This paper is concerned with disjunctions of universal modals, such as ‘You have to clean your room or you have to walk the dog’, and disjunctions of conditionals, such as ‘If Alice dances, Charlie will dance, or if Bob dances, Charlie will dance’. We aim to provide a uniform account of their surprising behaviour. Our proposal combines three independently attested components. Firstly, disjunction's dynamic effect, familiar from presupposition projection: when we evaluate a disjunction ‘A or B’, we typically (...) interpret B assuming the negation of A, and optionally, also interpret A assuming the negation of B. Secondly, the fact that disjunctions often receive a conjunctive interpretation, familiar from free choice phenomena. Thirdly, that modal bases are restricted to local contexts, what Mandelkern has called ‘bounded modality’. (shrink)

I explore constructions which contain an embedded disjunction ⌜p or q⌝which is interpreted as (p∨q) ∧♢p∧♢q, where ♢is a possibility modal whose flavor is epistemic, circumstantial, or deontic. I argue that no extant theory can account for these interpretations. I propose that the best way to do so is with a direct theory on which ⌜p or q⌝ simply means (p∨q) ∧♢p∧♢q. In addition to accounting for the novel cases I discuss, this theory explains both wide- and narrow-scope free (...) choice inferences, in a similar way as the theories of Zimmermann (2000); Geurts (2005); Goldstein (2019). It also accounts for recent observations about the relation between disjunction and possibility from Degano et al. 2025; Feinmann 2023. (shrink)

Disjunctive antecedent conditionals —conditionals of the form if A or B, C—sometimes seem to entail both of their simplifications and sometimes seem not to. I argue that this behavior reveals a genuine ambiguity in DACs. Along the way, I discuss a new observation about the role of focal stress in distinguishing the two interpretations of DACs. I propose a new theory, according to which the surface form of a DAC underdetermines its logical form: on one possible logical form, if A (...) or B, C does entail both of its simplifications, while on the other, it does not. (shrink)

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality (...) problem, but none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

This paper defends the case against (sparse) disjunctive properties by means of four Armstrongian arguments. The first of these is a logical atomist argument from truthmaking, which is, broadly speaking, ‘Armstrongian’ (Armstrong 1997). This argument is strong – although it stands or falls with the relevant notion of truthmaking, as it were. However, three arguments, which are prima facie independent of truthmaking, can be found explicitly early in Armstrong’s middle period. Two of these early arguments face a serious objection put (...) forward forcefully by Louise Antony (2003) and Alan Penczek (1997), respectively. I consider these objections and argue that they fail. Thus, even if the argument from truthmaking is indecisive, disjunctive properties should be rejected. (shrink)

This article re-examines Friedrich W. J. Schelling’s philosophical divergence from dialectical philosophy, with a focus on his Freedom Essay. While traditionally viewed as rejecting dialectics—particularly following the publication of Georg W. F. Hegel’s Phenomenology of Spirit—this study challenges that perception by arguing that Schelling employs a dialectical understanding of identity centred on disjunction (§ 1). It demonstrates how Schelling’s metaphysics, developed to accommodate freedom, incorporates the notion of identity of contradictory elements (§ 2). By exploring the central role of (...) disjunction in Schelling’s “dialectical argument” (§ 3) and critically engaging with recent interpretations by Manfred Frank and Mark J. Thomas (§ 4), the article reassesses the Freedom Essay as a pivotal contribution to dialectical philosophy, broadly construed. Ultimately, it aims to facilitate a more nuanced comparison between Schelling’s and dialectical philosophies, challenging the entrenched narrative of their fundamental opposition (§ 5). (shrink)

This paper is a response to replies by Dan López de Sa and Mark Jago to my ‘Truthmaking, Entailment, and the Conjuction Thesis’. In that paper, my main aim was to argue against the Entailment Principle by arguing against the Conjunction Thesis, which is entailed by the Entailment Principle. In the course of so doing, although not essential for my project in that paper, I defended the Disjunction Thesis. López de Sa has objected both to my defence of the (...) Disjunction Thesis and my case against the Conjunction Thesis. I shall show that his objections are unfounded and based on serious misunderstandings of my position, what the relevant debate is, and some fundamental notions of Truthmaker Theory. Jago argues that accepting the Disjunction Thesis and rejecting the Conjunction Thesis is hard to maintain. But I show that Jago has not shown that accepting the Disjunction Thesis while rejecting the Conjunction Thesis is impossible or even hard to maintain. Jago believes that, to accept the Disjunction Thesis while rejecting the Conjunction Thesis, one needs to reject his axiom (T3), which says that all the truthmakers for <P&P> are truthmakers for <P>. I argue that there are reasons to reject such a principle, and the version of it that says that what makes <P&P> true makes <P> true. (shrink)

A comparison of disjunctive theories of action and perception. The development of a theory of action that warrants the name, a disjunctive theory. On this theory, there is an exclusive disjunction: either an action or an event (in one sense). It follows that in that sense basic actions do not have events intrinsic to them.

We consider the problem of moral disjunction in professional and business activities from a virtue-ethical perspective. Moral disjunction arises when the behavioral demands of a role conflict with personal morality; it is an important problem because most people in modern societies occupy several complex roles that can cause this clash to occur. We argue that moral disjunction, and the psychological mechanisms that people use to cope with it, are problematic because they make it hard to pursue virtue (...) and to live with integrity. We present role coadunation as a process with epistemic and behavioral aspects that people can use to resolve moral disjunction with integrity. When role coadunation is successful, it enables people to live virtuous lives of appropriate narrative disunity and to honor their identity-conferring commitments. We show how role coadunation can be facilitated by interpretive communities and discuss the emergence and ideal features of those communities. (shrink)

In this paper I deal with the relation between the disjunction thesis—that the truthmaking relation is distributed over a disjunction—and the necessary connection thesis—that the existence of some entities requires the existence of other distinct entities. I will first show that because of this very relation, the arguments for and against the disjunction thesis that overlook its metaphysical considerations will fail. Finally, I will show that the commitment produced by truthmaker maximalism to totality states of affairs, or (...) some relevantly similar things, requires one to accept a necessary connection that disaffirms the disjunction thesis. (shrink)

Fine (2017a) sets out a theory of content based on truthmaker semantics which distinguishes two kinds of consequence between contents. There is entailment, corresponding to the relationship between disjunct and disjunction, and there is containment, corresponding to the relationship between conjunctions and their conjuncts. Fine associates these with two notions of parthood: disjunctive and conjunctive. Conjunctive parthood is a very useful notion, allowing us to analyse partial content and partial truth. In this chapter, I extend the notion of disjunctive (...) parthood in terms of a structural relation of refinement, which stands to disjunctive parthood much as mereological parthood stands to conjunctive parthood. Philosophically, this relation may be modelled on the determinable- determinate relation, or on a fact-to-fact notion of grounding. I discuss its connection to two other Finean notions: vagueness (understood via precisification) and arbitrary objects. I then investigate what a logic of truthmaking with refinement might look like. I argue that (i) parthood naturally gives rise to a relevant conditional; (ii) refinement underlies a relevant notion of disjunction; and so (iii) truthmaker semantics with refinement is a natural home for relevant logic. The resulting formal models draw on Fine’s (1974) semantics for relevant logics. Finally, I use this understanding of relevant semantics to investigate the status of the mingle axiom. (shrink)

Gonzalo Rodriguez-Pereyra (2006) argues against attempts to preserve the entailment principle (or a restriction of it) while avoiding the explosion of truthmakers for necessities and truthmaker triviality. In doing so, he both defends the disjunction thesis--if something makes true a disjunctive truth, then it makes true one of its disjuncts--, and rejects the conjunction thesis--if something makes tue a conjunctive truth, then it makes true each of its conjuncts. In my discussion, I provide plausible counterexamples to the disjunction (...) thesis, and contend that Rodriguez-Pereyra's general defence of it fails. Then I defend the conjunction thesis from Rodriguez-Pereyra's case against it. (shrink)

Monism regarding hypocrisy’s wrongness maintains that there is a single, sui generis wrong of hypocrisy. This paper challenges hypocrisy monism and offers an alternative, hypocrisy disjunctivism, which maintains that the wrongness present in any token case of hypocrisy is always reducible to other, more basic wrongs. Hypocrisy disjunctivism, however, faces a fruitfulness challenge: why have a concept that names a disjunction of wrongs at all in our normative vocabulary? I answer that “hypocrisy” solves a unique practical problem in allowing (...) speakers to hold normatively inconsistent agents accountable for the wrongs, whatever they may be, that beget these agents’ normative inconsistency. (shrink)

A logic L has the disjunction property just in case $$\models _{L} \varphi \vee \psi $$ implies $$\models _{L} \varphi $$ or $$\models _{L} \psi $$. This property is important to constructivists and is a well-known feature of intuitionistic logic. In this paper we use model-theoretic techniques to show that the disjunction property holds in Urquhart’s operational relevance logics $${\textbf {R}}_U^+$$, $${\textbf {T}}_U^+$$, $${\textbf {RW}}_U^+$$, $${\textbf {TW}}_U^+$$, and $${\textbf {E}}_U^+$$. These results suggest that operational relevance logics merit further (...) attention from a constructivist perspective. Along the way, we also provide a novel proof that the disjunction property holds in intuitionistic logic. (shrink)

This text introduces Hetrology, a new framework proposing that humanity’s historical inability to reach consensus on Truth is not accidental but structural. Across 2,500 years of philosophy, the same pattern recurs: each era redefines Truth yet never unifies Being and Truth within a measurable frame. Hetrology interprets this persistent divergence as evidence of an ontological law — the Ontological Disjunction — dividing humankind into two responses to reality: endurance or flight. The essay presents this idea in accessible terms, tracing (...) how philosophy, science, and culture may all express the same hidden structure. Rather than replacing previous systems, it reveals the continuity between them: from Plato’s cave to neuroscience, the same fracture reappears. By reading this silence as data, Hetrology argues that the history of thought itself is an unintentional experiment — one whose outcome shows that Truth acts as a selective field. This popular version condenses the manifesto Theory of the Disjunction of Being and Truth, making its core intuition graspable: philosophy did not fail — it reached its limit. What begins beyond that limit is not speculation, but the science of Being. (shrink)

We argue in favor of merely disjunctive effects, namely cases in which an event or fact, C, is not a cause of an effect, E1, and is also not a cause of a distinct effect, E2, and yet C is a cause of the disjunctive effect (E1 orE2). Disjunctive effects let us retain the additivity and the distributivity of causation. According to additivity, if C is a cause of E1 and C is a cause of E2, then C is a (...) cause of E1 and E2. According to distributivity, if C is a cause of E1 and E2, then C is a cause of E1 and C is a cause of E2. We draw an analogy between causation and intensional notions like believing, wanting, and owing, which also admit of merely disjunctive cases. We argue that both the Lewisian counterfactual account of causation (including its recent emendation by Sartorio) and the contrastive account of causation fail to properly account for this phenomenon. (shrink)

The paper explores the disjunctive riddle for induction: If we know the sample Ks to be P, we also know that they are P or F. Assuming that we also know that the future Ks are non-P, we can conclude that they are F, if only we can inductively infer the evidentially supported P-or-F hypothesis. Yet this is absurd. We cannot predict that future Ks are F based on the knowledge that the samples, and only they, are P. The ensuing (...) challenge is to account for the unprojectibility of the disjunctive hypothesis. I provide an explanation in terms of epistemic dependence. The P-or-F hypothesis is unprojectible because the evidence supporting it depends epistemically on the evidence for the defeated P-hypothesis. The paper also shows that the disjunctive riddle covers the essence of Goodman's infamous grue-problem, which, therefore, can be resolved by the same means: In contrast to the green-hypothesis, the grue-hypothesis is unprojectible because the grue-evidence depends on the evidence for a defeated hypothesis. (shrink)

Perceptual experiences are often divided into the following three broad categories: veridical perceptions, illusions, and hallucinations. For example, when one has a visual experience as of a red object, it may be that one is really seeing an object and its red colour (veridical perception), that one is seeing a green object (illusion), or that one is not seeing an object at all (hallucination). Many maintain that the same account should be given of the nature of the conscious experience that (...) occurs in each of these three cases. Those who hold a disjunctive theory of perception deny this. Disjunctivists typically reject the claim that the same kind of experience is common to all three cases because they hold views about the nature of veridical perception that are inconsistent with it. (shrink)

The relation between ex falso and disjunctive syllogism, or even the justification of ex falso based on disjunctive syllogism, is an old topic in the history of logic. This old topic reappears in contemporary logic since the introduction of minimal logic by Johansson. The disjunctive syllogism seems to be part of our general non-problematic inferential practices and superficially it does not seem to be related to or to depend on our acceptance of the frequently disputable ex falso rule. We know (...) that the acceptance of the ex falso is a sufficient condition for the acceptance of the disjunctive syllogism, but the interesting question is: is the ex falso a necessary condition for the acceptance of the disjunctive syllogism? The aim of the present paper is to discuss some possible ways to define systems that combines the preservation of the disjunctive syllogism with the rejection of the ex falso. (shrink)

By a well-known result of Kotlarski et al., first-order Peano arithmetic \ can be conservatively extended to the theory \ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth predicate is correct on atomic formulae and commutes with all the propositional connectives and quantifiers. This result motivates the general question of determining natural axioms concerning the truth predicate that can be added to \ while maintaining conservativity over \. Our main result shows that conservativity fails even (...) for the extension of \ obtained by the seemingly weak axiom of disjunctive correctness \ that asserts that the truth predicate commutes with disjunctions of arbitrary finite size. In particular, \ implies \\). Our main result states that the theory \ coincides with the theory \ obtained by adding \-induction in the language with the truth predicate. This result strengthens earlier work by Kotlarski and Cieśliński. For our proof we develop a new general form of Visser’s theorem on non-existence of infinite descending chains of truth definitions and prove it by reduction to Gödel’s second incompleteness theorem, rather than by using the Visser–Yablo paradox, as in Visser’s original proof. (shrink)

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the case that either disjunct holds of every (...) individual in the domain of the quantifier, \Every A is P &\Every A is Q. As we show, this derivation faces a challenge in that distributive inferences may obtain in the absence of plain negated inferences. We address this challenge by showing that on particular assumptions about alternatives, a derivation of distributive inferences as scalar implicatures can be maintained without in fact necessitating plain negated inferences. These assumptions accord naturally with the grammatical approach to scalar implicatures. We also present experimental data that suggest that plain negated inferences are not only unnecessary for deriving distributive inferences, but might in fact be unavailable. (shrink)

Many philosophers have been attracted to the idea of using the logical form of a true sentence as a guide to the metaphysical grounds of the fact stated by that sentence. This paper looks at a particular instance of that idea: the widely accepted principle that disjunctions are grounded in their true disjuncts. I will argue that an unrestricted version of this principle has several problematic consequences and that it’s not obvious how the principle might be restricted in order to (...) avoid them. My suggestion is that, instead of trying to restrict the principle, we should distinguish between metaphysical and conceptual grounds and take the principle to apply exclusively to the latter. This suggestion, if correct, carries over to other prominent attempts at using logical form as a guide to ground. (shrink)

There is an initial presumption against disjunctive causes. First of all, for some people causation is a relation between events. But, arguably, there are no disjunctive events, since events are particulars and thus they have spatiotemporal locations, while it is unclear what the spatiotemporal location of a disjunctive event could be.1 More importantly, even if one believes that entities like facts can enter in causal relations, and even if there are disjunctive facts, it is still hard to see how disjunctive (...) facts could be causes. Imagine, for instance, the following scenario. I have a gun filled with red paint and another gun filled with blue paint, and I fire both guns at my neighbor’s white wall. A moment later, there is a graffiti on the wall and my neighbor notifies the police. He would have done so regardless of the graffiti’s color, since all he cares about is the existence of a graffiti on his wall. Is it plausible to claim that a disjunctive fact is a cause of his notifying the police? In particular, is it plausible to claim that he notified the police because I fired the red-paint gun or the blue-paint gun (the thought being that my firing paint of either color would have sufficed)? It seems not. The police was notified because of the actual graffiti on the wall, and the actual graffiti on the wall is made of a certain pattern of colored patches. Imagine, that, as it turns out, there are patches of both colors on the wall. Then it seems that both my firing the red-paint gun and my firing the blue-paint gun were causes of my neighbor’s notifying the police. In other words, my firing the red-paint gun and my firing the blue-paint gun jointly caused the outcome: each of them was a contributory cause of the outcome’s occurrence. On the other hand, imagine that there are only patches of one color on the wall. Then it seems that my firing only one of the guns was a cause. Either way, the disjunction fails to be a cause: either my firing the red-paint gun was a cause, or my firing the blue-paint gun was a cause, or they were both causes, but their disjunction was not.. (shrink)

The natural interpretation of counterfactuals with disjunctive antecedents involves selecting from each of the disjuncts the worlds that come closest to the world of evaluation. It has been long noticed that capturing this interpretation poses a problem for a minimal change semantics for counterfactuals, because selecting the closest worlds from each disjunct requires accessing the denotation of the disjuncts from the denotation of the disjunctive antecedent, which the standard boolean analysis of or does not allow (Creary and Hill, Philosophy of (...) Science 43:341–344, 1975; Nute, Journal of Philosophy 72:773–778, 1975; Fine, Mind 84(335):451–458, 1975; Ellis et al. Journal of Philosophical Logic 6:335–357, 1977). This paper argues that the failure to capture the natural interpretation of disjunctive counterfactuals provides no reason to abandon a minimal change semantics. It shows that the natural interpretation of disjunctive counterfactuals is expected once we refine our assumptions about the semantics of or and the logical form of conditionals, and (i) we assume that disjunctions introduce propositional alternatives in the semantic derivation, in line with independently motivated proposals about the semantics of or (Aloni, 2003a; Simons, Natural Language Semantics 13:271–316, 2005; Alonso-Ovalle, Disjunction in Alternative Semantics. PhD thesis, 2006); and (ii) we treat conditionals as correlative constructions, as advocated in von Fintel (1994), Izvorski (Proceedings of NELS 26, 1996), Bhatt and Pancheva (2006), and Schlenker (2004). (shrink)

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them (...) discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

In contrast to Hintikka’s enormously complex distributive normal forms of first- order logic, this paper shows how to generate minimized disjunctive normal forms of first-order logic. An effective algorithm for this purpose is outlined, and the benefits of using minimized disjunctive normal forms to explain the truth conditions of propo- sitions expressible within pure first-order logic are presented.

This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than (...) disjunctive in character. These conjunctive uses have puzzled philosophers and logicians, and have been discussed extensively under such headings as "free choice permission." This study examines the textbook myths that have clouded our understanding of how or and other "logical" vocabulary comes to have something approaching its logical meaning in natural languages. It considers the various historical conceptions of disjunction and its place in logic from the Stoics to the present day. (shrink)

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the (...) lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

We systematically study several versions of the disjunction and the existence properties in modal arithmetic. First, we newly introduce three classes $\mathrm {B}$, $\Delta (\mathrm {B})$, and $\Sigma (\mathrm {B})$ of formulas of modal arithmetic and study basic properties of them. Then, we prove several implications between the properties. In particular, among other things, we prove that for any consistent recursively enumerable extension T of $\mathbf {PA}(\mathbf {K})$ with $T \nvdash \Box \bot $, the $\Sigma (\mathrm {B})$ -disjunction (...) property, the $\Sigma (\mathrm {B})$ -existence property, and the $\mathrm {B}$ -existence property are pairwise equivalent. Moreover, we introduce the notion of the $\Sigma (\mathrm {B})$ -soundness of theories and prove that for any consistent recursively enumerable extension of $\mathbf {PA}(\mathbf {K4})$, the modal disjunction property is equivalent to the $\Sigma (\mathrm {B})$ -soundness. (shrink)

Critical-Level Utilitarianism entails one of the Repugnant Conclusion and the Sadistic Conclusion, depending on the critical level. Indeterminate Critical-Level Utilitarianism is a version of Critical-Level Utilitarianism where it is indeterminate which well-being level is the critical level. Undistinguished Critical-Range Utilitarianism is a variant of Critical-Level Utilitarianism where additions of lives in a range of well-being between the good and the bad lives make the resulting outcome incomparable to the original outcome. These views avoid the Repugnant Conclusion, they avoid the Sadistic (...) Conclusion, and they agree on all outcome comparisons not involving indeterminacy or incomparability. So it may seem unclear whether we have any reason to favour one of these theories over the other. But I argue that Indeterminate Critical-Level Utilitarianism still entails the disjunction of the Repugnant Conclusion and the Sadistic Conclusion, which is also repugnant. By contrast, Undistinguished Critical-Range Utilitarianism does not entail this conclusion. (shrink)

The inference pattern known as disjunctive syllogism (DS) appears as a derived rule in Gentzen’s natural deduction calculi ni and nk. This is a paradoxical feature of Gentzen’s calculi in so far as DS is sometimes thought of as appearing intuitively more elementary than the rules $$\vee $$ E, $$\lnot $$ E, and EFQ that figure in its derivation. For this reason, many contemporary presentations of natural deduction depart from Gentzen and include DS as a primitive rule. However, such departures (...) violate the spirit of natural deduction, according to which primitive rules are meant to relationally define logical connectives via universal properties (§2). This situation raises the question: Can disjunction be relationally defined with DS instead of with Gentzen’s $$\vee $$ I and $$\vee $$ E rules? We answer this question in the affirmative and explore the duality between Gentzen’s definition and our own (§3). We argue further that the two universal characterizations, rather than provide competing relational definitions of a single disjunction operator, disambiguate natural language’s “or” (§4). Finally, this disambiguation is shown to correspond exactly with the additive and multiplicative disjunctions of linear logic (§5). The hope is that this analysis sheds new light on the latter connective, so often deemed mysterious in writing about linear logic. (shrink)

This paper is a survey of results concerning the disjunction property, Halldén-completeness, and other related properties of intermediate prepositional logics and normal modal logics containing S4.

John McDowell's conception of perceptual knowledge commits him to the claim that if I perceive that P then I am in a position to know that I perceive that P. In the first part of this essay, I present some reasons to be suspicious of this claim - reasons which derive from a general argument against 'luminosity' - and suggest that McDowell can reject this claim, while holding on to almost all of the rest of his conception of perceptual knowledge, (...) by supplementing his existing disjunctive conception of experience with a new disjunctive conception of perceiving. In the second part of the essay, I present some reasons for thinking that one's justification, in cases of perceptual knowledge, consists not in the fact that one perceives that P but in the fact that one perceives such-and-such. I end by suggesting that the disjunctive conception of perceiving should be understood as a disjunctive conception of perceiving such-and-such. (shrink)

Ali Enayat had asked whether two halves of Disjunctive Correctness ([Formula: see text]) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that the principle “every true disjunction has a true disjunct” is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication “any disjunction with a true disjunct is true” can be conservatively added to [Formula: see text]. The (...) methods introduced here allow us to give a direct nonconservativeness proof for [Formula: see text]. (shrink)

Classical first-order logic \ is commonly used to study logical connections between statements, that is sentences that in every context have an associated truth-value. Inquisitive first-order logic \ is a conservative extension of \ which captures not only connections between statements, but also between questions. In this paper we prove the disjunction and existence properties for \ relative to inquisitive disjunction Open image in new window and inquisitive existential quantifier \. Moreover we extend these results to several families (...) of theories, among which the one in the language of \. To this end, we initiate a model-theoretic approach to the study of \. In particular, we develop a toolkit of basic constructions in order to transform and combine models of \. (shrink)

This paper investigates propositional hyperintensionality in counterfactuals. It starts with a scenario describing two children playing on a seesaw and studies the truth-value predictions for counterfactuals by four different semantic theories. The theories in question are Kit Fine’s truthmaker semantics, Luis Alonso-Ovalle’s alternative semantics, inquisitive semantics and Paolo Santorio’s syntactic truthmaker semantics. These predictions suggest that the theories that distinguish more of a given set of intensionally equivalent sentences (Fine and Alonso-Ovalle’s) fare better than those that do not (inquisitive semantics (...) and Santorio’s). Then we investigate how inquisitive semantics and Santorio can respond to these results. They can respond to them by helping themselves to considerations from Hurford disjunctions, disjunctions whose disjuncts stand in an entailment relation to one another. I argue that considerations from Hurford disjunctions are ad hoc modifications merely to predict the expected results. I conclude that the scenarios suggest a need for more fine-grained theories of sentential meaning in general. (shrink)

Fine (J. Philos. Logic 46(6):625–674, 2017a) sets out a theory of content based on truthmaker semantics which distinguishes two kinds of consequence between contents. There is entailment, corresponding to the relationship between disjunct and disjunction, and there is containment, corresponding to the relationship between conjunctions and their conjuncts. Fine associates these with two notions of parthood: disjunctive and conjunctive. Conjunctive parthood is a very useful notion, allowing us to analyse partial content and partial truth. In this chapter, I extend (...) the notion of disjunctive parthood in terms of a structural relation of refinement, which stands to disjunctive parthood much as mereological parthood stands to conjunctive parthood. Philosophically, this relation may be modelled on the determinable-determinate relation, or on a fact-to-fact notion of grounding. I discuss its connection to two other Finean notions: vagueness (understood via precisification) and arbitrary objects. I then investigate what a logic of truthmaking with refinement might look like. I argue that (i) parthood naturally gives rise to a relevant conditional; (ii) refinement underlies a relevant notion of disjunction; and so (iii) truthmaker semantics with refinement is a natural home for relevant logic. The resulting formal models draw on Fine’s (J. Philos. Logic 3(4):347–372, 1974) semantics for relevant logics. Finally, I use this understanding of relevant semantics to investigate the status of the mingle axiom. (shrink)

This paper suggests that art cannot be defined in terms of individually necessary and jointly sufficient conditions. Instead, we propose that there are several sufficient conditions for something's being art, and that a successful definition will consist of a disjunction of minimally sufficient conditions. Our proposal owes much to the insights of Berys Gaut's ‘“Art” as a Cluster Concept’ but offers a much simpler logical formulation, which, in addition, is immune to the objections that have been raised to Gaut's (...) account. This paper agrees with Gaut's claim that there are borderline cases of art, and suggests that they arise from indeterminacy about the content of some of the minimally sufficient conditions. It is argued that this disjunctive account is superior to classical theories, resemblance-to-paradigm theories, and prototype theories of art. (shrink)

I investigate the structure of pro-tempore disjunctive intentions: intentions directed at two or more eventually incompatible goals that are nonetheless kept open for the time being, while the agent is waiting to acquire more information to determine which option is better. These intentions are the basic tool for balancing, in our planning agency, rigidity and flexibility, stability and responsiveness to changing circumstances. They are a pervasive feature of intentional diachronic agency and contribute to secure dynamic consistency in our plans. I (...) show how they differ from simple disjunctive intentions, where the agent is indifferent between the options. I argue that pro-tempore disjunctive intentions meet the distinctive pressures of intentions and that, contrary to the initial impressions, they are both stable and successful at settling practical matters. In closing, I argue that pro-tempore disjunctive intentions are all-out intentions that are more explanatorily powerful than Holton's "partial" intentions. (shrink)

This paper proves that the disjunction property, the numerical existence property, Church’s rule, and several other metamathematical properties hold true for Constructive Zermelo-Fraenkel Set Theory, CZF, and also for the theory CZF augmented by the Regular Extension Axiom.As regards the proof technique, it features a self-validating semantics for CZF that combines realizability for extensional set theory and truth.

Rodriguez-Pereyra (2006) argues for the disjunction thesis but against the conjunction thesis. I argue that accepting the disjunction thesis undermines his argument against the conjunction thesis.

Reflection on skeptical scenarios in the philosophy of perception, made vivid in the arguments from illusion and hallucination, have led to the formulation of theories of the metaphysical and epistemological nature of perceptual experience. In recent times, the locus of the debate concerning the nature of perceptual experience has been the dispute between disjunctivists and common-kind theorists. Disjunctivists have held that there are substantial dissimilarities (either metaphysical or epistemological or both) between veridical perceptual experiences occurring when one perceives and perceptual (...) experiences involved in hallucination. Common-kind theorists have denied this. In this paper, I examine the nature of introspection – a faculty that has often been compared and contrasted to perception. I reflect on cases where introspection goes wrong in ways analogous to that in which our perceptual faculties can go wrong and formulate, what I take to be, an attractive theory of introspection. The cases that I focus on in which things go wrong are the case of zombies and the case of subjects with Anton’s syndrome. (Anton’s syndrome is a condition in which people who are blind claim that they can see.) I suggest that, just as it is possible to be a disjunctivist about perception, it is possible to be a disjunctivist about introspection. I argue that this is a good view of one type of introspection, namely, introspection of states that have phenomenal character, such as perceptual experiences. It has a good account to give of the cases in which such introspection seems to go wrong and it yields a plausible metaphysical and epistemological view of the nature of introspection. However, while I favour a disjunctive view of introspection, I do not favour a disjunctive view of perception. And, I suspect, that many disjunctivists about perception would not wish to condone my disjunctivist theory of introspection. I therefore go on to examine to what extent.. (shrink)

In this paper, we introduce a notion of ‘disjunctive ignorance’, which is a weak combination of two forms of ignorance in the literature. We propose a logical language with ‘disjunctive ignorance’ as a sole modality, explore the logical properties of this notion and its related notions, and axiomatize it over various frame classes. By finding suitable reduction axioms, we extend the results to the case of public announcements and apply it to Moore-like sentences.

Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with two RM-phenomena, namely, splittings and disjunctions. As to splittings, there are some examples in RM of theorems A, B, C such that A↔, that is, A can be split into two (...) independent parts B and C. As to disjunctions, there are examples in RM of theorems D, E, F such that D↔, that is, D can be written as the disjunction of two independent parts E and F. By contrast, we show in this paper that there is a plethora of splittings and disjunctions in Kohlenbach’s higher-order RM. (shrink)

The general kind of disjunctions enjoying the proof by cases property obtained for substructural logics in the previous chapter (given by a set of formulas instead of a single disjunction connective) motivates the abstract study of generalized disjunctions that we present in the fifth chapter.First, we introduce several forms of proof by cases property and corresponding generalized disjunctions, yielding a hierarchy of logics that we illustrate and separate with suitable examples. We continue by providing several (groups of) characterizations of (...) generalized disjunctions.The first characterization is based on the notion of special forms of a rule, which is obtained from the original rule by disjuncting its premises and conclusion with an arbitrary formula. This notion allows us to characterize logics with a strong p-disjunction as those closed under the formation of these forms of its rules. This characterization is then used to study the preservation of the proof by cases property in expansions and to prove its transfer to the general matrix semantics in terms of generated filters. The second group of characterizations is based on various generalized distributivity properties of the lattice of filters. The third characterization is based on prime filters, a generalization of the well-known notion for classical and intuitionistic logic and its relation to the intersection-prime filters. Finally, we use generalized disjunctions in order to: (1) obtain some axiomatizations of interesting extensions of a given logic, (2) introduce a symmetric notion of consequence relation with a disjunctive reading on the right-hand side, (3) improve some of the characterizations of completeness properties seen in Chapter 3, and, finally, (4) study completeness with respect to finite matrices and matrices with prime filters. (shrink)

Mandarin Chinese lexically distinguishes the disjunctors in alternative questions (háishi) and in disjunctive assertions (huòzhe), reflecting a distinction that Haspelmath (2007) and others have called interrogative versus standard disjunction. I argue that the two disjunctors share their basic syntax and semantics as junction heads (J) that project their disjuncts as Roothian alternatives, which are then interpreted by a corresponding question-forming operator or existential operator. I motivate this view from island insensitivity and focus intervention effects, which I show to apply (...) in parallel to both alternative question formation with háishi and the scope-taking of huòzhe. Háishi also allows for a number of non-interrogative uses, subject to significant speaker variation. I argue that these patterns reflect broadly two types of grammars: those where háishi syntactically enforces that its alternatives be interpreted by certain operators, and those that do not. For the latter, more liberal speakers, háishi can be used non-interrogatively in the same environments that wh-phrases can be. The study and analysis of this pattern of variation leads to the conclusion that a so-called “interrogative disjunction” could be so specified via its syntactic specification or through its semantics alone, with both strategies being attested by different sets of Mandarin Chinese speakers. (shrink)