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  1. All men are animals: hypothetical, categorical, or material?Rani Lill Anjum & Johan Arnt Myrstad - manuscript
    The conditional interpretation of general categorical statements like ‘All men are animals’ as universally quantified material conditionals ‘For all x, if x is F, then x is G’ suggests that the logical structure of law statements is conditional rather than categorical. Disregarding the problem that the universally quantified material conditional is trivially true whenever there are no xs that are F, there are some reasons to be sceptical of Frege’s equivalence between categorical and conditional expressions. -/- Now many philosophers will (...)
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  2. In defence of a naïve conditional epistemology.Andrew Bacon - manuscript
    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 (...)
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  3. The Paradox of Counterfactual Tolerance.Daniel Berntson - manuscript
    Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...)
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  4. Near Closeness and Conditionals.Daniel Berntson - manuscript
    This paper presents a new system of conditional logic B2, which is strictly intermediate in strength between the existing systems B1 and B3 from John Burgess (1981) and David Lewis (1973a). After presenting and motivating the new system, we will show that it is characterized by a natural class of frames. These frames correspond to the idea that conditionals are about which worlds are nearly closest, rather than which worlds are closest. Along the way, we will also give new characterization (...)
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  5. Fictional Reality.Kyle Blumberg & Ben Holguín - manuscript
    This paper defends a theory of fictional truth. According to this theory, there is a fact of the matter concerning the number of hairs on Sherlock Holmes' head, and likewise for any other meaningful question one could ask about what's true in a work of fiction. We argue that a theory of this form is needed to account for the patterns in our judgments about attitude reports that embed fictional claims. We contrast our view with one of the dominant approaches (...)
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  6. Breaking de Morgan's law in counterfactual antecedents.Lucas Champollion, Ivano Ciardelli & Linmin Zhang - manuscript
    The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. (...)
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  7. Trivalent Conditionals: Stalnaker's Thesis and Bayesian Inference.Paul Égré, Lorenzo Rossi & Jan Sprenger - manuscript
    This paper develops a trivalent semantics for indicative conditionals and extends it to a probabilistic theory of valid inference and inductive learning with conditionals. On this account, (i) all complex conditionals can be rephrased as simple conditionals, connecting our account to Adams's theory of p-valid inference; (ii) we obtain Stalnaker's Thesis as a theorem while avoiding the well-known triviality results; (iii) we generalize Bayesian conditionalization to an updating principle for conditional sentences. The final result is a unified semantic and probabilistic (...)
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  8. The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - manuscript
    Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that (...)
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  9. The Inextricable Link Between Conditionals and Logical Consequence.Matheus Silva - manuscript
    There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of (...)
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  10. Conditionals all the way down.Matheus Silva - manuscript
    It is commonly accepted that unconditional statements are clearer and less problematic than conditional ones. This article challenges this belief by proposing that all unconditional statements can be reduced to conditional ones since epistemic justification is inherently conditional in nature. The distinction between unconditional and conditional statements is similar to the distinction between assumptions and premises, which is an idealization that results from our attempts to limit epistemic complexity. This has perplexing consequences: (1) since any ordinary statement can be viewed (...)
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  11. The Logical Web.Matheus Silva - manuscript
    Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...)
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  12. Directional Bias.Matheus Silva - manuscript
    There is almost a consensus among conditional experts that indicative conditionals are not material. Their thought hinges on the idea that if indicative conditionals were material, A → B could be vacuously true when A is false, even if B would be false in a context where A is true. But since this consequence is implausible, the material account is usually regarded as false. It is argued that this point of view is motivated by the grammatical form of conditional sentences (...)
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  13. The Triviality Result is not Counter-Intuitive.Matheus Silva - manuscript
    The Equation (TE) states that the probability of A → B is the probability of B given A. Lewis (1976) has shown that the acceptance of TE implies that the probability of A → B is the probability of B, which is implausible: the probability of a conditional cannot plausibly be the same as the probability of its consequent, e.g., the probability that the match will light given that is struck is not intuitively the same as the probability that it (...)
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  14. "If-then" as a version of "Implies".Matheus Silva - manuscript
    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 to 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 (...)
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  15. Subjunctive Conditionals are Material.Matheus Silva - manuscript
    The material account proposes that indicative conditionals are material, but it is widely believed that this account cannot be applied to subjunctive conditionals. There are three reasons for this consensus: (1) the concern that most subjunctive conditionals would be vacuously true if they were material, which seems implausible; (2) the inconsistency with Adams pair, which suggests that indicative and subjunctive conditionals have different truth conditions; and (3) the belief that the possible world theories are a superior alternative to the material (...)
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  16. Indicative Conditionals are Material - Expanding the Survey.Matheus Martins Silva - manuscript
    Adam Rieger (2013) has carried out a survey of arguments in favour of the material account of indicative conditionals. These arguments involve simple and direct demonstrations of the material account. I extend the survey with new arguments and clarify the logical connections among them. I also show that the main counter-examples against these arguments are not successful either because their premises are just as counter-intuitive as the conclusions, or because they depend on contextual fallacies. The conclusion is that the unpopularity (...)
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  17. Some Strong Conditionals for Sentential Logics.Jason Zarri - manuscript
    In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language (...)
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  18. The logic of counterfactuals in causal inference.Judea Pearl - manuscript
  19. Experimenting with (Conditional) Perfection.Fabrizio Cariani & Lance J. Rips - forthcoming - In Stefan Kaufmann, David Over & Ghanshyam Sharma (eds.), Conditionals: Logic, Semantics, Psychology.
    Conditional perfection is the phenomenon in which conditionals are strengthened to biconditionals. In some contexts, “If A, B” is understood as if it meant “A if and only if B.” We present and discuss a series of experiments designed to test one of the most promising pragmatic accounts of conditional perfection. This is the idea that conditional perfection is a form of exhaustification—that is a strengthening to an exhaustive reading, triggered by a question that the conditional answers. If a speaker (...)
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  20. A Suppositional Theory of Conditionals.Sam Carter - forthcoming - Mind:fzaa071.
    Suppositional theories of conditionals take apparent similarities between supposition and conditionals as a starting point, appealing to features of the former to provide an account of the latter. This paper develops a novel form of suppositional theory, one which characterizes the relationship at the level of semantics rather than at the level of speech acts. In the course of doing so, it considers a range of novel data which shed additional light on how conditionals and supposition interact.
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  21. Certain and Uncertain Inference with Indicative Conditionals.Paul Égré, Lorenzo Rossi & Jan Sprenger - forthcoming - Australasian Journal of Philosophy.
    This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by Cooper (1968) and Belnap (1973) and it yields two logics of conditional reasoning: (i) a logic C of certainty-preserving inference; and (ii) a logic U for uncertain reasoning that preserves the probability of the premises. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use (...)
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  22. A problem not peculiar to counterfactual sufficiency.Chaoan He - forthcoming - Analysis.
    The Consequence Argument for incompatibilism is beset by two rival interpretations: the counterfactual sufficiency interpretation and the counterfactual might interpretation. Waldrop recently argued that the counterfactual sufficiency interpretation conflicts with certain principles governing the logic of counterfactuals. In this paper, I show that Waldrop’s argument can be adapted to prove that the counterfactual might interpretation also conflicts with the same principles. So the problem Waldrop pointed out is not peculiar to the counterfactual sufficiency interpretation.
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  23. The Logic of Hyperlogic. Part B: Extensions and Restrictions.Alexander W. Kocurek - forthcoming - Review of Symbolic Logic:1-28.
    This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...)
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  24. The case of the missing ‘If’: Accessibility relations in Stalnaker’s theory of conditionals.Matthew Mandelkern - forthcoming - Semantics and Pragmatics.
    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.
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  25. Probability logic.Niki Pfeifer - forthcoming - In M. Knauff & Wolfgang Spohn (eds.), Handbook of Rationality. Cambridge, MA, USA:
    This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability logic is characterized as a generalization of bivalent truth-functional propositional logic (short “logic”), as being connexive, and as being nonmonotonic. The chapter discusses selected argument forms and associated uncertainty propagation rules. Throughout the chapter, the descriptive validity of probability logic is compared to logic, which was used as the gold standard (...)
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  26. Counterfactual skepticism is (just) skepticism.David Boylan - 2023 - Philosophy and Phenomenological Research 108 (1):259-286.
    Counterfactual skepticism says that most ordinary counterfactuals are false. While few endorse counterfactual skepticism, the precise costs of the view are disputed and not generally well-understood. I have two aims in this paper. My first and primary aim is to establish, on grounds acceptable to all parties, that counterfactual skepticism is not benign. I argue it leads to significant skepticism about the future: if counterfactual skepticism is true, then we can have only very limited knowledge about the future. I give (...)
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  27. Conditional Collapse.Sam Carter - 2023 - Mind 132 (528):971-1004.
    Indicative and subjunctive conditionals are in non-complimentary distribution: there are conversational contexts at which both are licensed (Stalnaker 1975; Karttunen and 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 (...)
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  28. Modus Ponens and the Logic of Decision.Nate Charlow - 2023 - Journal of Philosophical Logic 52 (3):859-888.
  29. Sufficient Conditions for Counterfactual Transitivity and Antecedent Strengthening.Tristan Grøtvedt Haze - 2023 - American Philosophical Quarterly 60 (3):237-247.
    This paper is about two controversial inference-patterns involving counterfactual or subjunctive conditionals. Given a plausible assumption about the truth-conditions of counterfactuals, it is shown that one can't go wrong in applying hypothetical syllogism (i.e., transitivity) so long as the set of worlds relevant for the conclusion is a subset of the sets of worlds relevant for the premises. It is also shown that one can't go wrong in applying antecedent strengthening so long as the set of worlds relevant for the (...)
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  30. A fundamental non-classical logic.Wesley Holliday - 2023 - Logics 1 (1):36-79.
    We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...)
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  31. Connexivity in the Logic of Reasons.Andrea Iacona - 2023 - Studia Logica:1-18.
    This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘_p_ is a reason for _q_’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts of (...)
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  32. Valid Arguments as True Conditionals.Andrea Iacona - 2023 - Mind 132 (526):428-451.
    This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...)
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  33. A puzzle about scope for restricted deontic modals.Brian Rabern & Patrick Todd - 2023 - Snippets 44:8-10.
    Deontic necessity modals (e.g. 'have to', 'ought to', 'must', 'need to', 'should', etc.) seem to vary in how they interact with negation. According to some accounts, what forces modals like 'ought' and 'should' to outscope negation is their polarity sensitivity -- modals that scope over negation do so because they are positive polarity items. But there is a conflict between this account and a widely assumed theory of if-clauses, namely the restrictor analysis. In particular, the conflict arises for constructions containing (...)
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  34. An Axiomatic System for Concessive Conditionals.Eric Raidl, Andrea Iacona & Vincenzo Crupi - 2023 - Studia Logica 1:1-21.
    According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional \(p{{\,\mathrm{\hookrightarrow }\,}}q\) is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.
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  35. The Qualitative Thesis.David Boylan & Ginger Schultheis - 2022 - Journal of Philosophy 119 (4):196-229.
    The Qualitative Thesis says that if you leave open P, then you are sure of if P, then Q just in case you are sure of the corresponding material conditional. We argue the Qualitative Thesis provides compelling reasons to accept a thesis that we call Conditional Locality, which says, roughly, the interpretation of an indicative conditional depends, in part, on the conditional’s local embedding environment. In the first part of the paper, we present an argument—due to Ben Holguín—showing that, without (...)
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  36. Revisiting McGee’s Probabilistic Analysis of Conditionals.John Cantwell - 2022 - Journal of Philosophical Logic (5):1-45.
    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 (...)
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  37. The Evidential Conditional.Vincenzo Crupi & Andrea Iacona - 2022 - Erkenntnis 87 (6):2897-2921.
    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 (...)
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  38. Three Ways of Being Non-Material.Vincenzo Crupi & Andrea Iacona - 2022 - Studia Logica 110:47-93.
    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.
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  39. On the Logical Form of Concessive Conditionals.Vincenzo Crupi & Andrea Iacona - 2022 - Journal of Philosophical Logic 51 (3):633-651.
    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 (...)
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  40. Counterparts and Counterpossibles: Impossibility without Impossible Worlds.Michael Townsen Hicks - 2022 - Journal of Philosophy 119 (10):542-574.
    Standard accounts of counterfactuals with metaphysically impossible antecedents take them to by trivially true. But recent work shows that nontrivial countermetaphysicals are frequently appealed to in scientific modeling and are indispensable for a number of metaphysical projects. I focus on three recent discussions of counterpossible counterfactuals, which apply counterpossibles in both scientific and metaphysical modeling. I show that a sufficiently developed modal counterpart theory can provide a semantics for a wide range of counterpossibles without any inconsistent possibilities or other forms (...)
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  41. Special-science counterfactuals.Christian List - 2022 - The Monist 105 (2):194–213.
    On the standard analysis, a counterfactual conditional such as “If P had been the case, then Q would have been the case” is true in the actual world if, in all nearest possible worlds in which its antecedent (P) is true, its consequent (Q) is also true. Despite its elegance, this analysis faces a difficulty if the laws of nature are deterministic. Then the antecedent could not have been true, given prior conditions. So, it is unclear what the relevant “nearest (...)
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  42. Aboutness and Modality.Dean McHugh - 2022 - Proceedings of the 23Rd Amsterdam Colloquium.
    In this paper I would like to offer a new framework for hypothetical reasoning, with the goal of predicting what scenarios we consider when we interpret a conditional or causal claim (such as a sentence containing the word ‘because‘). The idea is that when we interpret a conditional or causal claim, we identify a part of the world to change and imagine changing that. Sentences are about parts of the world: when we interpret a conditional antecedent or because clause, we (...)
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  43. Context-indexed Counterfactuals.Mariusz Popieluch - 2022 - Studia Semiotyczne 35 (2):89-123.
    It is commonly believed that the role of context cannot be ignored in the analysis of conditionals, and counterfactuals in particular. On truth conditional accounts involving possible worlds semantics, conditionals have been analysed as expressions of relative necessity: “If A, then B” is true at some world w if B is true at all the A-worlds deemed relevant to the evaluation of the conditional at w. A drawback of this approach is that for the evaluation of conditionals with the same (...)
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  44. Semantics for Pure Theories of Connexive Implication.Yale Weiss - 2022 - Review of Symbolic Logic 15 (3):591-606.
    In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...)
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  45. Indicative Conditionals: Probabilities and Relevance.Franz Berto & Aybüke Özgün - 2021 - Philosophical Studies (11):3697-3730.
    We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) (...)
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  46. Dialetheism and Modus Tollens.Ben Blumson & Theresa Helke - 2021 - The Reasoner 15 (4):30.
    Suppose that some contradictions are true – for example, that as I walk through the door, I’m inside and I’m not inside. Then we argue 'if I'm walking through the door, I'm inside; I'm not inside; therefore, I'm not walking through the door' is an invalid instance of modus tollens.
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  47. How Strong Is a Counterfactual?David Boylan & Ginger Schultheis - 2021 - Journal of Philosophy 118 (7):373-404.
    The literature on counterfactuals is dominated by strict accounts and variably strict accounts. Counterexamples to the principle of Antecedent Strengthening were thought to be fatal to SA; but it has been shown that by adding dynamic resources to the view, such examples can be accounted for. We broaden the debate between VSA and SA by focusing on a new strengthening principle, Strengthening with a Possibility. We show dynamic SA classically validates this principle. We give a counterexample to it and show (...)
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  48. Probability, Evidential Support, and the Logic of Conditionals.Vincenzo Crupi & Andrea Iacona - 2021 - Argumenta 6:211-222.
    Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently ap- peared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more tra- ditional counterparts) cannot generate (...)
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  49. Indicative and counterfactual conditionals: a causal-modeling semantics.Duen-Min Deng & Kok Yong Lee - 2021 - Synthese 199 (1-2):3993-4014.
    We construct a causal-modeling semantics for both indicative and counterfactual conditionals. As regards counterfactuals, we adopt the orthodox view that a counterfactual conditional is true in a causal model M just in case its consequent is true in the submodel M∗, generated by intervening in M, in which its antecedent is true. We supplement the orthodox semantics by introducing a new manipulation called extrapolation. We argue that an indicative conditional is true in a causal model M just in case its (...)
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  50. Counterfactuals and modality.Gabriel Greenberg - 2021 - Linguistics and Philosophy 44 (6):1255-1280.
    This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...)
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