In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working (...) in the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. (shrink)

In Categories 12 (14b11–22), Aristotle famously claims that [1] true sentences and reality stand in a mutually implicative relationship, and that [2] reality causes the truth of sentences but not vice versa. In this paper, I first argue that Boethius’ reading of the above passage led medieval logicians to assess [1] and [2] within the framework of a theory of consequence. Then, I consider two important questions raised by Boethius and later logicians in relation to [1] and [2], and, namely, (...) whether the implication described in [1] really satisfies the requirement for consequence, and whether the truthmaking relation posited in [2] can be boiled down to the relation of consequence. Boethius himself, I argue, answered affirmatively to both questions and thus (much like some contemporary truthmaker theorists) committed himself to an account of truthmaking as entailment. I then consider criticisms to Boethius’ account found in the writings of William of Champeaux, two anonymous authors connected to the school of Jocelyn of Soissons, Peter Abelard, and the author of the Ars Meliduna. Here, I argue that the emergence of a concern for relevance drives the need for abandoning Boethius’ account as well as his conception of truthmaking as entailment. (shrink)

The paper is concerned with the rational requirements for suspended judgment, or what suspending judgment about a question rationally commits one to. It shows that two purported rational requirements for suspended judgment cannot both be true at the same time, at least when the entailment relation between questions is understood a certain way. The first one says that one is rationally required to suspend judgment about those questions that are entailed by the questions that one already suspends judgment about. (...) The second one says that one is rationally required to believe the presuppositions of the questions one suspends judgment about. Two plausible solutions to the problem are discussed. One of them explicates the relation of entailment between questions in an alternative manner, and the other one rejects the presupposition requirement. Either way, a closure requirement for suspended judgment can be maintained which is analogous to the closure requirement for belief. Whereas belief is ideally closed under entailment between propositions, suspended judgment is ideally closed under entailment between questions. (shrink)

In this paper I undermine the Entailment Principle according to which if an entity is a truthmaker for a certain proposition and this proposition entails another, then the entity in question is a truthmaker for the latter proposition. I argue that the two most promising versions of the principle entail the popular but false Conjunction Thesis, namely that a truthmaker for a conjunction is a truthmaker for its conjuncts. One promising version of the principle understands entailment as strict (...) implication but restricts the field of application of the principle to purely contingent truths (i.e. those that contain no necessary proposition at any level of analysis). But a conjunction of purely contingent truths strictly implies its conjuncts. So this version of the principle is committed to the Conjunction Thesis. The same is true of the version of the principle where entailment is understood in the sense of systems T, R, and E of relevant logic, since in these systems conjunctions entail their conjuncts. I argue that the Conjunction Thesis is false because a truthmaker is that in virtue of what a certain proposition is true and it is false that, for example, what the proposition that Peter is a man is true in virtue of is the conjunctive fact that Peter is man and Saturn is a planet (or the facts that Peter is a man and that Saturn is a planet taken together). I also argue against other versions of the principle. (shrink)

Knowledge is widely thought to entail belief. But Radford has claimed to offer a counterexample: the case of the unconfident examinee. And Myers-Schulz and Schwitzgebel have claimed empirical vindication of Radford. We argue, in defense of orthodoxy, that the unconfident examinee does indeed have belief, in the epistemically relevant sense of dispositional belief. We buttress this with empirical results showing that when the dispositional conception of belief is specifically elicited, people’s intuitions then conform with the view that knowledge entails (dispositional) (...) belief. (shrink)

We show that actuality entailments arise with goal-oriented modality only and endorse Belnap’s view of that goal-oriented modals use historical accessibility with a fixed past and an open future. This modal-theoretic assumption allows us to spell out the precise modal-temporal configuration in which the actuality entailment arises and our predictions are borne out by the data, cross-linguistically. We also show that, when any assumption about the identity of worlds at branching point is leveled - which appears to be the (...) case with generic deontic and opportunity modals, the actuality entailments disappear. We also predict that the entailment disappears with prospectivity. Finally, we argue that modal sentences giving rise to actuality entailments are informative, insofar as the contribution of the modality survives as a presupposition that the modal base is non-homogeneous. (shrink)

This book provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. Its fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval [0,1]. We examine the iterated conditional (B|K)|(A|H), by showing that A|H p-entails B|K if and only if (B|K)|(A|H) = 1. Then, we show that a p-consistent family F={E1|H1, E2|H2} p-entails a conditional event E3|H3 if and only if E3|H3= 1, or (E3|H3)|QC(S) = 1 for some nonempty subset S (...) of F, where QC(S) is the quasi conjunction of the conditional events in S. Then, we examine the inference rules And, Cut, Cautious Monotonicity, and Or of System P and other well known inference rules (Modus Ponens, Modus Tollens, Bayes). We also show that QC(F)|C(F) = 1, where C(F) is the conjunction of the conditional events in F. We characterize p-entailment by showing that F p-entails E3|H3 if and only if (E3|H3)|C(F) = 1. Finally, we examine Denial of the antecedent and Affirmation of the consequent, where the p-entailment of (E3|H3) from F does not hold, by showing that (E3|H3)|C(F) is not equal to 1. (shrink)

T. J. Smiley; XII.—Entailment and Deducibility, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 233–254, https://doi.org/10.1093.

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of (...) time the ”niches” which constitute the boundary conditions on selec- tion. More generally, by the mathematical unprestatability of the ”phase space”, no laws of mo- tion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound concep- tual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of symmetries as invariant preserving transformations will allow us to under- stand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to differential cases. Mutations or other causal differ- ences will allow us to stress that ”non conservation princi- ples” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as sym- metries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter. (shrink)

We show that there is a simple derivation of triviality with very few assumptions involving the formula that the negated conditional entails the antecedent of the conditional.

Do grounding claims entail corresponding supervenience claims? The question matters, as a positive answer would help grounding theorists address worries that their hyperintensional primitive is obscure, and also increase the argumentative strategies that are available within ground-theoretic frameworks for metaphysical inquiry. Leuenberger (Erkenntnis 79:227–240, 2014a) argues for a negative response, by specifying some candidate principles of entailment and then claiming that each of them is subject to counterexamples. In this paper, I critically assess those principles and the objections he (...) raises against them, and advocate a novel entailment principle that overcomes all the problems suffered by those other principles. The principle I defend places a supervenience-based constraint on grounding claims, and secures a substantive connection between grounding and modality, weaker than necessitation. (shrink)

Warrant is “that, whatever precisely it is, which makes the difference between knowledge and mere true belief.” S knows that p, therefore, if and only if S’s belief that p is warranted and p is true. This is a purely formal characterization of warrant. Warrant may, no doubt, be a messy item: a substantive analysis might be full of disjuncts and conjuncts and conditionals and caveats. But if there are true beliefs that are not knowledge, then there is something that (...) all beliefs that are knowledge share, and all merely true beliefs lack. This is warrant. I want to argue that warrant, whatever it is that makes the difference between mere true belief and knowledge, entails truth. (shrink)

Proponents of the subset account of property realization commonly make the assumption that the summing of properties entails the summing of their forward-looking causal features. This paper seeks to establish that this assumption is false. Moreover, it aims to demonstrate that without this assumption the fact that the subset account captures an entailment relation—which it must if it is to be of any use to non-reductive physicalism—becomes questionable.

Doxasticism is the view that propositional faith entails belief. A common criticism of doxasticism is that faith seems compatible with doubt in a way that belief is not. Thus, it seems possible to have faith without belief, and several non-doxasticist accounts of faith are motivated inter alia by the need to account for this type of doubt. I provide three avenues of response: (1) favored cases of faith without belief beg the question by stipulating faith-that-p-without-belief-that-p, or if the non-doxasticist provides (...) evidence that there is faith without belief, this evidence points to either (2) no-faith-that-p-because-disbelief-that-p or (3) faith-that-p-with-belief-that-p. (shrink)

I argue that an affirmative answer to the question whether entailments could figure as contents of CI is warranted. In particular, the two features of CI that could rule out entailments from the class of contents that could be conversationally implicated are cancellability and non-conventionality. Entailments are non-cancellable, but this is a reason to conclude that they cannot be CIs only if cancellability is a universal property of CIs; alternatively, one might accept CIs that are entailed by what is said (...) and, on this basis, reject the claim that all CIs are cancellable. I see no compelling reason to go one way or another. So, this criterion does not lead to a principled answer to our question. Turning to non-conventionality, this is a defining feature of CIs, according to Grice. I explore the reasons given in the literature for taking non-conventionality to be a defining feature of CI, and argued that none of them are compelling: lexicalization of dead metaphors does not lead to overgeneration of CIs, and calculability is sufficient to distinguish conventional from conversational implicatures. I propose a definition of CI in terms of calculability alone, which does not rule out entailments. So, the answer to our initial question is, eventually, a tentative ‘yes’. A notable consequence of this definition is that the argument against the cancellability test based on cases of CIs the content of which is entailed by what is said seems a good one after all. This means that CIs are not necessarily cancellable. However, that does not mean that the test is a bad one, inasmuch as non-entailed CIs are still expected to be cancellable. (shrink)

N. Tennant; XI*—Entailment and Proofs, Proceedings of the Aristotelian Society, Volume 79, Issue 1, 1 June 1979, Pages 167–190, https://doi.org/10.1093/aristote.

According to an intuitive picture of relevant entailment, an entailment is relevant if all the formulas it contains contribute to its validity. In this paper, we provide a ground-theoretic analysis of this notion of contribution, and as a result of relevant entailment. We build a system of bilateral logical grounding within which we can derive classical entailment and analyze the contribution of premises and conclusions, in terms of a certain type of connection between their respective logical (...) grounds. The resulting framework is shown to have a strong unifying and explanatory power by bringing together the notions of grounding and relevance and explaining the commonalities and differences between alternative contribution-based accounts of relevance. (shrink)

I argue that there are Leibnizian-style cosmological arguments for the existence of God which start from very mild premises which affirm the mere possibility of a principle of sufficient reason. The utilization of such premises gives a great deal of plausibility to such types of argumentation. I spend the majority of the paper defending three major objections to such mild premises viz., a reductio argument from Peter van Inwagen and William Rowe, which proffers and defends the idea that a necessary (...) proposition cannot explain a contingent one. I, then, turn to an amelioration of the Rowe/van Inwagen argument which attempts to appeal to an entailment relation between explanans and explanandum that is fettered out in terms of relevance logic. Subsequent to dispelling with that worry, I tackle objections to the utilization of weak principles of sufficient reason that depend essentially upon agglomerative accounts of explanation. (shrink)

This book provides a novel formulation and defence of moral error theory. It also provides a novel solution to the so-called now what question; viz., the question what we should do with our moral thought and talk after moral error theory. The novel formulation of moral error theory uses pragmatic presupposition rather than conceptual entailment to argue that moral judgments carry a non-negotiable commitment to categorical moral reasons. The new answer to the now what question is pragmatic presupposition substitutionism: (...) we should substitute our current moral judgments, which pragmatically presuppose the existence of categorical moral reasons with ‘schmoral’ judgments that pragmatically presuppose the existence of a specific class of prudential reasons. These are prudential reasons that, when we act on them, contribute to the satisfaction of what the author calls ‘the fundamental desire’; namely, the desire to live in a world with mutually beneficial cooperation. (shrink)

Warrant is “that, whatever precisely it is, which makes the difference between knowledge and mere true belief.” S knows that p, therefore, if and only if S’s belief that p is warranted and p is true. This is a purely formal characterization of warrant. Warrant may, no doubt, be a messy item: a substantive analysis might be full of disjuncts and conjuncts and conditionals and caveats. But if there are true beliefs that are not knowledge, then there is something that (...) all beliefs that are knowledge share, and all merely true beliefs lack. This is warrant. I want to argue that warrant, whatever it is that makes the difference between mere true belief and knowledge, entails truth. (shrink)

I argue that Universalism (the thesis that mereological composition is unrestricted) entails Extensionalism (the thesis that sameness of composition is sufficient for identity) as long as the parthood relation is transitive and satisfies the Weak Supplementation principle (to the effect that whenever a thing has a proper part, it has another part disjoint from the first).

Several philosophers have recently claimed that if a proposition is cancellable from an uttered sentence then that proposition is not entailed by that uttered sentence. The claim should be a familiar one. It has become a standard device in the philosopher's tool-kit. I argue that this claim is false. There is a kind of entailment—which I call “modal entailment”—that is context-sensitive and, because of this, cancellable. So cancellability does not show that a proposition is not entailed by an (...) uttered sentence. I close the paper by describing an implication this has for a disagreement between J. L. Austin and Grice concerning the relation between felicity and truth. (shrink)

Priest argued in Fusion and Confusion (Priest in Topoi 34(1):55–61, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of (...) consequence. Unlike the latter, however, Priest’s consequence relation does not satisfy a variant of the variable sharing property. This paper shows that how it can be modified so as to do so. Priest’s consequence relation turns out to be surprisingly weak in some respects. The prospects of strengthening it is raised and discussed in a broader philosophical context. (shrink)

The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. (...) While the entailment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas. (shrink)

Despite Radford’s (1966) case of the unconfident examinee, many epistemologists think that knowledge entails belief. Epistemologists have levelled two sorts of criticisms: first, they point out that Radford’s case isn’t a clear case of knowledge; second, they object that even if knowledge is granted in Radford-like cases, agents therein will still have dispositional belief. This paper offers a case that improves upon Radford’s. In my case, the agent’s evidence is intuitively sufficient for knowledge. And we do not need to posit (...) dispositional belief to make the case empirically plausible. My counterexample involves a distinctive type of agent: cautious believers. Cautious believers care more about avoiding false belief. When armed with evidence that is sufficient - though only barely sufficient - to justify some proposition p, cautious believers suspend judgment about p. Nevertheless, they remain minimally behaviourally sensitive to the evidence. Ultimately, I argue that such agents are in a mental state that falls short of belief. (shrink)

This article accomplishes two closely connected things. First, it refutes an influential view about the relationship between perception and knowledge. In particular, it demonstrates that perceiving does not entail knowing. Second, it leverages that refutation to demonstrate that knowledge is not the most general factive propositional attitude.

In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working (...) in the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

The standard view in philosophy is that responsibility entails causation. Most philosophers treat this entailment claim as an evident insight into the ordinary concepts of responsibility and causation. Further, it is taken to be equally obvious that the reversal of this claim does not hold: causation does not entail responsibility. In contrast, Sytsma and Livengood have put forward an account of the use of ordinary causal attributions (statements like “X caused Y”) that contends that they are typically used interchangeably (...) with responsibility attributions (statements like “X is responsible for Y”). Put in terms of the concepts at play in these attributions, this account suggests that the reversal of the entailment claim may also hold, and, a fortiori, there would be mutual entailment between the ordinary concepts of responsibility and causation. Using the cancellability test, we report the results of three pre-registered studies providing empirical evidence that causation and responsibility are mutually entailed by each other. (shrink)

entailment; families of sets; logic of questions.

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal (...) is achieved by taking Adams' (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams' logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of - C given B are both close to one but the bound on the former's deviation from 1 is much smaller than the latter's, then it may be concluded that in all likelihood the conditional probability of C given A ∧ B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor's rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl's System-Z⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their randomstructures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL. (shrink)

In this paper we extend some techniques from the theory of conse- quences operations and logical matrices into the wider area of entailment relations.

I explicate the crucial role played by efficient cause in Robert Rosen’s characterization of life, by elaborating on the topic of Aristotelian causality, and exploring the many alternate descriptions of causal and inferential entailments. In particular, I discuss the concepts of functional entailment and immanent causation, and examine how they fit into Robert Rosen’s relational-biology universe of living, anticipatory, and complex systems.

1. Anderson and Belnap's most explicit characterization of the fallacy of modality is as follows: "Modal fallacies arise when it is claimed that entailments follow from, or are entailed by, contingent propositions." The view which Nelson attributes to Anderson and Belnap, on the other hand, is "that necessary propositions are entailed only by necessary ones, never by contingent ones." Anderson and Belnap speak of "entailments," whereas Nelson generalizes to "necessary propostitions." The move is far from innocent, as we shall see. (...) For though Anderson and Belnap hold that every true entailment is a necessary proposition, not every necessary proposition is an entailment. In order to grasp the implications of this distinction more clearly, let us see how Anderson and Belnap's statement of the modal fallacy might legitimately be restated in terms of necessity. To that end we must draw a related distinction between necessary propositions and necessity propositions. A expresses a necessary proposition iff A → A → A holds. A expresses a necessity proposition iff A is of the form B → C. The particular form of these definitions is dependent on the fact that entailment rather than necessity is primitive in Anderson and Belnap's system; the forms in parentheses are the equivalents in terms of necessity. Now it follows from these definitions that every entailment is a necessity proposition and that every necessity proposition is an entailment. The modal fallacy may thus be equivalently characterized as the claim that a necessity proposition is entailed by a contingent proposition. That this is different from Nelson's formulation is clear from the following considerations. First, not every necessary proposition is a necessity proposition; example: "Either it is raining or it is not raining." Second, not every necessity proposition is a necessary proposition; example: any false necessity proposition. Thus the possibility is left open that some necessary proposition might be entailed by a contingent one. This is exactly the case with Nelson's example 2, "That every polychromatic surface is red entails that every polychromatic surface is colored." This might well be a theorem in a suitable extension of E. Such cases do not, however, arise among the theorems of EI. In that limited system, all that a contingent proposition can entail is itself. (shrink)

Does faith that p entail belief that p? If faith that p is identical with belief that p, it does. But it isn’t. Even so, faith that p might be necessarily partly constituted by belief that p, or at least entail it. Of course, even if faith that p entails belief that p, it does not follow that faith that p is necessarily partly constituted by belief that p. Still, showing that faith that p entails belief that p would be (...) a significant step in that direction. Can we take that step? In this essay, I assess, and reject, seven reasons to think we can. Along the way, I discuss having faith in a person, being a person of faith, believing something by faith, and believing a person. (shrink)

This paper outlines a non-reductive counterfactual account of grounding along interventionist lines, and uses the account to argue that taking grounding seriously requires ascribing non-trivial truth-conditions to a range of counterpossible counterfactuals. This result allows for a diagnosis of a route to scepticism about grounding, as deriving at least in part from scepticism about non-trivial counterpossible truth and falsity.

N. Tennant; XI*—Entailment and Proofs, Proceedings of the Aristotelian Society, Volume 79, Issue 1, 1 June 1979, Pages 167–190, https://doi.org/10.1093/aristote.

An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of (...) entailment, showing that it is compact and decidable. We then investigate the effect of various restrictions on the semantics. We also formulate a sequent-style proof system for exact entailment and give soundness and completeness results. (shrink)

Peter Long; V*—Entailment: A Modal Distinction, Proceedings of the Aristotelian Society, Volume 79, Issue 1, 1 June 1979, Pages 79–88, https://doi.org/10.1093/a.

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference (...) from a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency. (shrink)

In this paper, a critical discussion is made of the role of entailments in the so-called New Paradigm of psychology of reasoning based on Bayesian models of rationality (Elqayam & Over, 2013). It is argued that assessments of probabilistic coherence cannot stand on their own, but that they need to be integrated with empirical studies of intuitive entailment judgments. This need is motivated not just by the requirements of probability theory itself, but also by a need to enhance the (...) interdisciplinary integration of the psychology of reasoning with formal semantics in linguistics. The constructive goal of the paper is to introduce a new experimental paradigm, called the Dialogical Entailment task, to supplement current trends in the psychology of reasoning towards investigating knowledge-rich, social reasoning under uncertainty (Oaksford and Chater, 2019). As a case study, this experimental paradigm is applied to reasoning with conditionals and negation operators (e.g. CEM, wide and narrow negation). As part of the investigation, participants’ entailment judgments are evaluated against their probability evaluations to assess participants’ cross-task consistency over two experimental sessions. (shrink)