We contemplate Deleuze and Guattari's discussion of in/compossibility through engagement with practices of spatial planning and development at the urban fringe in Australia. In such sites of ecosystem transformation, the presence of wildlife, such as mosquitoes, is often deemed incompossible with felicitous human habitation. We suggest that regarding worlds like those of mosquitoes and humans as divergent, rather than incompossible, opens up opportunities for inclusive disjunctive syntheses which affirm the disjoined terms without excluding one from the other. Relating (...) class='Hi'>inclusive disjunction to intensive milieu, we call for development of a more milieu-based approach to planning to facilitate more-than-human coexistence differently. (shrink)

This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (...) (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). There is a related claim, that even when children respond as if they have access to a broader range of truth conditions, namely those associated with inclusive-or, children's adult-like responses are the result of a failure to distinguish or from and (Paris 1973). A different conclusion was reached in a recent study by Chierchia, Crain, Guasti and Thornton (1998), who conducted a series of experiments which revealed children's adult-like knowledge of logical connectives, including disjunction. To reconcile the findings from the Chierchia et al. study and those of previous research, Chierchia et al. (1998) draw upon a distinction between semantic and pragmatic knowledge. They argue that the acquisition of logical connectives is simply a process of mapping the appropriate truth conditions (associated with logical connectives in classical logic) onto the particular words of the language to which the child is exposed. In understanding sentences, however, children are also influenced by the pragmatic norms they follow. In many.. (shrink)

This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (...) (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). There is a related claim, that even when children respond as if they have access to a broader range of truth conditions, namely those associated with inclusive-or, children's adult-like responses are the result of a failure to distinguish or from and (Paris 1973). (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)

We present evidence that preschool children oftentimes understand disjunctive sentences as if they were conjunctive. The result holds for matrix disjunctions as well as disjunctions embedded under every. At the same time, there is evidence in the literature that children understand or as inclusive disjunction in downward-entailing contexts. We propose to explain this seemingly conflicting pattern of results by assuming that the child knows the inclusive disjunction semantics of or, and that the conjunctive inference is a (...) scalar implicature. We make two assumptions about implicature computation in the child: that children access only a proper subset of the adult alternatives, and that children possess the adult capacity to strengthen sentences with implicatures. As a consequence, children are expected to sometimes not compute any implicatures at all, but in other cases they are expected to compute an implicature that is different from the adult implicature. We argue that the child’s conjunctive strengthening of disjunctive sentences realizes the latter possibility: the adult infers that the conjunction is false but the child infers that the conjunction is true. This behaviour is predicted when our assumptions about child development are coupled with the assumption that a covert exhaustive operator is responsible for strengthening in both the child and the adult. Specifically, children’s conjunctive strengthening is predicted to follow from the same mechanism used by adults to compute conjunctive free choice implicatures in response to disjunctive permission sentences. We furthermore argue that this parallel between the child and the adult extends to disambiguation preferences. In particular, we present evidence that children prefer to strengthen disjunctions to conjunctions, in matrix and embedded positions ; this result mirrors previous findings that adults prefer to compute free choice, at the root and under every. We propose a disambiguation strategy that explains the preference for conjunctive strengthening – by both the child and the adult – even though there is no general preference for exhaustification. Specifically, we propose that the preference for a conjunctive strengthening follows from a pragmatic preference for a complete answer to the Question Under Discussion. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called 'affirming a disjunct' (AAD). It presents a few examples of fallacies in arguments caused by an ambiguity in the English word or. Because context makes the meaning clear in everyday usage, we might never have thought about this ambiguity before, but we actually use the word or in two very distinct ways. One type of or is known as “inclusive”, and the other type is known as (...) “exclusive”. AAD occurs when someone mistakenly believes that an inclusive or is an exclusive or. Importantly, not every or statement can fall prey to AAD. The argument known as a disjunctive syllogism sets out two possibilities that are mutually exclusive. When someone is dead, she/he is not alive, and when someone is alive, she/he is not dead. (shrink)

The theory of evolution makes sense of the emergence of consciousness. Reduction is not wrong as such, but must not be totalised. The fact that we are star stuff does not preclude the novelty of consciousness. Materialism is naturalism, but naturalism need not be materialism. Neural pathways are relevant but are not the total picture. The central thesis is about David Chalmers’s philosophy being based on an exclusive disjunction. An inclusive disjunction is, when explained, more appropriate. Functionalism (...) is appropriate. Thomas Nagel’s philosophy on first person ontology can still be maintained. Quantum and complexity theories’ hypothesis on consciousness is more compatible with freedom of decision than classical theories. (shrink)

The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature ( but not both ). We point to a class of situations that ought to predispose disjunctions (...) to inclusive interpretations and to situations that encourage exclusive interpretations. A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative. Our investigation leads to five experiments employing arbitrary materials. Among the problems expected to encourage inclusive interpretations are those that present disjunctions in the antecedents of conditionals and in question forms. The best candidates to produce implicatures are those disjunctions that underdetermine an expected conjunctive conclusion, although other disjunctive utterances that are more informative as exclusive are discussed and tested. (shrink)

This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, (...) children are supposed to interpret disjunction using the truth conditions that are associated with exclusive-or (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). A second, related claim is that even when children respond as if they have access to the complete range of truth conditions, their responses result from the failure to distinguish or from and (Paris, 1973). (shrink)

This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, (...) children are supposed to interpret disjunction using the truth conditions that are associated with exclusive-or (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). A second, related claim is that even when children respond as if they have access to the complete range of truth conditions, their responses result from the failure to distinguish or from and (Paris, 1973). Different conclusions were reached in recent work by Chierchia, Crain, Guasti and Thornton (1998). The experiments conducted by Chierchia et al. (1998) draw upon a distinction between linguistic contexts. In one type of context, the inclusive-or reading of disjunction is available. By contrast, in another type of context, the exclusive-or reading of disjunction is highly preferred; the truth conditions that are uniquely associated with the inclusive-or reading are eliminated in such contexts due to conversational implicatures. One context that cancels conversational implicatures is called the Prediction Mode by Chierchia et al. (1998). Notice that a prediction like (1) is consistent with different scenarios. (shrink)

In truth-functional analysis we need not worry about the purported ambiguity of the English ‘or,’ for we can assign different symbols and define each by means of a truth table. However, at least in classes in elementary logic, we often try to indicate that there is some rationale to the assignation of truth values by marshaling English disjunctive sentences which will clearly render an inclusive or an exclusive reading, without the explicit addition of one of the qualifying phrases, “or (...) both” or “but not both.” At this point one discovers people writing on logic saying quite different things about the English ‘or.’ In his Methods of Logic Quine takes the inclusive sense to be the more naturally intended and claims that “indisputable instances of the exclusive use” are rare. Yet in The Principles of Logic Bradley says that no one ever really intends to use ‘or’ in any other than an exclusive sense; and Bosanquet followed him in this. In this paper I am interested in attempting to discover why the British Idealists held that ‘or’ is always exclusive, especially in the face of various examples which, prima facie, establish both uses in English. Why would Bradley feel compelled to deny “any possible instance in which alternatives are not exclusive”? As it turns out, the position held by Bradley and Bosanquet is stronger and more interesting than one initially expects. (shrink)

Mody and Carey (2016) investigated children's capacity to reason by the disjunctive syllogism by hiding stickers within two pairs of cups (i.e., there is one sticker in cup A or B, and one in cup C or D) and then showing one cup to be empty. They found that children as young as 3 years of age chose the most likely cup (i.e., not A, therefore choose B; and disregard C and D) and suggested that these children were representing the (...) dependent relationship between A and B by applying the logical operator “or”. However, it is possible that children succeeded using simpler strategies, such as avoiding the empty cup and choosing within the manipulated pair. We devised a new version of the task in which a sticker was visibly removed from one of the four cups so that 2.5- to 5-year-old children (N = 100) would fail if they relied on such strategies. We also included a conceptual replication of Mody and Carey's (2016) original condition. Our results replicated their findings and showed that even younger children, 2.5 years of age, could pass above chance levels. Yet, 2.5-, 3- and 4-year-olds failed the new condition. Only 5-year-old children performed above chance in both conditions and so provided compelling evidence of deductive reasoning from the premise “A or B", where “or” is exclusive. We propose that younger children may instead conceive of the relationship between A and B as inclusive “or” across both versions of the task. (shrink)

Exclusivists interpret the ‘or’ of English (and other natural languages) exclusively, but may wish to introduce an inclusive sense of disjunction. A common natu.

I make a point concerning the construction ‘A or B or both’ in English, to the effect that if the connective ‘or’ is understood exclusively across the board then this familiar construction cannot convey the intended inclusive sense of disjunction. If we take ‘or’ inclusively, ‘A or B or both’ has the function of emphasizing that the disjunction is inclusive; taking ‘or’ exclusively, it does nothing.

We propose a modification of the exhaustivity operator from Fox Presupposition and implicature in compositional semantics, Palgrave Macmillan, London, pp 71–120, 2007. https://doi.org/10.1057/9780230210752_4) that on top of negating all the Innocently Excludable alternatives affirms all the ‘Innocently Includable’ ones. The main result of supplementing the notion of Innocent Exclusion with that of Innocent Inclusion is that it allows the exhaustivity operator to identify cells in the partition induced by the set of alternatives whenever possible. We argue for this property of (...) ‘cell identification’ based on the simplification of disjunctive antecedents and the effects on free choice that arise as the result of the introduction of universal quantifiers. We further argue for our proposal based on the interaction of only with free choice disjunction. (shrink)

Language employs various coordinators to connect propositions, a subset of which are “logical” in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction _and_ and (inclusive) disjunction _or_. Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go beyond (...) semantic/pragmatic properties (the result of reasoning processes). We provide a comprehensive review of the role of the logical connectives in language and argue that three sets of factors—semantic, pragmatic, and those related to reasoning—are separate and separable, though some details may differ cross-linguistically. As a way to showcase the argument, we present two experiments in language comprehension in Spanish wherein pragmatic content was minimised and reasoning processes neutered, thus potentially highlighting what might be the default meanings of the connectives under study. In Experiment 1 we show that the conjunctive reading of inclusive disjunction is available in positive contexts other than in syntactically intricate cases such as downward entailing and free choice contexts, contrary to what has been claimed in the literature. In Experiment 2 we show that negated conjunctions and disjunctions in Spanish can easily receive the same interpretation when contrasted against the same context and, moreover, that these interpretations match those available in English, despite claims from the literature that linguistic connectives and local negation interact differently in English and Romance languages. (shrink)

Deleuze's theory of difference revolves around the idea that fusion and fission--the extreme external limits of functioning systems--represent the death of these systems. In order to maintain their duree, qualitative difference and change, systems internalize the external limits in conditions of repeated contraction and dilatation which constitute the inclusive disjunctive law of their function. This basic idea permits Deleuze to articulate an ontology of difference and repetition, a minoritarian theory of language and a version of materialist politics which support (...) each other and strengthen the cause of radical pluralism. Deleuze's ontology substitutes Difference for Being, introduces the intensive media of space and time, takes intensity to be the sentiendum of quality and extension, holds the synthesizing Ideas to be problematic and problem-setting multiplicities of differentiated elements, and argues that the repetition of the eternal return guarantees different/ciation by dissolving the identity of the "unity of apperception". The minoritarian theory of language is similarly constituted. The external limit of language, represented by self-referential and self-predicative elements, would be the death of language. On the other hand, watchwords and poetic utterances through their self-referentiality and self-predication makes language possible. The former attempt to fuse language and to overcode sign-regimes, whereas the latter highlight the interval, the "estrangement-effects" and the rhizomatic proliferation of lines of escape. Finally, the emancipatory interest which animates Deleuze's theory of difference is grounded on the notion "body without organs". The ontological, schizoanalytic and political appropriation of this immanent-transcendent referance, together with Deleuze's claim that it is the body without organs which renders possible "energetic" desire--both in paranoid and schizophrenic "arrangements"--crown this theory of difference with critical aspirations. (shrink)

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, (...) for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P, P, P, disjunctions: P, P, P, and conditional probabilities P, P, P. They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. (shrink)

The aim of this paper is to provide an original account of the distinction between the spheres of Sitten that goes beyond the traditional one based on the nature of incentives, since this underestimates some of their characteristics. First, the paper identifies in obligatio a common source between Ethics and Right. Then, it explores how in the Metaphysics of Morals the connection between law and incentive constitutes a more relevant criterion to distinguish ethical lawgiving from juridical lawgiving. Specifically, it demonstrates (...) that such connection: to be ethical should be linear, understood as a necessary self-determined process of connecting law to incentive; to be juridical should be mediated, namely it comprises an inclusive disjunction between two modalities of connecting law to incentive: a non-necessary linear and a divergent one. It concludes by exploring the implications of such perspective on the notions of internalisation and externalisation associated to each lawgiving. (shrink)

The aim of this paper is to show that the definition of a possible world in the actualist tradition of A. Plantinga, R.M. Adams, R. Chisholm, J. Pollock and N. Wolterstorff is unable to accomodate tensed states of affairs. An example of a tensed state of affairs is the transiently obtaining state of affairs that the storm is present, which obtains only if its negation, it is not the case that the storm is present also obtains but at different times. (...) A possible world that includes tensed states of affairs and their negations cannot be defined in the traditional way, which states that a possible world is a state of affairs S that includes every state of affairs S' or (exclusive disjunction) the negation of S'. Rather, it must be defined in a new way: A possible world is a state of affairs S that includes every state of affairs S' or (inclusive disjunction) the negation of S', such that for every pair P of mutually contradictory tensed states of affairs entailed by S, the members of P obtain nonsimultaneously in S. (shrink)

The aim of this paper is to show that the definition of a possible world in the actualist tradition of A. Plantinga, R.M. Adams, R. Chisholm, J. Pollock and N. Wolterstorff is unable to accomodate tensed states of affairs. An example of a tensed state of affairs is the transiently obtaining state of affairs that the storm is present, which obtains only if its negation, it is not the case that the storm is present also obtains but at different times. (...) A possible world that includes tensed states of affairs and their negations cannot be defined in the traditional way, which states that a possible world is a state of affairs S that includes every state of affairs S' or (exclusive disjunction) the negation of S'. Rather, it must be defined in a new way: A possible world is a state of affairs S that includes every state of affairs S' or (inclusive disjunction) the negation of S', such that for every pair P of mutually contradictory tensed states of affairs entailed by S, the members of P obtain nonsimultaneously in S. (shrink)

In responding to five symposium articles that discuss my book Thinking through the Body and my theories of somaesthetics and pragmatism, this essay elaborates two central methodological orientations that guide my philosophical research. The first is transactional experiential inquiry in which inquiry can develop new directions, aims, methods, and standards through the dynamic experiences acquired in the course of the inquiry’s pursuit and in which its transactional experiences involve research that transcends familiar disciplinary limits and conventions. The second principle involves (...) mitigating problematic dualisms by a strategy of inclusive disjunction. I deploy these principles in replying to the five commentaries. Besides clarifying issues in somaesthetics, my reply focuses on such topics as everyday aesthetics, eroticism, architecture, dance, Chinese philosophy, meliorism, and pragmatism. (shrink)

John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their self-similarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...) argument, a particularly difficult task in Venn diagrams for more than four sets. Carroll diagrams can represent existential propositions easily, so they are capable of clearly representing more complex problems than Venn's system can. Finally, both Carroll and Venn diagrams are maximal, in the sense that no additional logic information like inclusive disjunctions is able to be represented by them. Carroll's logic diagrams and logic trees constitute his visual logic system. (shrink)

Much has been said about the logical difference between rules and principles, yet few authors have focused on the distinct logical connectives linking the normative conditions of both norms. I intend to demonstrate that principles, unlike rules, are norms whose antecedents are linguistically formulated in a generic fashion, and thus logically described as inclusive disjunctions. This core feature incorporates the relevance criteria of normative antecedents into the world of principles and also explains their aptitude to conflict with opposing norms, (...) namely that their consequents are fulfilled to varying extents more frequently than those of rules. I conclude that the property of genericity should be predicated to the norm antecedent of principles, more precisely to the hypothetical action. This is of paramount importance to explain, in terms of logical implication and exclusion, the expansibility of competing principles, in contrast with the exclusive character of conflicting rules. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

There is a well-known variety of contact paradoxes which are significantly linked to topology. The aim of this paper is to present a new paradox concerning contact with bodies composed of a denumerable infinity of parts. This paradox establishes the logical necessity, in a Newtonian context, of contact forces (herein called “phantom forces”) that violate what is probably our most basic causal intuition, embodied in what I call the Principle of Influence: any force exerted on a body B induces (causes) (...) change of movement of B or (inclusive disjunction) the emergence of internal forces in B. However, the above paradox can be made strictly compatible with a Newtonian framework by introducing phantom forces as ideal elements in the Hilbert sense, though it will be seen that this does not solve all the problems. (shrink)

The computation of scalar implicatures is sometimes costly relative to basic meanings. Among the costly computations are those that involve strengthening `some' to `not all' and strengthening inclusive disjunction to exclusive disjunction. The opposite is true for some other cases of strengthening, where the strengthened meaning is less costly than its corresponding basic meaning. These include conjunctive strengthenings of disjunctive sentences (e.g., free-choice inferences) and exactly-readings of numerals. Assuming that these are indeed all instances of strengthening via (...) implicature/exhaustification, the puzzle is to explain why strengthening sometimes increases costs while at other times it decreases costs. I develop a theory of processing costs that makes no reference to the strengthening mechanism or to other aspects of the derivation of the sentence's form/meaning. Instead, costs are determined by domain-general considerations of the grammar's output, and in particular by aspects of the meanings of ambiguous sentences and particular ways they update the context. Specifically, I propose that when the hearer has to disambiguate between a sentence's basic and strengthened meaning, the processing cost of any particular choice is a function of (i) a measure of the semantic complexity of the chosen meaning and (ii) a measure of how much relevant uncertainty it leaves behind in the context. I measure semantic complexity with Boolean Complexity in the propositional case and with semantic automata in the quantificational case, both of which give a domain-general measure of the minimal representational complexity needed to express the given meaning. I measure relevant uncertainty with the information-theoretic notion of entropy; this domain-general measure formalizes how `far' the meaning is from giving a complete answer to the question under discussion, and hence gives an indication of how much representational complexity is yet to come. Processing costs thus follow from domain-general considerations of current and anticipated representational complexity. The results might also speak to functional motivations for having strengthening mechanisms in the first place. Specifically, exhaustification allows language users to use simpler forms than would be available without it to both resolve relevant uncertainties and convey complex meanings. (shrink)

For many students, success or failure hinges on their ability to locate logic within the context of everyday thought. One way of accomplishing this task is to emphasize the connections between natural and symbolic language. Many students, however, find that symbolic logic occasionally deviates from their expectations. In particular, they commonly have difficulty understanding the rationale behind the false antecedent conditional and the inclusive disjunction. In this article, I outline a teaching strategy that employs promise keeping as an (...) analogy for these standard interpretations of the propositional operators. (shrink)

This article introduces and clarifies a neglected sense of the word ἤ (‘or’) employed by Aristotle and other authors. In this sense, called ‘indifferent’, ἤ signifies ‘one or the other, regardless of which’. It is shown how attention to this use makes it possible to explain the source of the ambiguity of certain sentences, most obviously, though not exclusively, sentences that make a necessity claim about an embedded disjunction, for example ‘It is necessary that A or B’. Why this (...) sense cannot be explained, as some scholars have suggested, by the distinction between exclusive and inclusive ἤ is also discussed. Finally, it is shown how awareness of this sense might rescue Aristotle from a gross inconsistency. (shrink)

We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by (...) observing how adults use disjunction. Findings from studies of child language acquisition and from cross-linguistic research invite the conclusion that children do not learn to be logical—it comes naturally to them. (shrink)

This two-volume work provides a new understanding of Western subjectivity as theorized in the Augustinian Rule. A theopolitical synthesis of Antiquity, the Rule is a humble, yet extremely influential example of subjectivity production. In these volumes, Jodra argues that the Classical and Late-Ancient communitarian practices along the Mediterranean provide historical proof of a worldview in which the self and the other are not disjunctive components, but mutually inclusive forces. The Augustinian Rule is a culmination of this process and also (...) the beginning of something new: The paradigm of the monastic self as protagonist of the new, medieval worldview. Three main theoretical challenges leading to, and present in the Rule are tackled: What are the sources of our modern understanding of subjectivity? Can Ancient sources provide an alternative genealogy that resists the individualistic turn of Modernity? And can the commons be saved without suppressing individuality? Jodra seeks to prove that the synthesis-which is also an appropriation-of Greek and Judaic sources carried out by the first Christians allowed for two contrasting models of subjectivity, the self-less and the other-less, to 'take turns' to dominate our understanding of human nature. The Greek world provided the political dimension and the Jewish world established the key theological principles of a Mediterranean synthesis which took place in Rome. Coherently and progressively, Jodra emphasizes the theopolitical nature of our worldview even today, and claim that the subject of the primitive Church is its most visible incarnation. These volumes therefore restore the unity of the Hellenistic and Judaic world as found by the first Christians, proving that the self and the other are two essential pieces in the construction of our world. (shrink)

Larry Horn is justifiably famous for his work on the semantics of the English conjunction or and both its relationship to the formal logic truth functions ∨ and @ (“inclusive” and “exclusive” disjunction respectively1) and its relationship to the ways people employ or in natural discourse. These interests have been present since his 1972 dissertation, where he argued for a “scalar implicature-based” account of many of these relationships as opposed to a presuppositional account. They have surfaced in his (...) “Greek Grice” paper (Horn 1973) as well as in his Negation book (Horn 1989) and his recent “Border Wars” paper (Horn, forthcoming) where he defends the position that there are two types of implicatures at work here: Q- implicatures based on Grice’s first maxim of Quantity (“Say Enough”) and R-implicatures based on Grice’s second maxim of Quantity (“Don’t Say Too Much”). In a nutshell, the idea is that when a speaker employs a sentence with a disjunction, the meaning (that is, the semantic value) of the or is inclusive. With careful and judicious use of the Q- and R-implicatures, Larry’s theory allows the hearer (often) to infer that the speaker wanted to convey an exclusive disjunction. (shrink)

There are two basic positions where tolerance as political strategy and moral viewpoint is rejected or made redundant. We are hostile to tolerance when we hold that we are defending an objective truth—religious or secular—which should also be defended and maintained by means of political and legal power. And tolerance become superfluous also when the affirmation of plurality becomes total, and tolerance identical to a vive la difference. As recent developments in my own country—the Netherlands—have demonstrated, the political outcome of (...) this last position is remarkably enough not necessarily an all-inclusive relativistic tolerance. It may just as well be one of intolerance towards ‘believers’ of all kinds, in short: tolerance becomes polemical and belligerent. Turning to religious fundamentalism or ultra-orthodoxy could then become a possible reaction to this relativistic and subjectivist position, as demonstrated in Isaac Bashevis Singer’s novel The Penitent. Between these two positions of hostility or indifference towards tolerance, we can situate that democratic attitude which may rightly be called ‘tolerance’. As ethical position, the tolerant citizen accepts the democratic disjunction between my truth and the symmetrical justice between citizens. As political strategy, a tolerant democratic regime is based upon a political act of exclusion of what I will here call ‘political fundamentalism’. (shrink)

We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and (...) we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula, which can be interpreted by introducing a suitable distributive property. Moreover, under logical independence of basic unconditional events, we give two necessary and sufficient coherence conditions. The first condition gives a geometrical characterization for the coherence of prevision assessments on a family F constituted by n conditional events and all possible conjunctions among them. The second condition characterizes the coherence of prevision assessments defined on $F\cup K$, where $K$ is the set of conditional constituents associated with the conditional events in $F$. Then, we give some further theoretical results and we examine some examples and counterexamples. Finally, we make a comparison with other approaches and we illustrate some theoretical aspects and applications. (shrink)

This work examines how people interpret the sentential connective “or”, which can be viewed either inclusively (A or B or both) or exclusively (A or B but not both). Following up on prior work concerning quantifiers (Noveck, 2001; Noveck & Posada, 2003; Bott & Noveck, 2004) which shows that the common pragmatic interpretation of “some,” some but not all, is conveyed as part of an effortful step, we investigate how extra effort applied to disjunctive statements leads to a pragmatic interpretation (...) of “or”, or but not both. Experiment 1 compelled participants to wait for three seconds before answering, hence giving them the opportunity to process the utterance more deeply. Experiments 2 and 3 emphasized “or”, either by visual means (“OR”) or by prosodic means (contrastive stress) as another way to encourage participants to apply more effort. Following a relevance-theoretic line of argument, we hypothesized that conditions encouraging more processing effort would give rise to more pragmatic inferences and hence to more exclusive interpretations of the disjunction. This prediction was confirmed in the three experiments. (shrink)

The Reading Augustine series presents short, engaging books offering personal readings of St. Augustine of Hippo's contributions to western philosophical, literary, and religious life. This two-volume work provides a new understanding of Western subjectivity as theorized in the Augustinian Rule. A theopolitical synthesis of Antiquity, the Rule is a humble, yet extremely influential example of subjectivity production. In these volumes, Jodra argues that the Classical and Late-Ancient communitarian practices along the Mediterranean provide historical proof of a worldview in which the (...) self and the other are not disjunctive components, but mutually inclusive forces. The Augustinian Rule is a culmination of this process and also the beginning of something new: The paradigm of the monastic self as protagonist of the new, medieval worldview. Three main theoretical challenges leading to, and present in the Rule are tackled: What are the sources of our modern understanding of subjectivity? Can Ancient sources provide an alternative genealogy that resists the individualistic turn of Modernity? And can the commons be saved without suppressing individuality? Jodra seeks to prove that the synthesis-which is also an appropriation-of Greek and Judaic sources carried out by the first Christians allowed for two contrasting models of subjectivity, the self-less and the other-less, to 'take turns' to dominate our understanding of human nature. The Greek world provided the political dimension and the Jewish world established the key theological principles of a Mediterranean synthesis which took place in Rome. Coherently and progressively, Jodra emphasizes the theopolitical nature of our worldview even today, and claim that the subject of the primitive Church is its most visible incarnation. These volumes therefore restore the unity of the Hellenistic and Judaic world as found by the first Christians, proving that the self and the other are two essential pieces in the construction of our world. (shrink)

In this paper is constructed an analogue of the square of opposition for propositions about relations between two non-empty sets. Unlike the classical square of opposition, the proposed scheme uses all logically possible syllogistic constants, formulated in V.I. Markin’s universal language for traditional positive syllogistic theories. This scheme can be called “Logical lantern”. The basic constants of this language are representing the five basic relations between two non-empty sets: equity, strict inclusion, reversed strict inclusion, intersection and exclusion (considered are only (...) the relations between sets, but not the relations of the sets to the universe). The other relations between sets are combinations (disjunctions) of the basic ones. There are 32 constants and 32 respective propositions, and the proposed diagram expresses and/or allows to deduce the logical relations among those propositions. The constructed scheme, making it possible to visually see the logical relations among propositions about relations between two non-empty sets, allows us to suggest considering logical relations not discussed previously: many-place Aristotelian-like logical relations among propositions: exhaustive _n_-place contrariety and exhaustive _n_-place subcontrariety (_n_ is a natural number, \(n>2\) ). (shrink)

Economics presents the paradox of the entropy of the law of diminishing returns and infinity of the substitution effect. Resolution assumes the substitution effect is greater than diminishing returns. Technology presupposing entropy, introduced is a new paradox of entropic technology generating infinite growth. Resolution assumes serial substitution of technologies, generating an infinite continuum. Physics and economics contest mechanic entropy and organic growth conceptions. A mechanic conception resolves set disjunctives exclusively, every set disjoined from a contiguous set, constituting entropy. An organic (...) conception resolves set disjunctives inclusively, every set conjoined with a contiguous set, constituting growth. Causally each instance of something decreases the preexistent set of all possible instances by one, dying. Functionally each instance of something increases the postexistent set of all possible instances by one, living. Economists have the advantage here. Endlessly divisible, substance is something constituted of nothing, ungoverned by the law of conservation of energy. Physicists implicitly concede this assuming substance emerges from a Big Bang. Alas lunch is not free. Product of an economic growth equation being endless and non-repetitive, calculation is irrational, rendering growth economics irrelevant. Calculation requires marginal analysis, sequences initiating anywhere within a set governed by conservation of energy and entropy converging in parallel upon a common limit, “the unseen hand.” Energy conserved, however, economic growth is bounded. (shrink)

Examples of hypotheses about the number of planets are frequently used to introduce the topic of (actual) truthlikeness but never analyzed in detail. In this paper we first deal with the truthlikeness of singular quantity hypotheses, with reference to several ‘the number of planets’ examples, such as ‘The number of planets is 10 _versus_ 10 billion (instead of 8).’ For the relevant ratio scale of quantities we will propose two, strongly related, normalized metrics, the proportional metric and the (simplest and (...) hence favorite) fractional metric, to express e.g. the distance from a hypothetical number to the true number of planets, i.e. the distance between quantities. We argue that they are, in view of the examples and plausible conditions of adequacy, much more appropriate, than the standardly suggested, normalized absolute difference, metric. Next we deal with disjunctive hypotheses, such as ‘The number of planets is between 7 and 10 inclusive is much more truthlike than between 1 and 10 billion inclusive.’ We compare three (clusters of) general ways of dealing with such hypotheses, one from Ilkka Niiniluoto, one from Pavel Tichý and Graham Oddie, and a trio of ways from Theo Kuipers. Using primarily the fractional metric, we conclude that all five measures can be used for expressing the distance of disjunctive hypotheses from the actual truth, that all of them have their strong and weak points, but that (the combined) one of the trio is, in view of principle and practical considerations, the most plausible measure. (shrink)

In The Crisis of the European Sciences and Transcendental Phenomenology, Husserl argues that the only way to respond to the scientific Krisis of which he speaks is with phenomenological reflections on the history, method, and task of philosophy. On the assumption that an accurate diagnosis of a malady is a necessary condition for an effective remedy, this paper aims to formulate a precise concept of the Krisis of the European sciences with which Husserl operates in this work. Thus it seeks (...) an answer to the question: What exactly, according to Husserl, is “the ‘crisis’ [Krisis] of the European sciences”? There are two different tendencies in the literature on this question. According to the traditional interpretation, the Krisis of the European sciences lies not in the inadequacy of their scientificity but in the loss of their meaningfulness for life. According to an innovative suggestion, the Krisis lies not in the loss of their meaningfulness for life but in the inadequacy of their scientificity. These readings are mutually exclusive because each claims that the other misidentifies the Krisis as something that it is not. The argument of this paper, however, is that, given the many different senses of Krisis in The Crisis, an adequate understanding of the Krisis that Husserl identifies requires not a disjunctive but an inclusive approach. Therefore the paper proposes that Husserl’s Krisis of the European sciences is both a crisis of their scientificity and a crisis of their meaningfulness for life. The relevance of this result to Husserl’s philosophical and historical sense-investigations in The Crisis—as well as to the present critical situation of philosophy—is self-evident. (shrink)

We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also show (...) how extracted programs can be translated into Haskell. As an application we extract a program converting the signed digit representation of real numbers to infinite Gray code from a proof of inclusion of the corresponding coinductive predicates. (shrink)

Definitions of disability are useful for different purposes and carry normative significance. However, defining disability has proven a difficult task. Communities with different theoretical backgrounds and practical aims disagree about how to define disability. Recently, Chong‐Ming Lim (2018) has attempted to define disability in a manner accommodating of the different interests and theoretical commitments of the disability and the medical communities. His account aims at broadening Elizabeth Barnes' (2016) definition of disability, which is not sufficiently inclusive of the interests (...) of the medical community and leaves out cases other than physical disabilities. Under the most plausible interpretation of his account, however, the account becomes more restrictive than that of Barnes. In this paper, I propose instead two kinds of accounts: a disjunctive one based on a reinterpretation of Lim's, and a cluster concept account of disability. Both accounts can avoid the restrictiveness problem faced by Lim's and Barnes' original accounts. (shrink)

The era of AI-based decision-making fast approaches, and anxiety is mounting about when, and why, we should keep “humans in the loop” (“HITL”). Thus far, commentary has focused primarily on two questions: whether, and when, keeping humans involved will improve the results of decision-making (making them safer or more accurate), and whether, and when, non-accuracy-related values—legitimacy, dignity, and so forth—are vindicated by the inclusion of humans in decision-making. Here, we take up a related but distinct question, which has eluded the (...) scholarship thus far: does it matter if humans appear to be in the loop of decision-making, independent from whether they actually are? In other words, what is stake in the disjunction between whether humans in fact have ultimate authority over decision-making versus whether humans merely seem, from the outside, to have such authority? Our argument proceeds in four parts. First, we build our formal model, enriching the HITL question to include not only whether humans are actually in the loop of decision-making, but also whether they appear to be so. Second, we describe situations in which the actuality and appearance of HITL align: those that seem to involve human judgment and actually do, and those that seem automated and actually are. Third, we explore instances of misalignment: situations in which systems that seem to involve human judgment actually do not, and situations in which systems that hold themselves out as automated actually rely on humans operating “behind the curtain.” Fourth, we examine the normative issues that result from HITL misalignment, arguing that it challenges individual decision-making about automated systems and complicates collective governance of automation. (shrink)

A 22-month longitudinal study of (self)employed disabled workers (_Following the preference of the lead author who identifies as disabled, the linguistic self-presentation by our participants, the precedent of _(Hein and Ansari, Academy of Management Journal 65:749–783, 2022)_, and the clarification note included in Jammaers & Zanoni’s recent review of ableism _(Jammaers and Zanoni, Organization Studies 42:429–452, 2021)_, we chose, and consistently use, the term “disabled employees” throughout the paper. We do so to underscore the premise of the social model of (...) disability, which explains that “people are disabled first and foremost by society, not by their individual, biological impairment. To us this term most clearly highlights that it is society (and possibly organizations) that disable and oppress people with impairments, by preventing their access, integration and inclusion to all walks of life, making them ‘disabled’.” _(Jammaers and Zanoni, Organization Studies 42:429–452, 2021_: 448_)) models the growing centrality of the body in meaning-making. We inductively explain how body dramas of suffering or thriving initially instigate cycles of meaning deflation and inflation at work. Our disjunctive process model shows that, at the beginning of the pandemic, disabled workers performed either dramas of suffering or on dramas of thriving. However, as the global pandemic unfolded, disabled workers begun crafting composite dramas that deliberately juxtaposed thriving and suffering. This conjunctive process model stabilized meaning-making at work by acknowledging the duality of the disabled body, as both anomaly and asset. Our findings elaborate, and bridge, emerging theories of body work and recursive meaning-making to explain how disabled workers explicitly enroll their bodies to make meaning at work during periods of societal upheaval. (shrink)

This paper considers three general dilemmas that tend to undermine successful configurations of unity: the either/or dilemma, the synthesis dilemma and the relativism dilemma. It argues that, in his aesthetic writings, Schiller’s critique of Kantian dualisms leads him to an adualistic conception of unity that operates with a different, more inclusive approach to opposition and unification. In order to clarify Schiller’s innovative and often misunderstood position, the paper draws on the disjunctive logic recently developed by Friedrich Kümmel.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:John Venn. A Life in Logic by Lukas M. VerburgtClaudia CristalliLukas M. VerburgtJohn Venn. A Life in Logic Chicago and London: The University of Chicago Press, 2022. 411 pp., incl. indexThis is the first intellectual biography of John Venn (1834–1923), British logician, “philosopher and antiquarian” (DNB). Until now, Venn had not been studied as a philosophical figure in its own right. He is mostly remembered today for the (...) “Venn Diagrams,” a graphical device illustrating logical relations such as inclusion, exclusion, conjunction, disjunction, and for having systematically articulated a frequentist theory of probability. Together with an in-depth account of Venn’s logical developments, of his studies in probability theory, and of its applications to history and to anthropometry, Lukas M. Verburgt brings to life Venn’s spiritual struggles within—and eventually out of— his family’s religion, evangelicalism. Verburgt’s reconstruction is substantiated by many extracts from Venn’s correspondence and private notes, which add substantially to the value of this biography. (Of note is Verburgt’s 2022 editon of Venn’s unpublished writings and slected correspondence, which can be considered a companion to this biography).While showing the connections of epistemology, religion and academic politics in Victorian Cambridge, Verburgt contributes an important chapter in the history of logic and of empiricist philosophy.The book opens with a chapter on Venn’s childhood and early youth (1834–53), largely drawn from manuscript material of the Venn family—the “Parentalia”—and from Venn’s Annals of a Clerical Family, where he included “autobiographical recollections” (p. 2). The chapter introduces the reader to the values of a prominent evangelical family and to their peculiar way of understanding Christianity as a faith to be embedded in habit and to be taught by example. The following two [End Page 385] chapters follow Venn’s development, first as a student at Caius college, Cambridge (1853–57) and then as a country curate; the chapters elaborate on the institutional history of the college and on parish life from the perspective of evangelical orthodoxy. Chapter 4 is still chronologically situated within Venn’s early clerical service but is arranged thematically around his first publication (1862), “Science of History,” which contains some elements of the fundamental ideas elaborated in the Logic of Chance (1866): namely, that probability theory could only make predictions about long-run frequencies of events, and never about individual cases (p. 77). The core of Venn’s argument in 1862 revolved around possible atheistic implications of a science of history. If at some point it would be possible to predict future events, would there still be free will? Or a God? In his reply, Venn maintained that any prediction concerning individual agents could be defeated by assuming that the agent gets to know the prediction and changes her actions accordingly (pp. 74–76).After the publication of the “Science of History” essay, Venn left the parish for Cambridge, where he worked first as a Catechist (1862– 1867) and then as a moral sciences lecturer. Verburgt devotes chapter 5 to that and to the Cambridge milieu, where Venn sides for university reforms and engages with the Grote Club, all while drifting away from evangelical orthodoxy. After laying out Venn’s theory of probability (Chapter 6), Verburgt returns to an integrated analysis of Venn’s scientific and religious thought in chapter 7. This chapter may be particularly relevant for pragmatist readers, since here Verburgt highlights the commonalities between Venn’s “religious logic” and the notion of belief that will be expressed in more detail by pragmatism. Verburgt focuses on Venn’s logic in three subsequent chapters (Chapters 8, 9 and 11). Considered together, they provide a comprehensive history of Venn’s logical development, which Verburgt proudly announces as the first of this kind (p. xx). The last chapter on Venn’s logic (Chapter 11) also includes Verburgt’s argument for “includ[ing] Venn in the local history of early analytic philosophy at Cambridge” (p. 262). Chapters 10 and 12 recount Venn’s last years with particular emphasis on his interests in natural and historical sciences; they provide relevant material for scholars interested in the history and philosophy of... (shrink)

This chapter presents detailed empirical work on several aspects of children's linguistic performance, focusing in particular on evidence that even two-year-old children understand that the meanings of determiners are ‘conservative’, that the meaning of natural language disjunction is ‘inclusive–or’, and that the structural notion of ‘c-command’ governs a range of linguistic phenomena. This and other works are used to defend three related versions of the argument from the poverty of the stimulus, each of which strongly supports the existence (...) of an innate language faculty. (shrink)

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993 ) concerning the modelling conditions for the axioms of assertion A → (( A → B ) → B ) (there called c 6) and permutation ( A → ( B → C )) → ( B → ( A → C )) (there called c 7). We show that the modelling conditions for assertion and permutation proposed (...) in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001 ), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose two different corrections. (shrink)