Inclusive Disjunction Research Articles

Cultivating Trees: Lewis Carroll’s Method of Solving (and Creating) Multi-literal Branching Sorites Problems

Abstract Lewis Carroll has been credited for developing a “Method of Trees” for solving multi-literal sorites problems, which anticipates several aspects of contemporary “tableau” or tree systems of logical proof. In particular, Carroll’s method pioneers the use of branching paths as a means of displaying or illustrating inclusive disjunction. However, rather than focusing on the respects in which Carroll’s tree diagrams resemble contemporary tree systems, I propose to focus instead on significant aspects in which they differ. In particular, I will show how the sorts of multi-literal sorites problems that Carroll’s method of trees is designed to solve are particularly ill-suited for resolution by more contemporary tree methods. I will also show how Carroll likely used something like this method, not only to solve but also to craft some of the trickier logical puzzles for which he is also famous.

Образы желающего производства в научном познании

The aim of this article is to explicate the epistemological aspects of Deleuze and Guattari’s conception of desire presented in Anti-Oedipus. Capitalism and Schizophrenia. I show that the schizoanalytic concept of desire as a “production of machines” is reflected in studies on a laboratory science. The epistemological meaning of the image of the “desiringmachine” is revealed, which is that to cognize means to experience the possibilities of the man-dimension to be involved in the various entanglements of the world – psychophysical, natural-technical, sociocultural. Through the use of historical and scientific material, I show that the concept of the nomadic subject is relevant to the description of a laboratory cognitive subject. I note that, on the one hand, the scientist is aware of himself as a researcher through territorialization, i.e. attribution of himself to tradition. On the other hand, the scientific cognition must also be treated as deterritorialization, i.e. the desire of consciousness to retreat themselves into a space in which it was possible to be outside of itself – outside of existing tradition. Thus, for the subject of cognition, it is immutable not only the requirement that “The ‘I think’ must be able to accompany all my representations” (Kant), but also the need to leave the sphere of the conscious as already thought out, held in the area of “the unconscious as passive syntheses of desire” (Deleuze and Guattari). I also demonstrate that in laboratory life the scientist is immersed in free syntheses of desire with non-linear, multivalued connections and inclusive disjunctions. However, in the narrations of historians and philosophers, as well as in scientific articles and reports, all this heterogeneous plurality and ambiguity is reduced. Scientific articles, reports, interviews are written, on the contrary, using linear, unambiguous connections and exclusive disjunctions, that is, in accordance with the Oedipal code. This circumstance points to a certain “Oedipalization of knowledge”, analogous to the “Oedipalization of desire” that Deleuze and Guattari identified in relation to Freudian psychoanalysis.

Discourse context cannot make ‘or’ inclusive (only experimental task can)

The canonical view in linguistics is that the core meaning of ‘p or q’ is inclusive disjunction, but that its most common interpretation is exclusive disjunction. Nevertheless, the idea persists that an inclusive interpretation is possible given the proper discourse context. Experimental evidence for this idea comes from studies using truth-value judgment, showing that some participants judge ‘p or q’ as true when both p and q are true. We present evidence against the idea that discourse context alone licenses an inclusive interpretation, proposing that it is only the task of truth-value judgment that ostensibly licenses this interpretation. We conducted an experiment using both truth-value judgment and a reply-anticipation task, where participants anticipated an interlocutor's answer to how many of p and q are true, based on their interpretation of ‘p or q’. Target utterances appeared in discourse contexts encouraging an inclusive interpretation by making it maximally informative and relevant. Despite this, most participants anticipated that the interlocutor would answer that exactly one of p and q were true. We therefore believe the onus is now on those claiming that discourse context can license an inclusive interpretation to explain why it is conspicuously absent in tasks other than truth-value judgment.

A New Contact 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.

Default meanings: language’s logical connectives between comprehension and reasoning

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.

Towns within Towns: From Incompossibility to Inclusive Disjunction in Urban Spatial Planning

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 inclusive disjunction to intensive milieu, we call for development of a more milieu-based approach to planning to facilitate more-than-human coexistence differently.

Does the inclusive disjunction really mean the conjunction of possibilities?

There is an ongoing dispute in the psychology of reasoning about how people interpret disjunctions, p or q. In the original mental models theory (MMT1) people interpret p or q as the disjunction of three possibilities (possibly p¬q, or possibly ¬pq, or possibly pq, where “¬” = not). p or q is true if one disjunct is actually true. In a recent revision of mental models theory (MMT2), people interpret p or q as a conjunction of the three possibilities, and they treat it as true only if each is possible and ¬p¬q is impossible. Two experiments investigated possibility and truth judgments about disjunctions given sets consisting of one or more of the four cases (p¬q, ¬pq, pq, and ¬p¬q). The results showed that in both possibility and truth judgments, participants' interpretations of disjunctions were only consistent with MMT1. Inclusive disjunctions imply the disjunction of the three possibilities, and they are true when one of the three cases (p¬q, ¬pq, and pq) is actual. These findings support MMT1, but not MMT2. In conclusion, the revised mental models theory may be unnecessary for disjunctions.

Fingersi è conoscersi. L’ontologia del personaggio e quello stato o qualità del sé chiamato ‘sincerità’

The aim of this essay is to enhance the potential of literary and theatrical ‘fiction’ according to three different registers: logical, gnoseological, modal. From the logical point of view, the poetic-dramaturgical fiction challenges the Aristotelian principle of non-contradiction: in the symbolic act in which x simulates being y, x doesn’t cease to be himself/herself to become other. Fiction does not imply abandoning an identity to conquer a new and different one: it is the coexistence of sameness and difference, of identity and its inexhaustible alteration. It is a contradictory coexistence in relation to classical logic, but this contradiction is the irrevocable nature of the symbolic-imaginative activity of the human being. According to the gnoseological perspective, a careful analysis leads to a re-thinking of the static opposition between true and false, so that in the ‘simulation’ x and y are either both true or both false; a gnoseology based on an inclusive disjunction replaces the one based on an exclusive logic. Finally, from the modal point of view, the poetic-literary fiction breaks the mechanism that submits the possible to the real, relegating it to non-existence and non-actuality. The great novel, when it is really a great novel, actualizes the possible and at the same time makes the real possible. Neither the static nature of reality, nor the evanescence of possibility, but the vertigo of virtuality is the proper dimension of narrative fiction, that is, no longer the dimension of the individual but of its pathic and unintentional background: the singularity.

Context, Content, and the Occasional Costs of Implicature Computation.

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.

The Analytic Truth and Falsity of Disjunctions.

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such asEither A or B, they tended to evaluate the four cases in its 'partition': A and B, A and not-B, not-A and B, not-A and not-B, as 'possible' or 'impossible' in ways that bore out the difference between inclusive disjunctions ('or both') and exclusive disjunctions ('but not both'). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer 'mirror-image' evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.

Lexicalizing disjunction scope

Tiwa (Tibeto-Burman; India) has two disjunctive particles, which give rise to different interpretations in sentences with other operators. I argue that this semantic distinction is not one of inclusive vs. exclusive disjunction, but one of scope. I provide an analysis that captures this scopal distinction: one particle lexicalizes a choice function variable (subject to existential closure high in the structure), and the other lexicalizes an alternative-set former which interacts with higher operators. I also show that wide scope disjunction in Tiwa behaves differently from wide scope readings of English "or", and suggest that they warrant different analyses.

The Syntax of Principles: Genericity as a Logical Distinction between Rules and Principles

AbstractMuch 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.

Children interpret disjunction as conjunction: Consequences for theories of implicature and child development

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: (i) that children access only a proper subset of the adult alternatives (specifically, they do not access the lexicon when generating alternatives), and (ii) 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 (recursive exhaustification). 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 (under every); 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.

STRUCTURER LE LEXIQUE DE L’ESPAGNOL MOYENNANT DES CLASSES SÉMANTIQUES

Nous présentons la hiérarchie d’étiquettes sémantiques de l’espagnol que nous sommes en train d’élaborer dans le cadre du projet de recherche FFI2013-44185-P Hiérarchie d’étiquettes sémantiques pour les genres prochains de la définition lexicographique (UAB). Nous décrivons les notions d’étiquette sémantique (qui représente une classe sémantique ou un ensemble de classes sémantiques) et de formule actancielle (qui permet d’indiquer les actants sémantiques d’un prédicat ou d’un quasi-prédicat et ses structures syntaxiques profondes). Nous commentons différents mécanismes de description sémantique, comme les disjontions inclusives et exclusives ou la fission de variables. Nous illustrons nos propos par de nombreux exemples en espagnol en proposant les traductions françaises correspondantes.

Confronting connectivity: feminist challenges to the metropolis

ABSTRACTGoogle suggests that connectivity is the new paradigm for politics in the digital age. I argue that the effect of connectivity is a shift in the operation of power from the centralized institutions of the state to the decentralized logistics of inclusion of the digital metropolis. Explaining this power's features, I elaborate a media theory of inclusive disjunction and a feminist theory of pornographic exposure. Locating cultural resistance to connectivity, I look to feminist artistic responses to the city, from which I explore the feminist imagining of connectivity through the metaphor of the storm to reclaim their bodies as sites of contestation.

Transactional Experiential Inquiry: From Pragmatism to Somaesthetics

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.

JEWISH LAW AND MEDIEVAL LOGIC: WHY EATING HORSE MEAT IS A PUNISHABLE OFFENSE

AbstractThis article presents a case study of the influence of Muslim and Christian logicians on medieval Jewish law. The case in question is why it is a punishable offense for Jews to eat mammals that do not have either sign of purity—that is, neither have split hooves nor chew their cud—and the article examines the answers given by three medieval Jewish sages: Rashi, Maimonides, and Naḥmanides. The Written Law of the Torah explicitly allows the consumption of mammals, such as cattle, with both signs of purity. It also explicitly prohibits the eating of mammals, such as camels or pigs, with one sign but not the other. It does not, however, appear to explicitly prohibit the consumption of mammals, such as horses, with neither sign. Using a fortiori logic, Rashi derives a punishable prohibition against eating horses from the prohibition against eating camels and pigs. Maimonides ascribes this prohibition to the Oral Law of the Talmud. Naḥmanides, by contrast, attributes it directly to the Written Law without relying on either a fortiori logic or the Oral Law. This article argues that this solution was available to Naḥmanides because he adopted inclusive disjunction from Christian logicians, but it was not available to Maimonides because he adopted exclusive disjunction from Muslim logicians. The choice between inclusive and exclusive disjunction is shown to continue to be of importance in modern American law.

The challenge of consciousness with special reference to the exclusive disjunction

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.

Naive Probability: Model-Based Estimates of Unique Events.

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(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). 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.

The compatibility heuristic in non-categorical hypothetical reasoning: Inferences between conditionals and disjunctions

A new theory explains how people make hypothetical inferences from a premise consistent with several alternatives to a conclusion consistent with several alternatives. The key proposal is that people rely on a heuristic that identifies compatible possibilities. It is tested in 7 experiments that examine inferences between conditionals and disjunctions. Participants accepted inferences between conditionals and inclusive disjunctions when a compatible possibility was immediately available, in their binary judgments that a conclusion followed or not (Experiment 1a) and ternary judgments that included it was not possible to know (Experiment 1b). The compatibility effect was amplified when compatible possibilities were more readily available, e.g., for ‘A only if B’ conditionals (Experiment 2). It was eliminated when compatible possibilities were not available, e.g., for ‘if and only if A B’ bi-conditionals and exclusive disjunctions (Experiment 3). The compatibility heuristic occurs even for inferences based on implicit negation e.g., ‘A or B, therefore if C D’ (Experiment 4), and between universals ‘All A’s are B’s’ and disjunctions (Experiment 5a) and universals and conditionals (Experiment 5b). The implications of the results for alternative theories of the cognitive processes underlying hypothetical deductions are discussed.