic, C, be considered as a serious candidate for formally representing and faithfully capturing various (possibly all) formalized notions of nonmonotonic inference. The purpose of the present paper is to develop evaluative criteria for critically assessing such claims. Inference patterns are described in terms of the presence or absence of residual classical monotonicity and intrinsic nonmonotonicity. The concept of a faithful representation is then developed for a formalism purported to encode a (...) pattern of nonmonotonic inference already captured by another. In the main body of the paper these evaluative criteria are applied to assess (negatively) whether C or any conditional logic provides a faithful representation for nonmonotonic patterns of inference captured by inference operators and relations modeling the dynamics of belief change. (shrink)
Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. (...) Another justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (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)
This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl (2000) to formalize a (...) causal notion of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman (1976) and Kratzer (1979) will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)
This chapter illustrates a theory that describes how certain modal statements, including counterfactual sentences, are dependent on context. Building on the work of Robert Stalnaker and David Lewis, its application to a familiar argument for fatalism and a recent exchange about time-traveler freedom between Kadri Vihvelin and Ted Sider is considered. This chapter presents a new perspective on the flaws and the seductiveness of both the fatalist argument and the freedom paradox. This new perspective may be applied to arguments for (...) incompatibilism advanced by Carl Ginet and Peter van Inwagen. The issue of the compatibility of free will and determinism is generally regarded as one of the most serious metaphysical issues about human freedom. Consequence arguments of the sort made famous by Inwagen and Ginet are the leading arguments in favor of incompatibilism. (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 Philosophical Guide to Conditionals, the fullest and most authoritative treatment of the subject. An ideal introduction for undergraduates with a philosophical grounding, it also offers a rich source of illumination and stimulation for graduate (...) students and professional philosophers. (shrink)
One of the great successes in the study of language has been the application of formal methods, including those of formal logic. Even so, this chapter argues against one way of accounting for this success, by arguing that the study of natural language semantics and of logical consequence relations are not the same. There is indeed a lot we can glean about logic from looking at our languages, and at our inferential practices, but the semantic properties of natural languages (...) do not determine genuine logical consequence relations. We can get from natural language semantics to logical consequence, but only by a significant process of identification of logical constants, abstraction, and idealization. The chapter also discusses different approaches to the nature of logical consequence, and examines which allow logic and natural language to come closer together. (shrink)
Recent work in philosophical logic has taken interesting and unexpected turns. It has seen not only a proliferation of logical systems, but new applications of a wide range of different formal theories to philosophical questions. As a result, philosophers have been forced to revisit the nature and foundation of core logical concepts, chief amongst which is the concept of logical consequence. This essay sets the contributions of the volume in context and identifies how they advance important debates within the (...) philosophy of logic. (shrink)
I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.
More than a decade of research has found strong evidence for P(if A, then C) = P(C|A) (“the Equation”). We argue, however, that this hypothesis provides an overly simplified picture due to its inability to account for relevance. We manipulated relevance in the evaluation of the probability and acceptability of indicative conditionals and found that relevance moderates the effect of P(C|A). This corroborates the Default and Penalty Hypothesis put forward in this paper. Finally, the probability and acceptability of concessive (...)conditionals (“Even if A, then still C”) were investigated and it was found that the Equation provides a better account of concessive conditionals than of indicatives across relevance manipulations. (shrink)
Deflationists about truth seek to undermine debates about the nature of truth by arguing that the truth predicate is merely a device that allows us to express a certain kind of generality. I argue that a parallel approach is available in the case of logical consequence. Just as deflationism about truth offers an alternative to accounts of truth's nature in terms of correspondence or justification, deflationism about consequence promises an alternative to model-theoretic or proof-theoretic accounts of consequence's (...) nature. I then argue, against considerations put forward by Field and Beall, that Curry's paradox no more rules out deflationism about consequence than the liar paradox rules out deflationism about truth. (shrink)
According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that (...) assessment by presenting data that cast doubt on an assumption underlying all triviality arguments. (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.
Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.
Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general (...) interpretive scheme that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)
A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in (...) the study of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)
The Ramseyan thesis that the probability of an indicative conditional is equal to the corresponding conditional probability of its consequent given its antecedent is both widely confirmed and subject to attested counterexamples (e.g., McGee 2000, Kaufmann 2004). This raises several puzzling questions. For instance, why are there interpretations of conditionals that violate this Ramseyan thesis in certain contexts, and why are they otherwise very rare? In this paper, I raise some challenges to Stefan Kaufmann's account of why the Ramseyan (...) thesis sometimes fails, and motivate my own theory. On my theory, the proposition expressed by an indicative conditional is partially determined by a background partition, and hence its probability depends on the choice of such a partition. I hold that this background partition is contextually determined, and in certain conditions is set by a salient question under discussion in the context. I show how the resulting theory offers compelling answers to the puzzling questions raised by failures of the Ramseyan thesis. (shrink)
Compare the following conditionals: -/- Bad: #If John is not in Paris, he is in France. Good: If John is in France, he is not in Paris. -/- Good sounds entirely natural, whereas Bad sounds quite strange. This contrast is puzzling, because Bad and Good have the same structure at a certain level of logical abstraction: -/- (1) If ¬p+, then p. -/- We argue that existing theories of informational oddness do not distinguish between Bad and Good. We do (...) not have an account of the divergence in judgments about the two, but we think this is a fascinating puzzle which we pose here in the hope others will be able to solve it. (shrink)
There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability (...) theory provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view. (shrink)
Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each (...) other, but in agreement . We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6). (shrink)
We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from (...) a disjunction. (shrink)
We investigated how people interpret conditionals and how stable their interpretation is over a long series of trials. Participants were shown the colored patterns on each side of a six-sided die, and were asked how sure they were that a conditional holds of the side landing upwards when the die is randomly thrown. Participants were presented with 71 trials consisting of all combinations of binary dimensions of shape (e.g., circles and squares) and color (e.g., blue and red) painted onto (...) the sides of each die. In two experiments (N1 = 66, N2 = 65), the conditional event was the dominant interpretation, followed by conjunction, and material conditional responses were negligible. In both experiments, the percentage of participants giving a conditional event response increased from around 40% at the beginning of the task to nearly 80% at the end, with most participants shifting from a conjunction interpretation. The shift was moderated by the order of shape and color in each conditional’s antecedent and consequent: participants were more likely to shift if the antecedent referred to a color. In Experiment 2 we collected response times: conditional event interpretations took longer to process than conjunction interpretations (mean diﬀerence 500 ms). We discuss implications of our results for mental models theory and probabilistic theories of reasoning. (shrink)
I argue that taking the Practical Conditionals Thesis seriously demands a new understanding of the semantics of such conditionals. Practical Conditionals Thesis: A practical conditional [if A][ought] expresses B’s conditional preferability given A Paul Weirich has argued that the conditional utility of a state of affairs B on A is to be identified as the degree to which it is desired under indicative supposition that A. Similarly, exploiting the PCT, I will argue that the proper analysis of (...) indicative practical conditionals is in terms of what is planned, desired, or preferred, given suppositional changes to an agent’s information. Implementing such a conception of conditional preference in a semantic analysis of indicative practical conditionals turns out to be incompatible with any approach which treats the indicative conditional as expressing non-vacuous universal quantification over some domain of relevant antecedent-possibilities. Such analyses, I argue, encode a fundamental misunderstanding of what it is to be best, given some condition. The analysis that does the best vis-à-vis the PCT is, instead, one that blends a Context-Shifty account of indicative antecedents with an Expressivistic, or non-propositional, treatment of their practical consequents. (shrink)
Perszyk has argued that Molinists cannot consistently endorse the consequence argument because of a structurally similar argument for the incompatibility of true Molinist counterfactuals of freedom and the ability to do otherwise. Wierenga has argued that on the proper understanding of CCFs, there is a relevant difference between the consequence argument and the anti-Molinist argument. I argue that, even on Wierenga’s understanding of CCFs, there is in fact no relevant difference between the two arguments. Moreover, I strengthen Perszyk’s (...) challenge by highlighting further relevant similarities between CCFs and facts about the laws. (shrink)
In an earlier paper in these pages (2008), we explored the puzzling link between dispositions and conditionals. First, we rehearsed the standard counterexamples to the simple conditional analysis and the refined conditional analysis defended by David Lewis. Second, we attacked a tempting response to these counterexamples: what we called the ‘getting specific strategy’. Third, we presented a series of structural considerations that pose problems for many attempts to understand the link between dispositions and conditionals. Finally, we developed our (...) own account of this link, which avoids all of the standard counterexamples and comports with the relevant structural considerations. In this paper, we reply to some objections. (shrink)
Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in  that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in . Other authors have extended this result to the cases (...) of k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)
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 judgments 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 aim is to theoretically motivate a relevance approach to (indicative) conditionals in a comparative discussion of the main alternatives. In particular, it will be argued that a relevance approach to conditionals is better motivated than the suppositional theory currently enjoying wide endorsement. In the course of this discussion, an argument will be presented of why failures of the epistemic relevance of the antecedent for the consequent should be counted as genuine semantic defects (as opposed to be relegated (...) to pragmatics). Furthermore, strategies for dealing with compositionality and the perceived objective purport of indicative conditionals will be put forward. (shrink)
(2014). Capturing the relationship between conditionals and conditional probability with a trivalent semantics. Journal of Applied Non-Classical Logics: Vol. 24, Three-Valued Logics and their Applications, pp. 144-152. doi: 10.1080/11663081.2014.911535.
According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.
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)
We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.
The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on (...) the interpretation of indicatives and relies on the notion of causal (in)dependence. (shrink)
Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of (...) context-dependent languages, for that tradition has focussed on arguments whose premises and conclusions are taken at the same context. I first argue for the desiderability of having a logic that accounts for mid-argument context change and I explain how one can informally understand such context change in a standard framework in which the relation of logical consequence holds among sentences. I then propose a family of simple temporal “intercontextual” logics that adequately model the validity of certain arguments in which the context changes. In particular, such logics validate the apparently valid argument in the Fregean example. The logics lack many traditional structural properties (reflexivity, contraction, commutativity etc.) as a consequence of the logical significance acquired by the sequence structure of premises and conclusions. The logics are however strong enough to capture in the form of logical truths all the valid arguments of both classical logic and Kaplan-style “intracontextual” logic. Finally, I extend the framework by introducing new operations into the object language, such as intercontextual conjunction, disjunction and implication, which, contrary to intracontextual conjunction, disjunction and implication, perfectly match the metalinguistic, intercontextual notions of premise combination, conclusion combination and logical consequence by representing their respective two operands as taken at different contexts. (shrink)