I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture (...) the following results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

We agree with Cesario's premise but reject his conclusion: Although experimental studies of racial stereotyping, weapons perception, and shoot decisions typically exclude real-world contextual factors and thus have limited relevance to race disparities, these excluded factors comprise systemic, institutional, and individual-level biases that are more likely to amplify racial disparities than negate them.

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of (...) structurally diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

There is a widely held view that visual representations (images) do not depict negation, for example, as expressed by the sentence, “the train is not coming.” The present study focuses on the real-world visual representations of photographs and comic (manga) illustrations and empirically challenges the question of whether humans and machines, that is, modern deep neural networks, can recognize visual representations as expressing negation. By collecting data on the captions humans gave to images and analyzing the occurrences (...) of negation phrases, we show some evidence that humans recognize certain images as expressing negation. Furthermore, based on this finding, we examined whether or not humans and machines can classify novel images as expressing negation. The humans were able to correctly classify images to some extent, as expected from the analysis of the image captions. On the other hand, the machine learning model of image processing was only able to perform this classification at about the chance level, not at the same level of performance as the human. Based on these results, we discuss what makes humans capable of recognizing negation in visual representations, highlighting the role of the background commonsense knowledge that humans can exploit. Comparing human and machine learning performances suggests new ways to understand human cognitive abilities and to build artificial intelligence systems with more human-like abilities to understand logical concepts. (shrink)

Using logic-laden terms to translate and interpret what the ancient Indian Buddhist thinkers said when we are not sure what they spoke about when they spoke about ‘contradictions’, etc. in natural languages can sometimes make things frustrating. Keeping in mind Wittgenstein’s exhortation, “don’t think, but look!”, I approach the issues of contradiction, negation, and the catuṣkoṭi via case-by-case study on several pertinent passages in Dharmapāla’s Dasheng Guangbailun Shilun. The following are some interrelated observations which should not be overgeneralized, especially (...) considering the limited scope of this study and its methodological considerations. First, there is an implicit rule of non-opposition and there could be no real oppositions for apparent oppositions because of implicit qualifications. Moreover, these are not new since or after Dignāga. Second, Dharmapāla and his contemporaries are familiar with the two negative usages, and prasajya-pratiṣedha is used for negating the opponents’ theses and is related to the no-thesis view. It’s not a good idea to assign truth values to sentences using prasajya-pratiṣedha or to a thesis in which the terms have no real objects. And Dharmapāla’s theses are just therapeutic tools. Third, in Dharmapāla’s discussion of the negative catuṣkoṭi, one can see the rule of non-opposition, the strategy of qualifications, and the two negative usages. Although the four positions in the catuṣkoṭi are regarded as mutually exclusive and jointly exhaustive, they are jointly exhaustive in pragmatic context, and are mutually exclusive under some interpretations, but not all. My tentative suggestion is that the catuṣkoṭi is a loosely term-based way of categorization. Last but not least, in the text discussed, I do not see Buddhist thinkers endorsing any contradictions. (shrink)

The time has come to rehabilitate the history of ideas in French literary studies, primarily because we should retreat from the disrepute attached to all universalising approaches to the real in the name of an ever-increasing subdivision of knowledge which proves on occasion to be shortsighted or stultifying.

It is usually accepted in the literature that negation is a contradictory-forming operator and that two statements are contradictories if and only if it is logically impossible for both to be true and logically impossible for both to be false. These two premises have been used by Hartley Slater [Slater, 1995] to argue that paraconsistent negation is not a “real” negation because a sentence and its paraconsistent negation can be true together. In this paper we (...) claim that a counterpart of Slater´s argument can be directed against the negation operator of classical logic. Carnap’s discovery that there are models of classical propositional logic with non-standard or non-normal interpretations of the connectives will be used to build such an argument. One such non-normal valuation which can be added to the set of classically admissible valuations without altering the set of theorems or the set of valid consequences assigns true to every well-formed formula and, therefore, assigns a designated value to every formula and its negation. We ponder the consequences of these arguments for the claims that paraconsistent negations are not genuine negations and that the negation of classical logic is a contradictory-forming operator. (shrink)

G. H. von Wright proposed that a temporal interval exemplifies a real contradiction if at least one part of any division of this interval involves the presence of contradictorily related (though non-simultaneous) states. In connection with intervals, two negations must be discerned: 'does not hold at an interval' and 'fails throughout an interval'. Von Wright did not distinguish the two. As a consequence, he made a mistake in indicating how to use his logical symbolism to express the notion of (...) real contradiction. The present paper aims to reconstruct and philosophically motivate von Wright's argument for the possibility of real contradictions. (shrink)

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] (...) resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries. (shrink)

Expressivists have a problem with negation. The problem is that they have not, to date, been able to explain why ‘murdering is wrong’ and ‘murdering is not wrong’ are inconsistent sentences. In this paper, I explain the nature of the problem, and why the best efforts of Gibbard, Dreier, and Horgan and Timmons don’t solve it. Then I show how to diagnose where the problem comes from, and consequently how it is possible for expressivists to solve it. Expressivists should (...) accept this solution, I argue, because it is demonstrably the only way of avoiding the problem, and because it generalizes. Once we see how to solve the negation problem, I show, it becomes easy to state a constructive, compositional expressivist semantics for a purely normative language with the expressive power of propositional logic, in which we can for the first time give explanatory, formally adequate expressivist accounts of logical inconsistency, logical entailment, and logical validity. As a corollary, I give what I take to be the first real expressivist explanation of why Geach’s original moral modus ponens argument is genuinely logically valid. This proves that the problem with expressivism cannot be that it can’t account for the logical properties of complex normative sentences. But it does not show that the same solution can work for a language with both normative and descriptive predicates, let alone that expressivists are able to deal with more complex linguistic constructions like tense, modals, or even quantifiers. In the final section, I show what kind of constraints the solution offered here would place expressivists under, in answering these further questions. (shrink)

We introduce a new method for building models of [Formula: see text], together with [Formula: see text] statements over [Formula: see text], by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only [Formula: see text]-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at [Formula: see text] known as [Formula: see text] holds together with [Formula: see text], thereby answering a (...) well-known question of Moore. This construction can be described as a finite-support weak forcing iteration with side conditions consisting of suitable graphs of sets of models with markers. The [Formula: see text]-preservation is accomplished through the imposition of copying constraints on the information carried by the condition, as dictated by the edges in the graph. (shrink)

Studies have suggested that metaphors (Lawyers are sharks) and similes (Lawyers are like sharks) have distinct representations: metaphors engender more figurative and abstract properties, whereas similes engender more literal properties. We investigated to what extent access to such representations occurs automatically, during on-line reading. In particular, we examined whether similes convey a more literal meaning by following the metaphors and similes with explanations that expressed either a figurative (dangerous) or a literal property (fish) of the vehicle. In a self-paced reading (...) with a moving window paradigm, we presented participants with negated simile and metaphor main clauses (Lawyers are not (like) sharks) followed by explanations that also negated either a figurative (because lawyers are not dangerous) or a literal property of the vehicle (because lawyers are not fish). We found that vehicles (sharks) in metaphors were read significantly faster than those in similes. In addition, explanations negating a figurative property were read faster after metaphors, whereas explanations negating a literal property were read faster after similes. These results support the hypothesis that metaphors and similes rely on different interpretive processes, suggesting that similes access literal representations while metaphor access figurative ones in real time. (shrink)

The aim of this paper is to show that the binary notions of reality and negation play an important role in the philosophical agenda of Kant, Maimon and Fichte. The paper has three sections. The first section illustrates the metaphysical significance of Kant’s introduction of the quantitative opposition between reality and negation, which informs the phenomena-noumena distinction and the attribution of intensive magnitude. The second section argues that Maimon’s speculative appropriation of differentials took up Kant’s conception of (...) class='Hi'>real opposition between reality and negation but fundamentally revised the theory of space and time to dissolve the problem of applicability in Kant, leading to the consequence of obliterating the pure categories. The third section shows how Fichte inherited the Kantian-Maimonian quantitative opposition of reality and negation in his characterization of the interdetermination between the I and the Not-I and how he developed an immanent account of the relational categories such as causality and substantiality on that basis. (shrink)

The aim of this paper is to show that the binary notions of reality and negation play an important role in the philosophical agenda of Kant, Maimon and Fichte. The paper has three sections. The first section illustrates the metaphysical significance of Kant’s introduction of the quantitative opposition between reality and negation, which informs the phenomena-noumena distinction and the attribution of intensive magnitude. The second section argues that Maimon’s speculative appropriation of differentials took up Kant’s conception of (...) class='Hi'>real opposition between reality and negation but fundamentally revised the theory of space and time to dissolve the problem of applicability in Kant, leading to the consequence of obliterating the pure categories. The third section shows how Fichte inherited the Kantian-Maimonian quantitative opposition of reality and negation in his characterization of the interdetermination between the I and the Not-I and how he developed an immanent account of the relational categories such as causality and substantiality on that basis. (shrink)

We will give a simple philosophical "proof" of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpinski and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will in (...) fact show why there must be an infinity of cardinalities between the integers and the reals. We will also show why Martin's Axiom must be false, and we will prove the extension of Fubini's Theorem for Lebesgue measure where joint measurability is not assumed. Following the philosophy--if you reject CH you are only two steps away from rejecting the axiom of choice (AC)--we will point out along the way some extensions of our intuition which contradict AC. (shrink)

v. 1. Propedêutica filosófia. v. 2. Ontognoseologia juridica.

A presente obra trata, de forma inigualável, das preliminares ao estudo da teoria tridimensional do direito, examinando a Filosofia e a Ciência do Direito, as dimensões da experiência jurídica, a posição do tridimensionalismo jurídico concreto, a dialética de complementaridade, o personalismo e o historicismo axiológico, as estruturas e os modelos do Direito no processo cultural e a visão integral do mundo jurídico.

Em linguagem didática e exposição sistemática, esta obra examina a relação existente entre o Direito e a História, permitindo a compreensão de diversos institutos jurídicos. O leitor poderá apreciar temas fundamentais da História do homem, como o Direito na cultura helênica, o Direito romano, o contratualismo e o Direito no Brasil, contando com citações de Rui Barbosa e Silvio Romero. Constitui leitura obrigatória aos cultores das ciências sociais e jurídicas que buscam uma visão aprofundada dos fundamentos do Direito.

Notas à margem de um estudo de Clovis Bevilaqua; separata da Revista de Faculdade de Direito de São Paulo, ano 1947, pgs. 51 a 96.--A doutrina de Kant nos primórdios de nossa emancipação cultural. O padre Feijó.

Aristoteles (384-322 a.C.), es uno de los pensadores mas influyentes de la historia de la humanidad. Filosofo y cientifico, su obra incorpora una gran variedad de conocimientos que, a traves de la pedagogia directa, transmitio a sus alumnos. Metafisica es una obra magna del pensamiento occidental, compuesta de catorce libros -de los que presentamos una seleccion- representa un compendio de todo el saber aristotelico en el campo de la filosofia y, tambien, un elemento basico de la misma como ciencia del (...) saber y del conocimiento. Todos los problemas que ha debatido la metafisica hasta hoy tienen su origen en las ideas que Aristoteles plantea y desarrolla en este libro de libros. (shrink)