Four weak positional calculi are constructed and examined. They refer to the use of the connective of negation within the scope of the positional connective “R” of realization. The connective of negation may be fully classical, partially analogical or independent from the classical, truth-functional negation. It has been also proved that the strongest system, containing fully classical connective of negation, is deductively equivalent to the system MR from Jarmużek and Pietruszczak.

Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, (...) and used to conclude that the considered logical systems are PSPACE-complete. (shrink)

In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further (...) research. (shrink)

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended (...) class='Hi'>positive logic are offered. (shrink)

Our question is: can we embed minimal negation in implicative logics weaker than I→? Previous results show how to define minimal negation in the positive fragment of the logic of relevance R and in contractionless intuitionistic logic. Is it possible to endow weaker positive logics with minimal negation? This paper prooves that minimal negation can be embedded in even such a weak system as Anderson and Belnap’s minimal positive logic.

Aristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is not ill’ (...) are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics. (shrink)

We argue that, if taken seriously, Kripke's view that a language for science can dispense with a negation operator is to be rejected. Part of the argument is a proof that positive logic, i.e., classical propositional logic without negation, is not categorical.

We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that (...) has a characteristic semantics. We also show that Shramko's falsification logic FL can be incorporated into some extension of this basic logic Ku. Finally, we unite the two basic logics Ki and Ku together to get a negative modal logic K-, which is dual to the positive modal logic K+ in [7]. Shramko has suggested an extension of Dunn 's kite and also a dual version in [12]. He also suggested combining them into a “united” kite. We give a united semantics for this united kite of negations. (shrink)

The present essay includes six thematically connected papers on negation in the areas of the philosophy of logic, philosophical logic and metaphysics. Each of the chapters besides the first, which puts each the chapters to follow into context, highlights a central problem negation poses to a certain area of philosophy. Chapter 2 discusses the problem of logical revisionism and whether there is any room for genuine disagreement, and hence shared meaning, between the classicist and deviant's respective uses of (...) 'not'. If there is not, revision is impossible. I argue that revision is indeed possible and provide an account of negation as contradictoriness according to which a number of alleged negations are declared genuine. Among them are the negations of FDE and a wide family of other relevant logics, LP, Kleene weak and strong 3-valued logics with either "exclusion" or "choice" negation, and intuitionistic logic. Chapter 3 discusses the problem of furnishing intuitionistic logic with an empirical negation for adequately expressing claims of the form 'A is undecided at present' or 'A may never be decided' the latter of which has been argued to be intuitionistically inconsistent. Chapter 4 highlights the importance of various notions of consequence-as-s-preservation where s may be falsity, indeterminacy or some other semantic value, in formulating rationality constraints on speech acts and propositional attitudes such as rejection, denial and dubitability. Chapter 5 provides an account of the nature of truth values regarded as objects. It is argued that only truth exists as the maximal truthmaker. The consequences this has for semantics representationally construed are considered and it is argued that every logic, from classical to non-classical, is gappy. Moreover, a truthmaker theory is developed whereby only positive truths, an account of which is also developed therein, have truthmakers. Chapter 6 investigates the definability of negation as "absolute" impossibility, i.e. where the notion of necessity or possibility in question corresponds to the global modality. The modality is not readily definable in the usual Kripkean languages and so neither is impossibility taken in the broadest sense. The languages considered here include one with counterfactual operators and propositional quantification and another bimodal language with a modality and its complementary. Among the definability results we give some preservation and translation results as well. (shrink)

Entendemos el concepto de “negación mínima” en el sentido clásico definido por Johansson. El propósito de este artículo es definir la lógica positiva mínima Bp+, y probar que la negación mínima puede introducirse en ella. Además, comentaremos algunas de las múltiples extensiones negativas de Bp+.“Minimal negation” is classically understood in a Johansson sense. The aim of this paper is to define the minimal positive logic Bp+ and prove that a minimal negation can be inroduced in it. In (...) addition, some of the many possible negation extensions of Bp+ are commented. (shrink)

Entendemos el concepto de “negación mínima” en el sentido clásico definido por Johansson. El propósito de este artículo es definir la lógica positiva mínima Bp+, y probar que la negación mínima puede introducirse en ella. Además, comentaremos algunas de las múltiples extensiones negativas de Bp+.“Minimal negation” is classically understood in a Johansson sense. The aim of this paper is to define the minimal positive logic Bp+ and prove that a minimal negation can be inroduced in it. In (...) addition, some of the many possible negation extensions of Bp+ are commented. (shrink)

A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.

We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...) philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference —all inferences, not just those chosen from consistent domains!) and so on. This paper has not attempted to address these issues in general. All it demonstrates is that the charge that a dialetheist solution to the semantic paradoxes can be maintained only by making some intelligible notion ineffable cannot be made to stick. The dialetheist has a coherent position, endorsing the T-scheme, but rejecting DS, EFQ (even Boolean DS and EFQ) and ABS. And any argument to the effect that the relevant notions are both ineffable and intelligible begs the question. The case against consistent “solutions” to the semantic paradoxes therefore remains intact. (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)

Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival (...) in recent years, especially in writings by Huw Price and Timothy Smiley. While agreeing that Frege's argument does not refute the position, we shall air some philosophical qualms about it in Section 5, after a thorough examination of the formal issues in Sections 1-4. This discussion draws on - and seeks to draw attention to - some pertinent work of Kent Bendall in the 1970s. (shrink)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is (...) obvious that matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

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)

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 advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.

As we’ve seen in the last chapter, there is good linguistic reason to categorize negations (and negative operators in general) by which De Morgan laws they support. The weakest negative operators (merely downward monotonic) support only two De Morgan laws;1 medium-strength negative operators support a third;2 and strong negative operators support all four. As we’ve also seen, techniques familiar from modal logic are of great use in giving unifying theories of negative operators. In particular, Dunn’s (1990) distributoid theory allows us (...) to generate relational semantics for many negations. However, the requirements of distributoid theory are a bit too strict for use in modeling the weakest negations. For a relational semantics to work, an operator must either distribute or antidistribute over either conjunction or disjunction; but the merely downward monotonic operators do not. Thus, a unifying semantics cannot be had in distributoid theory. In the (more familiar) study of positive modalities, there is a parallel result. Normal necessities distribute over conjunction, and normal possibilities over disjunction. When these distributions break down, a relational semantics is no longer appropriate. Here, there is a somewhat familiar solution: neighborhood semantics. In this chapter, I’ll adapt neighborhood semantics to the less familiar case of negative modalities, showing how it can be used to give a single semantic framework appropriate to all the pertinent sorts of negative operators. (shrink)

Contrary to the contemporary view that negation is a logical operation that modifies the mere content of a thought or judgment, but not the act of thinking or judging it, Kant maintains that negation is an act of logical apperception through which I exclude a thought or judgment from what ‘I think.’ In this paper, I argue against two interpretations of Kant’s account of logical negation. According to the first, negation is a subjective psychological act of (...) excluding an erroneous judgment. Against this, I will show that for Kant, negation is an operation of logical, not empirical apperception. The second interpretation views logical negation as an objective representation either of a relation of opposition or of non-being. I argue that, on the contrary, the logical function of negation is merely formal, not material, and therefore does not have semantic content. The paper’s final section develops a positive conception of logical negation as a formal function of judging. (shrink)

Etude de l'extension par la negation semi-intuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type Routley-Meyer pour le systeme d'Urquhart (CI) en tant que celle-la ne fournit que des theories consistantes pour la completude de celui-ci.

There are two main claims that Bradley makes concerning negative judgment in the Principles of Logic: Negative judgment ‘stands at a different level of reflection’ from affirmative judgment. Negative judgment ‘presupposes a positive ground’.I will consider what Bradley means by these claims, and draw comparisons with Wittgenstein's views on negation as they developed between the Tractatus and the Philosophical Remarks.

In positive logic the negation of a propositionA is defined byA X whereX is some fixed proposition. A number of standard properties of negation, includingreductio ad absurdum, can then be proved, but not the law of noncontradiction so that this forms a paraconsistent logic. Various stronger paraconsistent logics are then generated by putting in particular propositions forX. These propositions range from true through contingent to false.

This essay proposes a procedural interpretation of negative information in terms of split negation as procedural prohibition. Information frames and models are introduced, with negation defined as the implication of bottom, 0. A method for extracting the procedures prohibited by complex formulas is outlined, and the relationship between types of prohibited procedures is identified. Definitions of negation types in terms of the implication of 0 on an informational interpretation have been criticized. This criticism turns on the definitions (...) creating a purportedly unnatural asymmetry between positive and negative information. It is demonstrated below that a strong asymmetry between positive and negative information is in fact the case. As such, an asymmetry between positive and negative information is natural, and something that we should want an informational interpretation of negation to preserve. (shrink)

In the first part of this paper (Méndez and Robles 2008) a minimal and an intuitionistic negation is introduced in a wide spectrum of relevance logics extending Routley and Meyer's basic positive logic B+. It is proved that although all these logics have the characteristic paradoxes of consistency, they lack the K rule (and so, the K axiom). Negation is introduced with a propositional falsity constant. The aim of this paper is to build up logics definitionally equivalent (...) to those in the aforementioned paper, negation being now introduced with the unary connective. Relational ternary semantics are provided for the new logics and soundness and completeness results are proved. (shrink)

The German philosopher Rickert substituted for Hegel's formulation of the dialectic a "Heterological Principle of Thought" where identity and otherness become moments within the pure logical object of thought. The logical object of thought takes precedence over dialectical movement, and otherness takes precedence over negation. Flach expounds and defends Rickert's position against its critics. The discussion is specialized but contains some valuable insights into Hegel. --R. H. K.

We develop positive model theory, which is a non first order analogue of classical model theory where compactness is kept at the expense of negation. The analogue of a first order theory in this framework is a compact abstract theory: several equivalent yet conceptually different presentations of this notion are given. We prove in particular that Banach and Hilbert spaces are compact abstract theories, and in fact very well-behaved as such.

ZUSAMMENFASSUNGDer Einfluss Heinrich Barths auf die diastatische Auffassung der Gott-Mensch-Beziehung in der »dialektischen Theologie« seines Bruders Karl scheint bedeutend gewesen zu sein. Der Autor des vorliegenden Beitrags vertritt jedoch die Ansicht, dass sowohl Karl Barth wie auch eine gängige Einschätzung des Sachverhalts im Blick auf Heinrich Barths Position Opfer eines Missverständnisses geworden sind, demgegenüber diese Position in ihrem dauerhaft haltbaren Sinn zu rekonstruieren und zu rehabilitieren ist. Die für Heinrich Barths philosophisches Werk insgesamt in der Tat kennzeichnende Akzentuierung der Transzendenz (...) muss mit Bezug auf die Platonische Idee des Guten in erster Linie als Transzendenz gegenüber einer theoretischen Gesamtschau verstanden werden, welche die ethische Lebensproblematik bedenkenlos vereinnahmt und damit um ihre Aktualität bringt. So verstanden bedeutet Heinrich Barths Betonung der Transzendenz nicht das Aufreißen einer kaum mehr überbrückbaren Kluft, sondern verweist vielmehr auf die Aufgabe, das Gott-Mensch-Verhältnis, den Begriff einer »Gotteserkenntnis« und letztlich die Problematik der Transzendenz als solche von einem Gesichtspunkt aus neu zu bestimmen, für den die ethische Lebensproblematik im Zentrum der Aufmerksamkeit steht.SUMMARYHeinrich Barth's influence on the diastatical conception of the God-man-relationship in his brother Karl's Dialectical Theology seems to be important. The author of the following contribution however suggests the opinion, that both Karl Barth himself and a common view of the matter have been victims of a misunderstanding of Heinrich Barth's position, in contrast to which this position has to be reconstructed and rehabilitated in its durable sense. The accentuation of transcendence, relative to the transcendental principles respectively God, which is indeed significant of Heinrich Barth's work as a whole, has to be understood, in reference to Plato's Idea of the Good, first of all as transcendence in relation to a theoretical view of the whole, which does not hesitate to integrate the problematic of life and ethics by eliminating its actuality. In this understanding Heinrich Barth's emphasis of transcendence does not mean to tear open a gap which is hardly ever to be bridged, but refers to the task of a redefinition of the God-man-relationship, the notion of “Gotteserkenntnis” and, in last terms, the problem of transcendence as such, starting from a point of view for which the problematic of life and ethics is in the centre of attention. (shrink)

Recently, Irad Kimhi has argued that negation and falsehood can be made intelligible by understanding assertions/judgements as acts of two-way logical capacities. These are capacities that are, at the same time, for (1) positive and negative assertions/judgements and (2) positive and negative facts. Kimhi’s account of negation and falsehood, however, faces severe problems. I argue that these problems can be resolved, and that a new understanding of cases of negation and falsehood can be achieved, by (...) regarding two-way logical capacities for assertion/judgement and facts as established and undergirded by what Ludwig Wittgenstein calls “samples”. The standard metre sample, for instance, establishes and undergirds the capacity for asserting that something, x, is one metre long (meaning: x is like the standard metre in length). At the same time, it establishes and undergirds the capacity for the fact that x is one metre long (when x is like the standard metre in length). As I explain, invoking samples means we cannot say, as Kimhi wants to, what assertion/judgement, negation, and facts, in general, are but can only show what they are, one case at a time. This, however, is a boon not a disadvantage. (shrink)

ABSTRACT Prima facie, the philosophy of Emmanuel Levinas would seem to be inherently averse to literature as an ethical mode. Indeed, in his early work, up to and including Totality and Infinity (1961), literary art is often censured with what amounts to Platonic zeal. However, as I will demonstrate, this criticism stands alongside what is seemingly an incongruous use of literary art as a means of ethical exemplification. By exploring this tension, I will show how the contra-epistemic aesthetic of S. (...) Y. Agnon (1888–1970) can be read within ethical terms consistent with Levinas’s philosophical position. (shrink)

In this paper, my main aim is to analyse Mao’s conception of Marxist theory and his Marxist subjectivity in theory construction in his three articles. While doing so, I will use two main approaches, first is the idea that Karl Marx’s method in understanding social relations and his theory of knowledge is in many aspects compatible and in continuation with an epistemological reading of Hegel’s subjectivity, and the second is the general structure about the relationship between the object and subject’s (...) process of knowing is similar in all three thinkers. While doing so, I will advocate the position that Mao’s epistemology is compatible with the Marxist understanding of Hegelian epistemology, and that from such an epistemological understanding it is possible to investigate Mao’s three texts in a way that yields, not an orthodox or “end result” Marxism, but instead a more general, meta epistemological understanding of Marx, that is understood better structurally. Eventually, I will claim that while using “scientific” or “orthodox” Marxism as a method to understand society, Mao further uses the subjective element in the same way as Hegel and Marx used it, although eventually he diverts the Marxist subjective manoeuvre to another direction. (shrink)

Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and. We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a duality between so-called \-spaces and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.

This essay revisits Karl Marx’s understanding of consumption, in an effort to rescue it from the overshadowing legacy of critical theory which has construed Marx as inveighing against false needs. It is argued that Marx regarded the expansion of needs entailed by capitalism in a generally favourable way, but saw capitalism as a system yoking use-value to the imperatives of profit accumulation, hence limiting and subjugating the consumption of the masses. While Marx’s position was radically different from conventional anti-consumerism it (...) is equally incompatible with complacent affirmations of ‘the consumer society’ in that Marx at all times aimed at a revolutionary change which will transform consumption both quantitatively and qualitatively. Marx’s views are first discussed as expressed in the perennially-cited text, the 1844Economic and Philosophical Manuscripts. The second part moves on to examine the further evolution of Marx’s ideas as found in later texts, particularly theGrundrisse. (shrink)

The puzzle of English until is well-known. Karttunen 1974 argues that until is ambiguous between a durative and a punctual negative polarity (NPI) meaning. Mittwoch 1977 claims that there is no ambiguity and that the two meanings are due to scope differences: NPI-until is in fact until above negation. Mittwoch’s account relies crucially on the assumption that negation is an aspectual operator that ‘stativizes’ verb meanings (a position recently argued for in de Swart 1996, and de Swart and (...) Molendijk 1999; see also Klima 1964, Seuren 1974, Verkuyl 1993). Thus far, the correct analysis of until remains an open issue. (shrink)

What conception of negation a dialetheist might have, in holding that a statement and its negation can both be true, has been the subject to considerable debate. Several of the issues in play in this area—such as the unique characterization of negation, and the interplay between contrariety and subcontrariety—are broached here by considering some positions taken on them by Graham Priest and assorted critics. Some of the more intricate points, as well as detailed discussions of commentators on (...) Priest are handled in explicitly labelled Digressions and in two Appendices. (shrink)

The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. (...) In this article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics. (shrink)

Cet article se propose de présenter le point de vue logique de Frege (1848-1925) sur la négation. Celle-ci est considérée comme un opérateur de pensée qui s’inscrit dans un schéma d’opposition des pensées exprimées sans que cette opposition ait une valeur d’opposition des forces. La négation n’est pas le symétrique d’une assertion, elle n’est pas non plus un aimant pour le prédicat dans une proposition. C’est hors de la logique que ces deux dernières positions sur la négation peuvent être défendues.

We examined a large set of conditional inference data compiled from several previous studies and asked three questions: How is normative performance related to intelligence? Does negative conclusion bias stem from Type 1 or Type 2 processing? Does implicit negation bias stem from Type 1 or Type 2 processing? Our analysis demonstrated that rejecting denial of the antecedent and affirmation of the consequent inferences was positively correlated with intelligence, while endorsing modus tollens inferences was not; that the occurrence of (...) negative conclusion bias was related to the extent of Type 2 processing; and that the occurrence of implicit negation bias was not related to the extent of Type 2 processing. We conclude that negative conclusion bias is, at least in part, a product of Type 2 processing, while implicit negation bias is not. (shrink)

Positive polarity items (PPIs) are generally thought to have the boring property that they cannot scope below negation. The starting point of the paper is the observation that their distribution is significantly more complex; specifically, someone/something-type PPIs share properties with negative polarity items (NPIs). First, these PPIs are disallowed in the same environments that license yet type NPIs; second, adding any NPI-licenser rescues the illegitimate constellation. This leads to the conclusion that these PPIs have the combined properties of (...) yet-type and ever-type NPIs: what appears to be a prohibition is nothing but “halfway licensing”. The paper goes on to propose a unification of the analyses of rescuable PPIs, NPIs, and negative concord, and questions the grounding of polarity sensitivity in the scalar or the referential semantics of the items involved. (shrink)

We prove that any positive elementary (least fixed point) induction expressing the negation of transitive closure on finite nondirected graphs requires at least two recursion variables.

The negative particles lā/ ’al in Ugaritic change from positive to negative in modal contexts, conditional, questions, disjunctions, etc. They have usually been studied from a Semitic and linguistic points of view. On the basis of their occurrence in Ugaritic texts, we pretend to explain their uncommon behaviour from a philosophical and logico-semantic perspective. Is it possible to translate this linguistic structure in our Modern languages? Starting from a general view of their use in Ugaritic language, we claim that (...) this phenomenon can be more clearly understood in relation to modality. We interpret these negation as a negative evidential paradigm and we explain how they change in different contexts. Methodologically, we make use of formal tools of Dynamic Epistemic Logic in order to provide a more fine-grained understanding of these negations, and their dynamics. (shrink)

Negation has occupied a unique place in the history of ideas. Negation as opposed to truth-conditional affirmation has been very much present in Indian and Western thought from very early times. R. S. Bhatnagar of happy memory (1933–2019) in his “Many Splendoured Negation” (Bhatnagar in J Indian Counc Philos Res XXII(3):83–906, 2006) had shown many a facet that could be construed in “negation”. This paper is an attempt to revisit the notion of negation that R. (...) S. Bhatnagar brought to light and to further the germane thought that he had outlined in his concise exposé. Though Bhatnagar had stated that there could be negative and positive functions of negations, a vigilant reading of his article shows that the primary import of Bhatnagar is to examine the positive function of negation. According to R. S. Bhatnagar, even death, which could be the negative in its most feared form, the reality of which, has the positive effect on the soul force in its commitment to live well and die well. R. S. Bhatnagar’s engagement with negation is not complete unless one takes into consideration “negation” as an integral part of philosophizing in India, whether it is the Buddhist tradition or any other tradition. One encounters the philosophical “exercise” on negation enormously in Buddhist thought. The first part of the paper is a brief discussion on the views of Bhatnagar in his essay mentioned with the author’s considerable add-on, while the second part brings home the Buddhist facet and paradigm of negation, the missing link in Bhatnagar. The third part of the paper is an unveilment of the cogitation of R. S. Bhatnagar on “death” in terms of negation. (shrink)