In a previous work we studied, from the perspective ofAlgebraic Logic, the implicationless fragment of a logic introduced by O. Arieli and A. Avron using a class of bilattice-based logical matrices called logical bilattices. Here we complete this study by considering the Arieli-Avron logic in the full language, obtained by adding two implication connectives to the standard bilattice language. We prove that this logic is algebraizable and investigate its algebraic models, which turn out to be distributive bilattices with additional implication (...) operations. We axiomatize and state several results on these new classes of algebras, in particular representation theorems analogue to the well-known one for interlaced bilattices. (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.

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)

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)

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 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)

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)

In this paper a solution of Whitehead’s problem is presented: Starting with a purely mereological system of regions a topological space is constructed such that the class of regions is isomorphic to the Boolean lattice of regular open sets of that space. This construction may be considered as a generalized completion in analogy to the well-known Dedekind completion of the rational numbers yielding the real numbers . The argument of the paper relies on the theories of continuous lattices and (...) “pointless” topology.

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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)

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)

In this paper authors for the first time define a new notion called neutrosophic lattices. We define few properties related with them. Three types of neutrosophic lattices are defined and the special properties about these new class of lattices are discussed and developed. This paper is organised into three sections. First section introduces the concept of partially ordered neutrosophic set and neutrosophic lattices. Section two introduces different types of neutrosophic lattices and the final section studies neutrosophic Boolean algebras. Conclusions and (...) results are provided in section three. (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)

The de Morgan laws characterize how negation, conjunction, and disjunction interact with each other. They are fundamental in any semantics that bases itself on the propositional calculus/Boolean algebra. This paper is primarily concerned with the second law. In English, its validity is easy to demonstrate using linguistic examples. Consider the following: (3) Why is it so cold in here? We didn’t close the door or the window. The second sentence is ambiguous. It may mean that I suppose we did not (...) close the door or did not close the window, but I am not sure which. This `I am not sure which’ reading is irrelevant to us because it has disjunction scoping over negation. But the sentence may equally well mean (and indeed this is the preferred reading) that we didn’t close the door and did not close the window. This `neither’ reading bears out de Morgan law (2). (shrink)

Upward monotonic semantics for necessity modals give rise to Ross’s Puzzle: they predict that □φ entails □(φ ∨ ψ), but common intuitions about arguments of this form suggest they are invalid. It is widely assumed that the intuitive judgments involved in Ross’s Puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from □(φ ∨ ψ), interpreters infer that the truth of each disjunct (φ, ψ) is compatible with the relevant set of worlds. I introduce two pieces of (...) data that this analysis fails to explain. Analyzing this data, I argue, suggests that necessity modals with embedded disjunctions license ‘Independence’ inferences: from the truth of □(φ ∨ ψ), interpreters infer that φ-without-ψ and ψ-without-φ are each compatible with the relevant set of worlds. I outline a bilateral inquisitive semantics for necessity modals that predicts the validity of the Independence inferences. I then argue that the resulting theory should be understood as one on which disjunctions denote pluralities of propositions, and necessity modals behave like collective predicates applied to these pluralities. (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)

In this dissertation, I argue that all extant theories of prudential value are either a) enumeratively deficient, in that they are unable to accommodate everything that, intuitively, is a basic constituent of prudential value, b) explanatorily deficient, in that they are at least sometimes unable to offer a plausible story about what makes a given thing prudentially valuable, or c) both. In response to the unsatisfactory state of the literature, I present my own account, the Disjunctive Hybrid Theory or (...) DHT. DHT answers to and remedies each of the above inadequacies in a way that no other approach can. This account has the following general structure:Disjunctive Hybrid Theory (DHT): Thing x is basically good for person P if and only if x is either a) cared about (sufficiently and in the right way) by P, b) a bearer of (the right kind of) attitude-independent value, or c) both.Although it follows other recent accounts in combining elements from objective and subjective theories, DHT is a hybrid theory of a quite new kind. This is because it denies both subjective necessity (the constraint that, if thing x is to be basically good for person P, P must have some pro-attitude toward x) and objective necessity (the constraint that, if thing x is to be basically good for person P, x must have some attitude-independent value). I argue that the rejection of both necessity claims is called for if we are to move beyond the enumerative and explanatory limitations of existing accounts.I begin by outlining the general structure of DHT. I then argue, against various recent authors, that desire-satisfactionism remains the most appealing subjectivist approach to prudential value, in that it is best able to capture the central subjectivist insight. This insight is that a person can confer prudential value upon things by caring about them (sufficiently and in the right way). The subjectivist strand of DHT will thus be a version of desire-satisfactionism, which must be interpreted in line with what I call the object, as opposed to the combo, view. I move on to further motivate and develop the second, objectivist strand of DHT. This part of the theory involves a commitment to robustly attitude-independent prudential goods. I close by addressing some puzzles for the theory, and considering some of its more specific applications. (shrink)

Proves two simple identities relating the biconditional and exclusive disjunction. -/- The PDF has been made available gratis by the publisher.

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.

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)

Williamson's influential anti-luminosity argument aims to show that our own mental states are not “luminous,” and that we are thus “cognitively homeless.” Among other things, this argument represents a significant challenge to the idea that we enjoy basic self-knowledge of our own occurrent mental states. In this paper, I summarize Williamson's anti-luminosity argument, and discuss the role that the notion of “epistemic basis” plays in it. I argue that the anti-luminosity argument relies upon a particular version of the basis-relative safety (...) condition on knowledge. This commitment is significant because basic self-knowledge seemingly lacks any kind of distinct epistemic basis, such as inference, observation, testimony, etc., despite representing a genuine kind of knowledge of contingent matters of fact. I consider a disjunctivist account, according to which true basic self-beliefs indeed lack an epistemic basis in any kind of epistemic method, yet are still epistemically grounded in the mental states they concern. I argue that this account of self-knowledge is compatible with standard understandings of the basis relative safety condition on knowledge, but rejects the particular version required by the anti-luminosity argument. (shrink)

Perception can’t have disjunctive content. Whereas you can think that a box is blue or red, you can’t see a box as being blue or red. Based on this fact, I develop a new problem for the ambitious predictive processing theory, on which the brain is a machine for minimizing prediction error, which approximately implements Bayesian inference. I describe a simple case of updating a disjunctive belief given perceptual experience of one of the disjuncts, in which Bayesian inference (...) and predictive coding pull in opposite directions, with the former implying that one’s confidence in the belief should increase, and the latter implying that it should decrease. Thus, predictive coding fails to approximately implement Bayesian inference across the interface between belief and perception. (shrink)

A repository of clinically associated Staphylococcus aureus (Sa) isolates is used to semi‐automatically generate a set of application ontologies for specific subfamilies of Sa‐related disease. Each such application ontology is compatible with the Infectious Disease Ontology (IDO) and uses resources from the Open Biomedical Ontology (OBO) Foundry. The set of application ontologies forms a lattice structure beneath the IDO‐Core and IDO‐extension reference ontologies. We show how this lattice can be used to define a strategy for the construction of (...) a new taxonomy of infectious disease incorporating genetic, molecular, and clinical data. We also outline how faceted browsing and query of annotated data is supported using a lattice application ontology. (shrink)

In this paper, we make a case for the disjunctive view of phenomenal consciousness: consciousness is essentially disjunctive in being either physical or non-physical in the sense that it has both physical and non-physical possible instances. We motivate this view by showing that it undermines two well-known conceivability arguments in philosophy of mind: the zombie argument for anti-physicalism, and the anti-zombie argument for physicalism. By appealing to the disjunctive view, we argue that two hitherto unquestioned premises of (...) these arguments are false. Furthermore, making use of the resources of this view, we formulate distinct forms of both physicalism and anti-physicalism. On these formulations, it is easy to see how physicalists and anti-physicalists can accommodate the modal intuitions of their opponents regarding zombies and anti-zombies. We conclude that these formulations of physicalism and anti-physicalism are superior to their more traditional counterparts. (shrink)

Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators.

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 paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.

In the present paper, we prove the normalization theorem and the consistency of the first-order classical logic with disjunctive syllogism. First, we propose the natural deduction system SCD for classical propositional logic having rules for conjunction, implication, negation, and disjunction. The rules for disjunctive syllogism are regarded as the rules for disjunction. After we prove the normalization theorem and the consistency of SCD, we extend SCD to the system SPCD for the first-order classical logic with disjunctive syllogism. (...) It can be shown that SPCD is conservative extension to SCD. Then, the normalization theorem and the consistency of SPCD are given. (shrink)

(English translation of ...) This paper points out naturally-occurring examples, primarily in Hungarian but also to a more limited extent in English, in which disjunction (i) has a conjunctive force but (ii) its use highlights that the list is not intended to be exhaustive. The preliminary analysis is in terms of recursive proposition strengthening by exhaustification without a scalar alternative, assimilating exemplifications to known cases of conjunctively interpreted disjunctions in other languages.

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the (...) calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround. (shrink)

According to the Disjunction Problem, teleological theories of perceptual content are unable to explain why it is that a subject represents an F when an F causes the perception and not the disjunction F v G, given that the subject has mistaken G’s for F’s in the past. Without an adequate explanation these theories are stuck without an account of how non-veridical representation is possible, which would be an unsettling result. In this paper I defend Burge’s teleological theory of perception (...) against the Disjunction Problem, arguing that a perceptual state’s representing what I call an error-prohibiting disjunctive property is incompatible with the truth of perceptual anti-individualism. And because perceptual anti-individualism is at the heart of Burge’s theory, I conclude that Burgeans need not be concerned with the Disjunction Problem. (shrink)

Since the early 1980s, there has been a debate in the semantics literature pertaining to whether wh-interrogatives can be directly disjoined, as main clauses and as complements. Those who held that the direct disjunction of wh-interrogatives was in conflict with certain theoretical considerations proposed that they could be disjoined indirectly. Indirect disjunction proceeds by first lifting both wh-interrogatives and then disjoining them; it assigns matrix-level scope to OR. As we will see, the notorious theoretical need for indirect disjunction has disappeared (...) by today. But the factual question remains. Are wh-complements disjoined directly or indirectly? What is the fact of the matter? This paper argues that the case for indirect disjunction remains reasonably strong. (shrink)

I show that the model-theoretic meaning that can be read off the natural deduction rules for disjunction fails to have certain desirable properties. I use this result to argue against a modest form of inferentialism which uses natural deduction rules to fix model-theoretic truth-conditions for logical connectives.

Scientists often adjust their significance threshold during null hypothesis significance testing in order to take into account multiple testing and multiple comparisons. This alpha adjustment has become particularly relevant in the context of the replication crisis in science. The present article considers the conditions in which this alpha adjustment is appropriate and the conditions in which it is inappropriate. A distinction is drawn between three types of multiple testing: disjunction testing, conjunction testing, and individual testing. It is argued that alpha (...) adjustment is only appropriate in the case of disjunction testing, in which at least one test result must be significant in order to reject the associated joint null hypothesis. Alpha adjustment is inappropriate in the case of conjunction testing, in which all relevant results must be significant in order to reject the joint null hypothesis. Alpha adjustment is also inappropriate in the case of individual testing, in which each individual result must be significant in order to reject each associated individual null hypothesis. The conditions under which each of these three types of multiple testing is warranted are examined. It is concluded that researchers should not automatically assume that alpha adjustment is necessary during multiple testing. Illustrations are provided in relation to joint studywise hypotheses and joint multiway ANOVAwise hypotheses. (shrink)

According to the phenomenological argument for disjunctivism, the reasons why we should prefer the disjunctive theory over its rivals is that (1) the disjunctive theory conforms the most to our pretheoretical or natural convictions about perception (what Michael Martin calls naïve realism), and (2) we should commit ourselves to naïve realism because it conforms the most to the phenomenology of the perceptual experience of objects. In this paper, I try to explain why is the phenomenal argument exceptionally strong (...) argument for disjunctivism and at the same time against sense-datum and intentional theories. Furthermore, I try to show that the disjunctivist’s explanation of hallucination (which is allegedly the weak point of the theory) is as plausible as its rivals’. (shrink)

Humean promotionalists about reasons think that whether there is a reason for an agent to ϕ depends on whether her ϕ-ing promotes the satisfaction of at least one of her desires. Several authors have recently defended probabilistic accounts of promotion, according to which an agent’s ϕ-ing promotes the satisfaction of one of her desires just in case her ϕ-ing makes the satisfaction of that desire more probable relative to some baseline. In this paper I do three things. First, I formalize (...) an argument, due to Jeff Behrends and Joshua DiPaolo, to the effect that Mark Schroeder’s and Stephen Finlay’s probabilistic accounts of promotion cannot be correct. Next, I extend this argument to a recent alternative offered by D. Justin Coates and show how Coates’ attempt to avoid the argument by introducing a distinction between ‘intrinsic’ and ‘extrinsic’ probability doesn’t help. Finally, I suggest an alternative way of understanding promotion in terms of increase in degree of fit between the causal upshot of an action and the content of a desire. I show how this view, disjunctively paired with probabilism about promotion, solves the problems with previous accounts. (shrink)

A synthesis of trending topics in pancomputationalism. I introduce the notion that "strange loops" engender the most atomic levels of physical reality, and introduce a mechanism for global non-locality. Writen in a simple and accesssible style, it seeks to draw research in fundamental physics back to realism, and have a bit of fun in the process.

In this paper, I argue that the disjunction elimination rule presupposes the principle that a true disjunction contains at least one true disjunct. However, in some contexts such as supervaluationism or quantum logic, we have good reasons to reject this principle. Hence, disjunction elimination is restricted in at least one respect: it is not applicable to disjunctions for which this principle does not hold. The insight that disjunction elimination presupposes the principle that a true disjunction contains at least one true (...) disjunct is applied to two arguments which argue for this very principle. I show that these arguments are rule-circular since they rest on disjunction elimination. I claim that rule-circularity better explains why the arguments fail than the explanations provided by Rumfitt (2015), which, for instance, rely on controversial principles about truth. (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)

Austrian-born Kurt Gödel is widely considered the greatest logician of modern times. It is above all his celebrated incompleteness theorems—rigorous mathematical results about the necessary limits...

This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means Hilbert-style calculi that are finite. On the negative side, we provide a syntactic condition on the equational presentation of a variety that entails failure of finite axiomatizability for the corresponding logic. An application of this result is that the logic of all distributive lattices with negation is not finitely axiomatizable; we likewise establish (...) that the order-preserving logic of the variety of all Ockham algebras is also not finitely axiomatizable. On the positive side, we show that an arbitrary subvariety of semi-De Morgan algebras is axiomatized by a finite number of equations if and only if the corresponding order-preserving logic is axiomatized by a finite Hilbert-style calculus. This equivalence also holds for every subvariety of a Berman variety of Ockham algebras. We obtain, as a corollary, a new proof that the implication-free fragment of intuitionistic logic is finitely axiomatizable, as well as a new corresponding Hilbert-style calculus. Our proofs are constructive in that they allow us to effectively convert an equational presentation of a variety of algebras into a Hilbert-style calculus for the corresponding order-preserving logic, and vice versa. We also consider the assertional logics associated to the above-mentioned varieties, showing in particular that the assertional logics of finitely axiomatizable subvarieties of semi-De Morgan algebras are finitely axiomatizable as well. (shrink)

According to capacitism, to perceive is to employ personal-level, perceptual capacities. In a series of publications, Schellenberg (2016, 2018, 2019b, 2020) has argued that capacitism offers unified analyses of perceptual particularity, perceptual content, perceptual consciousness, perceptual evidence, and perceptual knowledge. “Capacities first” (2020: 715); appealing accounts of an impressive array of perceptual and epistemological phenomena will follow. We argue that, given the Schellenbergian way of individuating perceptual capacities which underpins the above analyses, perceiving an object does not require employing a (...) perceptual capacity which picks it out. Although each eye, used on its own, can suffice for perceiving objects in one’s environment, binocular vision allows one to see the same object(s) via both eyes, taking advantage of informational disparities registered by each eye. Yet in certain conditions it is possible to simultaneously see one object via the left eye and a distinct object via the right eye (at least when the inputs are sufficiently similar to prevent the onset of binocular rivalry). We argue that capacitism has trouble making sense of this. After surveying responses, we conclude that not all of the above phenomena can be unified under the capacitist framework. We then present a more nuanced, disjunctivist account of how capacities are individuated. While it may be illuminating to think of perceiving as the employment of perceptual capacities, this picture does not best favour a ‘common factor’ theory of perceptual content in the way existing presentations have envisaged. (shrink)

As far as we know the scientific search for the nature of reality in Europe started about 2500 years ago in ancient Greek. It was the ancient Greek philosopher Parmenides who reasoned that observable reality is created by an underlying reality. There are indications that the ancient Greek concept of the atom was (also) related to the proposed units of the structure of the underlying creating reality of Parmenides. However, an invisible underlying creating reality suggests that we cannot determine its (...) existence with the help of experimental physics. This paper describes an experiment that will show that Parmenides concept about an underlying reality is correct. (shrink)

This paper is divided in four parts. In the first part we introduce the method of internal critique of philosophical theories by examination of their external consistency with scientific theories. In the second part two metaphysical and one epistemological postulate of Wittgenstein's Tractatus are made explicit and formally expressed. In the third part we examine whether Tractarian metaphysical and epistemological postulates (the independence of simple states of affairs, the unique mode of their composition, possibility of complete empirical knowledge) are externally (...) consistent with the theory of quantum mechanics. The result of the inquiry is negative: Tractarian postulates ought to be be revised. Relying on the result we approach the question of the empirical character of logic in the fourth part. The description of theoretical transformations of the notion of disjunction, in its ontological, epistemological, and logical sense, is a common element of in all parts of the text. The conjecture on the existence of different types of disjunctive connectives in the language of quantum mechanics concludes the paper. (shrink)

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. (...) Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal. (shrink)