It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of (...) contradictory propositions, and Aristotelian contradictories always consist of an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations. (shrink)

In this paper, I argue that temporality, as described in Being and Nothingness , is a central theme in Nausea . In the first section I make the point that one of Sartre's guiding concerns at the time of publishing Nausea is temporality and the temporal nature of freedom. In the second section, the theme of melancholy and its relationship to temporality is explored. The third section explores Sartre's use of this image of being taken 'from behind'. I use this (...) temporal imagery as a guide for interpreting Roquentin's reaction to the rape and murder of Lucienne. By interpreting this scene by way of the temporality of Being and Nothingness , we can duly recognize the early Sartre's concern with temporality, understand the melancholia that arises because of the 'internal' negation of the past, and give a more satisfying account of a scene which is often ignored in the secondary literature. (shrink)

This discussion explores the possibility of distinguishing a tighter notion of contrariety evident in the Square of Opposition, especially in its modal incarnations, than as that binary relation holding statements that cannot both be true, with or without the added rider ‘though can both be false’. More than one theorist has voiced the intuition that the paradigmatic contraries of the traditional Square are related in some such tighter way—involving the specific role played by negation in contrasting them—that distinguishes them (...) from other pairs of incompatible statements constructed from the same conceptual materials. Prominent among examples, these other nonstandard pairs are the ‘new contraries’ presented by Robert Blanché’s hexagon(s) of opposition. With special, though not exclusive, attention to these cases, we investigate whether contrariety in the distinguished sense can be captured by adding to the incompatibility condition the further demand that the pair of statements concerned can be represented as the results of applying some sentence operator to the content in its scope, for one of the pair, and, for the other, the application of that same operator to the negation of that content. For one of the two cases, a Blanché case, of nonstandard contrariety singled out for attention, the question of whether such a representation is available is settled at the end of Section 4, and then in a more satisfying way in Section 5, though for the other case, noticed by Peter Simons, the question remains open, after some tentative discussion in one subsection, 6.2, of an Appendix (Section 6). (shrink)

In sentences with internal negation, Free Choice Inferences (FCIs) are cancelled (Chierchia 2013). The present study investigated the possibility that FCIs are negated, not cancelled, by external negation. In previous research, both Mandarin-speaking children and adults were found to license FCIs in affirmative sentences with a modal verb and the disjunction word huozhe ‘or’ (Zhou, Romoli & Crain 2103). The present study contrasted internal versus external negation in sentences that contained all the ingredients needed to (...) license FCIs. Four experiments were conducted using the Truth Value Judgment Task (Crain & Thornton 1998). Experiment 1 tested Mandarin-speaking children and adults using sentences with internal negation, a modal verb and disjunction. As expected, children did not license FCIs; rather, they assigned a ‘neither’ interpretation to disjunction. Also as expected, adults analyzed disjunction as taking scope over internal negation, yielding a ‘not both’ interpretation (Jing, Crain & Hsu 2005). Experiment 1 provided the benchmarks for sentences with external negation in Experiments 2-4. Experiment 2 confirmed that English-speaking adults distinguish between internal and external negation in sentences with disjunction. In Experiment 3, external negation was conveyed by the focus adverb zhiyou ‘only’. External negation eliminated the between-group differences observed in Experiment 1. Both children and adults analyzed external negation as taking scope over disjunction. Experiment 4 tested the effect of external negation on the computation of FCIs. The test sentences only differed from Experiment 1 by using external negation, rather than internal negation. Again, children and adults interpreted the test sentences in the same way. Most importantly, in contrast to Experiment 1 (with internal negation), both groups analysed external negation as negating, rather than cancelling, FCIs. The findings support the distinction between internal and external negation. (shrink)

This paper argues for the importance of the distinction between internal and external negation over expressions for belief. The common fallacy is to confuse statement like (1) and (2): (1) John believes that the school is not closed on Tuesday; (2) John does not believe that the school is closed on Tuesday. The fallacy has ramifications in teaching, reasoning, and argumentation. Analysis of the fallacy and suggestions for teaching are offered.

There are many kinds of negation and denial. Perhaps the most common is the Boolean negation not that applies to propositions-in-extension, i.e. truth-values. The others are, inter alia, the property of propositions of not being true which applies to propositions; the complement function which applies to sets; privation which applies to properties; negation as failure applied in logic programming; negation as argumentation ad absurdum, and many others. The goal of this paper is neither to provide a (...) complete list, nor to analyse all of them. Rather, I am going to deal with negation of propositions that come attached with a presupposition that is entailed by the positive as well as negated form of a given proposition. However, there are two kinds of negation, namely internal and external negation. I am going to prove that while the former is presupposition-preserving, the latter is presupposition-denying. This issue has much in common with the difference between topic and focus articulation within a sentence. Whereas articulating the topic of a sentence activates a presupposition, articulating the focus frequently yields merely an entailment. The main contribution of this paper is the proof that the two kinds of negation are not equivalent. While the Russellian wide-scope (external) negation gets the truthconditions of a sentence right for a subject occurring as a focus, Strawsonian narrow-scope (internal) negation is validly applicable for a subject occurring as the topic. I also deal with other kinds of presupposition triggers, in particular factive attitudes and prerequisites of a given property. My background theory is Transparent Intensional Logic (TIL). TIL is an expressive logic apt for the analysis of sentences with presuppositions, because in TIL we work with partial functions, in particular with propositions with truth-value gaps. Moreover, the procedural semantics of TIL make it possible to uncover the hidden semantic features of sentences, make them explicit and logically tractable. (shrink)

Four experiments and 2 corpus-based studies demonstrate that negation is a determinant factor affecting novel nonliteral utterance-interpretation by default. For a nonliteral utterance-interpretation to be favored by default, utterances should be potentially ambiguous between literal and nonliteral interpretations. They should therefore be (a) unfamiliar, (b) free of semantic anomaly or any kind of internal incongruity, and (c) unbiased by contextual information. Experiments 1–3 demonstrate that negative utterances, meeting these 3 conditions, were interpreted metaphorically (This is not a safe) (...) or sarcastically (Ambitious she is not) when presented in isolation and were therefore processed faster in contexts strongly biasing them toward their nonliteral than toward their (equally biased) literal interpretation. Experiment 4 reduces the possibility that it is structural markedness on its own that induces nonliteralness. Two corpus-based studies provide corroborating evidence, supporting the view of negation as an operator generating nonliteral interpretations by default. (shrink)

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition.

L’auteur discerne trois intuitions majeures dans la théorie éliminativiste de la négation développée par les idéalistes anglais, d’après laquelle une négation est l’élimination d’une alternative au sein d’un ensemble complet d’alternatives disjonctivement affirmées du sujet de la négation : premièrement, la détermination du sens d’une proposition est l’assignation à une proposition de coordonnées logiques dans un espace logique ; deuxièmement, le sens d’une proposition entretient une relation interne avec le sens de sa négation ; troisièmement, l’espace logique dans lequel une (...) négation acquiert un sens dépend du contexte. Il est montré que la théorie éliminativiste de la négation échoue à composer adéquatement les deux premiers aperçus en essayant de faire droit au troisième. A l’inverse, le Tractatus de Wittgenstein les combine adéquatement mais passe à côté du troisième. Une théorie adéquate de la négation devrait, minimalement, satisfaire simultanément les trois contraintes. (shrink)

This paper presents a new approach to theorizing and empirically investigating a phenomenon variously described by sociologists as internalized oppression or symbolic violence. Located at the intersection of internal worlds and external reality, the intrapsychic and the interpersonal and social, this object of inquiry—here termed self-negation—is crucial to many forms of societal domination. The paper explores its inner workings, analytically disaggregating it into an array of psychosocial processes drawn from the psychoanalytic theory of the defenses. Much of the (...) work’s originality consists in showing how these processes operate across multiple systems of domination and drive many and varied outward manifestations of the phenomenon. (shrink)

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: a review of the main concepts involved in the definition of logical negation; an explanation of the epistemological obstacles against the introduction of non-classical negations within diagrammatic logic.

This paper examines the relationships between the many-valued logics G~ and Gn~ of Esteva, Godo, Hajek, and Navara, i.e., Godel logic G enriched with Łukasiewicz negation, and neighbors of intuitionistic logic. The popular fragments of Rauszer's Heyting-Brouwer logic HB admit many-valued extensions similar to G which may likewise be enriched with Łukasiewicz negation; the fuzzy extensions of these logics, including HB, are equivalent to G ~, as are their n-valued extensions equivalent to Gn~ for any n ≥ 2. (...) These enriched systems extend Wansing's logic I4C4, showing that Łukasiewicz negation is a species of Nelson's negation of constructible falsity and yielding a Kripke-style semantics for G~ and Gn~ to complement the many-valued semantics. (shrink)

One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. (...) The paper then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature ‘Brouwerian logic’ or ‘closed-set logic’. (shrink)

The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...

In one of their papers, Michael De and Hitoshi Omori observed that the notion of classical negation is not uniquely determined in the context of so-called Belnap-Dunn logic, and in fact there are 16 unary operations that qualify to be called classical negation. These varieties are due to different falsity conditions one may assume for classical negation. The aim of this paper is to observe that there is an interesting way to make sense of classical negation (...) independent of falsity conditions. We discuss two equivalent semantics, and offer a Hilbert-style system that is sound and complete with respect to the semantics. (shrink)

This paper has two related goals. Firstly, after briefly clarifying the theoretical core of Solger's thought, it will analyse his metaphysics from Hegel's point of view, emphasizing that sacrifice is, for Solger, the fundamental structure of the relationship between the finite and the Infinite. Secondly, it will investigate the main reasons behind Hegel's criticism of Solger, showing that they have different conceptions of privation and negation and concluding that Solger and Hegel have different aims. Hegel's aim consists in recomposing (...) the unity of finite and infinite, whereas Solger's thought is structured on the rupture between these two. (shrink)

Was entspricht dem linguistischen Phänomen der Negation in der Welt? Der Ausgangspunkt, der mir geeignet scheint, um diese Frage zu beantworten, ist das so genannte Problem der negativen singulären Existenzsätze. Dieses Problem besteht darin, dass aus einem Satz, der die Existenz irgendeines Gegenstandes verneint, unter bestimmten Voraussetzungen zu folgen scheint, dass dieser Gegenstand existiert. Das Problem der negativen singulären Existenzsätze scheint wesentlich mit der Frage verknüpft zu sein, ob Existenz ein logisches Prädikat ist oder nicht. Lässt man diese Frage (...) offen, kann man zu einer Lösung des Problems der negativen singulären Existenzsätze kommen, nach welcher die Negation in einer ungewöhnlichen Weise zu interpretieren ist. Es wird sich dabei zeigen, dass die Negation einerseits als Satznegation und andererseits als Teil der Metasprache anzusehen ist. (shrink)

We investigate an information based generalization of the incompatibility-frame treatment of logics with non-classical negation connectives. Our framework can be viewed as an alternative to the neighbourhood semantics for extensions of lattice logic by various negation connectives, investigated by Hartonas. We set out the basic semantic framework, along with some correspondence results for extensions. We describe three kinds of constructions of canonical models and show that double negation law is not canonical with respect to any of these (...) constructions. We also compare our semantics to Hartonas’. (shrink)

We identify the ways the policies of leading international bioethics journals limit the participation of researchers working in the resource-constrained settings of low- and middle-income countries in the development of the field of bioethics. Lack of access to essential scholarly resources makes it extremely difficult, if not impossible, for many LMIC bioethicists to learn from, meaningfully engage in, and further contribute to the global bioethics discourse. Underrepresentation of LMIC perspectives in leading journals sustains the hegemony of Western bioethics, limits the (...) presentation of diverse moral visions of life, health, and medicine, and undermines aspirations to create a truly “global” bioethics. Limited attention to this problem indicates a lack of empathy and moral imagination on the part of bioethicists in high-income countries, raises questions about the ethics of bioethics, and highlights the urgent need to find ways to remedy this social injustice. (shrink)

In this paper I provide some linguistic evidence to the thesis that responsibility judgments are normative. I present an argument from negation, since the negation of descrip- tive judgments is structurally different from the negation of normative judgments. In particular, the negation of responsibility judgments seem to conform to the pattern of the negation of normative judgments, thus being a prima facie evidence for the normativity of responsibility judgments. I assume — for the argument’s sake (...) — Austin’s distinction be- tween justification and excuse, and I sketch how to accommodate the distinction between internal (justification) and external (excuse) nega- tion of responsibility within a language with a second-order analogous of existential generalization and λ operator. In the end I confront with and refute some objections against this argument. (shrink)

There are two standard ways to establish consistency in set theory. One is to prove consistency using inner models, in the way that Gödel proved the consistency of GCH using the inner model L. The other is to prove consistency using outer models, in the way that Cohen proved the consistency of the negation of CH by enlarging L to a forcing extension L[G].But we can demand more from the outer model method, and we illustrate this by examining Easton's (...) strengthening of Cohen's result:Theorem 1. There is a forcing extensionL[G] of L in which GCH fails at every regular cardinal.Assume that the universe V of all sets is rich in the sense that it contains inner models with large cardinals. Then what is the relationship between Easton's model L[G] and V? In particular, are these models compatible, in the sense that they are inner models of a common third model? If not, then the failure of GCH at every regular cardinal is consistent only in a weak sense, as it can only hold in universes which are incompatible with the universe of all sets. Ideally, we would like L[G] to not only be compatible with V, but to be an inner model of V.We say that a statement is internally consistent iff it holds in some inner model, under the assumption that there are innermodels with large cardinals. (shrink)

‘Semantic externalism’ is the view that the thought and speech of internally identical subjects can have different contents, depending on facts about their environments. ‘Semantic internalism’ is the negation of this view. The details of these two views depend on the definition of ‘internal identity’. Katalin Farkas has shown that the traditional definition of internal identity as physical identity is too permissive: it misclassifies certain bodily states as internal. She has proposed defining internal identity as (...) phenomenal identity instead. In the critical part of my paper, I argue that Farkas’s proposal fails for being too restrictive: it misclassifies non-conscious mental states, most notably dispositional belief, as external. I consider two interpretations of Farkas’s proposal but conclude that neither succeeds, because each requires internal features to influence the subject’s phenomenal life in a way in which dispositional belief does not. In the constructive part of my paper, I consider dispositional identity as an alternative definition of internal identity. I argue that the dispositional-identity definition avoids the phenomenal-identity definition’s shortcoming and retains its main attraction, viz., that of securing the subjective indistinguishability that obtains between Twin Earth duplicates. My argument that it does the latter, however, faces potentially decisive obstacles. Thus, I retreat to a disjunctive proposal: internal identity should be defined either as dispositional identity or as dispositional-plus-phenomenal identity. I conclude by defending my proposal against a different charge that may be levelled against it, viz., that of misclassifying Cartesian dualism as an externalist theory of the mind. (shrink)

Feature logics are the logical basis for so-called unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with negation and the functional uncertainty construct needed for the description of long-distance dependencies and obtain the following results: satisfiability of feature terms is undecidable, sort equations can be internalized, consistency of sort equations is decidable if there is at least one atom, and consistency of sort equations is undecidable if there is no atom.

Being built on the ground of mutual effect, facing the current state-isolation, international law is losing its grip on efficiency. This makes some of us to question (1) If law is not working, do we still need law? If we would say no, the history shows that such is the path to the state-suicide. As Smithian mutual benefits is the assurance of the individual benefits, we need international relationships to create the benefits for the individual states, hence international law, Yet (...) the current one is certainly not working, then, the question, (2) What should the international law be? The enforcement of the international law could be accomplished through the blockchain. As blockchain “went bypass” the national law, and simply negated it, yet it is still not immune to the scope of international jurisdiction. We also argue that the blockchain’ smart contract is not sufficient enough to operate smoothly. Human brain is structured as the mirror rather than a glass and transferring the law interpretation to the machine would not work, hence, we designed the formula of langue and parole, blockchain multiseg operating under the semiotics of the international law. Here the language learning is modelled with the supervisory and reinforcing algorithms, with supervisory predetermined with bias X,Y towards the values of law. Sort of form of constant repetends of Heidegger’s hermeneutics circle. The most important part in this paper is written with the purpose to explain that international law is at the same struggle that Kafka had. Carrying the weight of both, the clothed façade and true self, first being the morality guide and later the states will, and not being neither, international law is self-isolated from the real world, as Gregor Samsa was. Hence, this is not the paper of secularization, no customs, no higher purpose, nothing except the will of states, that can be constantly renewed with the signifier and signified being linked and re-linked. (shrink)

Children are the most sensitive part of a sciety, therefore the violence against them is considered a serious violation of their personal rights and their higher interests. In most of cases, children in Republic of Macedonia are very little or not at all informed concerning the possibilities of reporting the cases of violence against them by their parents or relatives. The issue of domestic violence is still considered a private problem which occurs within the home. Thus, in most of cases, (...) this problem remains unsolved in silence, without any alert for the state institutions or SOS phone lines for reporting domestic violence. Some children who are more aware for being subjected to violation of their rights are afraid to report the case because of further consequences. In this article some facts will be given about observing the symptoms and signs of violence against children, forms and types of violence against children, determination factors of the violence as well as the consequences and the impact of the domestic violence on the physical and psychological development of children. Based on the legal provisions and international conventions, parents, responsible institutions and the society in general are morally and legally obliged to respect and preserve the interest of the child. This article will show that in practice, these legal obligations are violated by parents and in specific cases also by the competent institutions because the lack of intervention. (shrink)

In Enjoy your Symptom, Slavoj Žižek’s notion of “trauma” is critical to understanding the scope and meaning of the “symptom.” This “symptom,” conceptually, is construed through the manner in which identity, authority, and phallophany come to bear psychologically on the meaning of being. Because of this, the definition of “symptom,” when viewed in a Heideggerian way, becomes an ontical representation of that which is oriented primordially. The symptom, as we experience it, is more than just at the level of its (...) ontics, but, instead, has a primordially to it, which is only revealed through the presence of trauma. (shrink)

How do bioethics gatekeepers located in wealthy nations treat bioethics workers from developing countries? Can the policies of leading international bioethics journals—based on a concern for profit that effectively restricts access for most researchers from developing countries—be ethically justified? We examined these policies focusing on the way they influence the ability of researchers in resource-poor countries to participate in the development of the field of bioethics. Eight of the fourteen leading bioethics journals are published by three transnational publishing houses, all (...) of which are based in wealthy nations. None of these eight journals participates in the Health InterNetwork Access to Research Initiative of the World Health Organization, a program that provides free or very low-cost online access to the major journals by researchers in developing countries. Lack of access to these essential resources makes it extremely difficult, if not impossible, for bioethicists in developing countries to learn from, and engage in, the global bioethics dialogue. Thus, exclusionary practices of leading bioethics journals sustain the hegemony of Western bioethics, raising serious questions about professed aspirations to create a truly “global” bioethics. This phenomenon indicates lack of empathy and moral imagination of bioethicists in developed countries, raises serious questions about the ethics of bioethics, and highlights the urgent need for creative solutions to remedy this social injustice. (shrink)

This paper seeks to illuminate Schopenhauer’s notion of the negation or denial of the will by investigating the figure of the saint within his philosophy. We argue that various discussions in Schop...

This essay represents part of an effort to rewrite the history metaphysics in terms of what philosophy never said, nor could say. It works from the Neoplatonic commentary tradition on Plato's Parmenides as the matrix for a distinctively apophatic thinking that takes the truth of metaphysical doctrines as something other than anything that can be logically articulated. It focuses on Damascius in the 5—6th century AD as the culmination of this tradition in the ancient world and emphasizes that Neoplatonism represents (...) the crisis of Greek metaphysics on account of the inability to give a rational account of foundations for knowing and of the ultimate principle of beings. Neoplatonism discovered how all such ultimate principles were necessarily beyond the reach of reason and speech. This apophatic insight is drawn out with the help of contemporary criticism of Neoplatonic philosophy, defining also some points of divergence. The essay then discusses the motives for thinking the unsayable in postmodern times on the basis of this parallel with Neoplatonic thought. Discourse's becoming critical of itself to the point of self-subversion animates them both. However, the tendency in postmodern thought to totally reject theology, including negative theology, is a betrayal of its own deepest motivations. This tendency is debated through an examination of the thought of Jean-Luc Nancy. While any traditional discourse can be negated, the negating and self-negating capacity of discourse itself is infinite, and this is where a perennial negative theological philosophy of the unsayable is to be located. Language, eminently the language of philosophy, as infinitely open, points in a direction which becomes equally and ineluctably theological. (shrink)