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)

In his contribution to the present volume, John McDowell proposes a distinctive kind of ‘transcendental’ argument for the disjunctive conception of experience, and renews his claim that the latter can be deployed to defuse certain kinds of sceptical doubt, responding _obiter_ to the misgivings advanced in Wright (2002) about its credentials for the latter task. This chapter queries the putative ‘transcendental’ authority of disjunctivism, and reinforces the misgivings. It is argued that the root of sceptical doubt has less to (...) do with a ‘highest common factor’ conception of the commonality between perceptions and illusions than with the possibility of phenomenological matching; and that scepticism can take a direct realist conception of sense experience in its stride once proper heed is given to the gap between direct awareness of a situation and the possession of warrant to believe that it obtains. (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 (...) class='Hi'>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)

In this paper, I argue that ‘art’, though an open concept, is not undefinable. I propose a particular kind of definition, a disjunctive definition, which comprises extant theories of art. I co-opt arguments from the philosophy of science, likening the concept ‘art’ to the concept ‘species’, to argue that we ought to be theoretical pluralists about art. That is, there are a number of legitimate, perhaps incompatible, criteria for a theory of art. In this paper, I consider three: functionalist (...) definitions, procedural definitions, and an intentional-historical definition. The motivation for this pluralism comes from an analysis of practice, because the term is of apparent value to practitioners. However, a closer analysis of the concept reveals that, while disjunctive definitions help us to understand how we use certain terms, they lack ontological import. In sum, I attempt to glean lessons from the philosophy of science about the philosophy of art. If my analysis is correct, we ought to be eliminative pluralists about art as a concept. (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)

Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) € C at a causal model M as a (...) weighted average of the probability of C in those submodels that truthmake A ∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (shrink)

Gödel argued that the incompleteness theorems entail that the mind is not a machine, or that certain arithmetical propositions are absolutely undecidable. His view was that the mind is not a machine, and that no arithmetical propositions are absolutely undecidable. I argue that his position presupposes that the idealized mathematician has an ability which I call the recursive-ordinal recognition ability. I show that we have this ability if, and only if, there are no absolutely undecidable arithmetical propositions. I argue that (...) there are such propositions, but that no recognizable example of one can be identified, even in principle. (shrink)

The multiple-realizability argument has been the mainstay ofanti-reductionist consensus in philosophy of mind for the past thirty years. Reductionist opposition to it has sometimes taken the form of the Disjunctive Move: If mental types are multiply-realizable, they are not coextensive with physical types; they might nevertheless be coextensive with disjunctionsof physical types, and those disjunctions could still underwrite psychophysical reduction. Among anti-reductionists, confidence is high that the Disjunctive Move fails; arguments to this effect, however, often leave something to (...) be desired. I raise difficulties for one anti-reductionist response to the DisjunctiveMove, the Explanatory Response. (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)

Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.

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 paper introduces two new paradoxes for standard deontic logic (SDL). They are importantly related to, but distinct from Ross' paradox. These two new paradoxes for SDL are the simple weakening paradox and the complex weakening paradox. Both of these paradoxes arise in virtue of the underlaying logic of SDL and are consequences of the fact that SDL incorporates the principle known as weakening. These two paradoxes then show that SDL has counter-intuitive implications related to disjunctive obligations that arise (...) in virtue of deontic weakening and in virtue of decisions concerning how to discharge such disjunctive obligations. The main result here is then that theorem T1 is a problematic component of SDL that needs to be addressed. (shrink)

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)