Saul Kripke’s work on the semantics of modal logics is well known, unlike his work on Anderson and Belnap’s system E of Entailment (a modal relevance logic), which included his proof of the decidability of its implicational fragment E_>, and also a counterexample to the conjecture of Belnap that E_> is the intersection of the implicational fragments of the relevance logic R and the modal logic S4. This led to Storrs McCall’s suggesting that the “mingle” axiom might be added (...) to E_>, and that this system might be used instead of S4_>. We give a counterexample to this conjecture. We also disprove the conjecture Anderson and Belnap attribute to McCall, in which “restricted mingle” is added to E_>. We use a modal extension of the lattice M_0 and follow ideas of Meyer. In the 1970s, Dunn showed that RM (R with the mingle axiom) can be modeled using a binary accessibility relation, like the accessibility relation in Kripke’s semantics for normal modal logics and his semantics for intuitionistic logic. Dunn also gave a variant interpretation for EM (E with the mingle axiom). We explore some other variations of these binary relational semantics. (shrink)

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 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)

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)

entailment; families of sets; logic of questions.

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)

The logic TM is the result of adding the mingle axiom, M to Ticket Entailment logic, T. In the present study, it is proved that TM has the variable-sharing property . Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed.

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)

R. W. Ashby; XI—Entailment and Modality, Proceedings of the Aristotelian Society, Volume 63, Issue 1, 1 June 1963, Pages 203–216, https://doi.org/10.1093/aristo.

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.

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)

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)

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)

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.

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)

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood (...) semantics meets the Routley-Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable. (shrink)

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.

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)

Last week, we talked a bit about the Anderson-Belnap logic of entailment, as discussed in Priest’s Introduction to Non-Classical Logic. For a quite different approach to entailment, we’ll look next week at Neil Tennant’s account. Doing things rather out of order, this week I’d like to say something more basic about the problems to which both Anderson and Belnap, on the one hand, and Tennant on the other, are responding. This will give me the chance for a bit (...) of nostalgic philosophical time-travelling, revisiting work by Casimir Lewy and Timothy Smiley from the Cambridge of fifty years ago. (shrink)

Following Moore, I use ‘P entails Q’ as a convenient shorthand for ‘Q can be deduced logically from P’, ‘From P, Q follows logically’, ‘There is a logically valid argument with P as sole premise and Q as conclusion’, and the like.1 Apart from a minor point to be raised in Section XVI, distinctions within this cluster do not matter for present purposes. An analysis of the concept of entailment is answerable to careful, educated uses of expressions such as (...) those. An analysis which condemned nearly everything we say about what follows from what simply would not be an analysis of the common concept of entailment. If the concept were inconsistent, some common uses of it would be condemned; but only by standards established by the others. C. I. Lewis maintained this: to say that P entails Q is to say that it is logically impossible that (P & ¬Q).2 If Quine is right, then ‘entails’ and ‘impossible’ are as suspect as all other intensional terms. So perhaps they are; but their uses are not wholly without structure, and there are wrong ways of interrelating them. Lewis’s contention is about the internal geography of the intensional area, not its relations to the surrounding conceptual territory: it is an attempted analysis of one intensional expression in terms of another. I shall argue that Lewis was right, and also - by implication - that his thesis is helpful and clarifying - that is, that it is a genuine analysis. As is well known, Lewis’s analysis implies that each impossible proposition entails every proposition. Accepting the analysis, I accept this result. For one thing, Lewis has an argument for it (I use ‘→’ to abbreviate ‘entails’): (1) P & ¬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)

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)

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)

Robert Maydole has recently presented a sophisticated ontological argument that he calls the Modal Perfection Argument for the existence of a supreme being. While this ontological argument is probably better than most of its peers, it is nonetheless open to at least one decisive objection. The purpose of this brief comment is to develop that objection. I claim that this objection indicates an important further point about the concept of entailment and its role in ontological arguments at large, the (...) recognition of which helps to refute other conceivable ontological arguments. (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.

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)

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

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 consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it (...) is possible to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations. (shrink)

Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts, then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How (...) is the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle – an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected. (shrink)

Peter Downing; V—Entailment, Proceedings of the Aristotelian Society, Volume 66, Issue 1, 1 June 1966, Pages 15–26, https://doi.org/10.1093/aristotelian/66.1.15.

C. Lewy; VI—Entailment and Propositional Identity, Proceedings of the Aristotelian Society, Volume 64, Issue 1, 1 June 1964, Pages 107–122, https://doi.org/10.1.

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.

In this paper we present a probabilistic notion of entailment for finite sets of premises, which has classical entailment as a special case, and show that it is well defined; i.e., that the problem of whether a sentence is entailed by a set of premises is computable. Further we present a natural deductive system and prove that it is the strongest deductive system possible without referring to probabilities.

I explicate how various relational interactions between (M,R)-systems may have realizations in pathophysiology, and how the possible reversals of the effects of these interactions then become therapeutic models. Functional entailment receives a rigorous category-theoretic treatment, and plays a crucial role in this continuing saga of relational biology.

Whether responsibility for actions and omissions requires the ability to do otherwise is an important issue in contemporary philosophy. However, a closely related but distinct issue, namely whether doxastic responsibility requires the ability to believe otherwise, has been largely neglected. This paper fills this remarkable lacuna by providing a defence of the thesis that doxastic responsibility entails the ability to believe otherwise. On the one hand, it is argued that the fact that unavoidability is normally an excuse counts in favour (...) of this thesis. On the other hand, three objections against this thesis are discussed and criticized. First, one might think that what suffices for doxastic responsibility is control over or influence on certain desirable or undesirable properties of beliefs. It is argued that this objection misrepresents the issue under consideration. Second, it may be objected that the thesis is contradicted by our intuitions in doxastic analogues of Frankfurt-style scenarios. It is argued that distinguishing between belief-universals and belief-particulars helps to see why this argument fails. Third and finally, one might draw an analogy with the asymmetry thesis in ethics by arguing that even if blameworthy belief requires the ability to believe otherwise, praiseworthy belief does not. It is argued that the main arguments in favour of this presumed asymmetry are wanting, partly because they fail to distinguish between two different kinds of praiseworthiness. Finally, the author sketches three implications of the thesis that doxastic responsibility entails the ability to believe otherwise: counterfactual construals of responsible belief might be tenable, the deontological conception of epistemic justification needs revision on an important point, and there might be an important asymmetry between beliefs on the one hand and actions and many non-doxastic consequences on the other. (shrink)

Entailment relations, introduced by Scott in the early 1970s, provide an abstract generalisation of Gentzen’s multi-conclusion logical inference. Originally applied to the study of multi-valued logics, this notion has then found plenty of applications, ranging from computer science to abstract algebra. In particular, an entailment relation can be regarded as a constructive presentation of a distributive lattice and in this guise it has proven to be a useful tool for the constructive reformulation of several classical theorems in commutative (...) algebra. In this paper, motivated by these concrete applications, we state and prove a cut-elimination result for inductively generated entailment relations. We analyse some of its consequences and describe the existing connections with analogous results in the literature. (shrink)

Although ‘warrant’ has been used to mean something like ‘justified to the degree required for knowledge’, it has recently come to mean something else. Alvin Plantinga has recently used the word ‘warrant’ to mean “that, whatever precisely it is, which makes the difference between knowledge and mere true belief.” So, in Plantinga’s sense of the word, warrant is the justification condition plus some other condition designed to rule out Gettier examples. In almost all cases, reliabilists, foundationalists, and coherentists have not (...) been giving theories about ‘warrant’ in Plantinga’s sense. They have been busy giving theories about justification. In his paper, “Warrant Entails Truth,” Trenton Merricks argues that warrant, in Plantinga’s sense, entails truth. In this paper, I will show that Merricks has not succeeded in showing that warrant entails truth. (shrink)

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)

Stephen Mumford, in his book on dispositions, argues that we can distinguish between dispositional and categorical properties in terms of entailing his 'conditional conditionals', which involve the concept of ideal conditions. I aim at defending Mumford's criterion for distinguishing between dispositional and categorical properties. To be specific, no categorical ascriptions entail Mumford's 'conditional conditionals'.