Negation (Logic)

On the Possibility of a Proof-Theoretical Solution to the Categoricity Problem for Logical Inferentialism

by James Kirkpatrick

BA Dissertation

Négativité et logos dialectique chez le jeune Heidegger

by Olivier Huot-Beaulieu

Symposium : Revue canadienne de philosophie continentale, vol. 16, no. 1, Printemps 2012.

Tout au long de sa carrière philosophique, Heidegger s’est livré à une constante explication avec Hegel, qu’il... more Tout au long de sa carrière philosophique, Heidegger s’est livré à une constante explication avec Hegel, qu’il considérait comme son plus vif antagoniste. Dans le cadre de cet article, nous entendons nous rapporter aux origines de leur différend et prendre la mesure des griefs du jeune Heidegger à l’endroit de la dialectique hégélienne. Nous tenterons en un second lieu de démontrer que son opposition frontale camoufle en fait une secrète appropriation, puisque Heidegger aurait préalablement fait sienne l’idée d’un usage productif de la négation en philosophie.

The Square of Opposition and the Paradoxes

by Teresa Marques

Can an appeal to the difference between contrary and contradictory statements, generated by a non-uniform behaviour of... more Can an appeal to the difference between contrary and contradictory statements, generated by a non-uniform behaviour of negation, deal adequately with paradoxical cases like the sorites or the liar? This paper offers a negative answer to the question. This is done by considering alternative ways of trying to construe and justify in a useful way (in this context) the distinction between contraries and contradictories by appealing to the behaviour of negation only. There are mainly two ways to try to do so: i) by considering differences in the scope of negation, ii) by considering the possibility that negation is semantically ambiguous. Both alternatives are shown to be inapt to handle the problematic cases. In each case, it is shown that the available alternatives for motivating or grounding the distinction, in a way useful to deal with the paradoxes, are either inapplicable, or produce new versions of the paradoxes, or both.

Truth and the Ambiguity of Negation

by Teresa Marques

published in Baptista, Luca / Rast, Erich (eds)
Meaning and Context
Series: Lisbon Philosophical Studies - Uses of Languages in Interdisciplinary Fields - Volume 2
Year of Publication: 2010

This article has one aim, to reject the claim that negation is semantically ambiguous. The first section presents the... more This article has one aim, to reject the claim that negation is semantically ambiguous. The first section presents the putative incompatibility between truth-value gaps and the truth-schema; the second section presents the motivation for the ambiguity thesis; the third section summarizes arguments against the claim that natural language negation is semantically ambiguous; and the fourth section indicates the problems of an introduction of two distinct negation operators in natural language.

Il n’y a pas de rapport sexuel: The Irresolvability of the Gadamer-Habermas Debate

by William J. Urban

class paper written Good Friday, April 6, 2012

On Negativity: Between the Dialectics of Adorno and Badiou

by Edwin Mak

Masters thesis

Incidental exposure to no-smoking signs primes craving for cigarettes

by Brian Earp

Earp, B. D., Dill, B., Harris, J., Ackerman, J., and Bargh, J. (2011). Incidental exposure to no-smoking signs primes craving for cigarettes: An ironic effect of unconscious semantic processing? Yale Review of Undergraduate Research in Psychology, Vol 2, No 1, 12-23.

The present study tests whether incidental exposure to no-smoking signs may ironically boost craving for cigarettes in... more The present study tests whether incidental exposure to no-smoking signs may ironically boost craving for cigarettes in smokers. Smokers viewed photographs in which no-smoking signs were either incon- spicuously embedded (prime) or edited out (control). Participants then used a joystick to make quick approach vs. avoid motions while viewing smoking-related and neutral stimuli on a computer screen (Chen & Bargh, 1999). We hypothesized that primed smokers, but not controls, would show an automatic reach bias toward the smoking-related stimuli. The data supported our prediction. Possible mechanisms for the effect are discussed, as well as implications for public health policy, negation-based social campaigns in general, and our understanding of the unconscious processing of semantic information.

Pluralism and the Logical Basis of Metaphysics

by Nils Kürbis

A paper I gave at Logica 2006.

Negation and Adverbs in Czech

by Peter Kosta

PETER KOSTA/JOANNA BLASZCZAK/JENS FRASEK/ LJUDMILA GEIST/MARZENA ZYGlS (EDS.):
INVESTIGATIONS INTO FORMAL SLAVIC LINGUISTICS
CONTRIßUTIONS of THE FOURTH EUROPEAN CONITRENCE ON FORMAL DESCRIPTION of SLAVIC LANGUACES - FDSL IV
HELD AT POTSDAM UNIVERSITY, NOVEMBER 28-30, 2001
PART II:

This paper recalls some basic facts on syntax of adverbs and negation in Czech. It has been proposed recently to... more This paper recalls some basic facts on syntax of adverbs and negation in Czech. It has been proposed recently to analyze adverb phrases (AdvP) as the unique specifiers of distinct maximal projections, rather than as adjuncts (ClNQUE 1999). Cinque argues for the existence o f a fixed universal hierarchy of clausal functional projections. Furthermore, he rejects the assumption that languages vary in the number and type of functional projections and their distribution. Instead, he tries to construct a plausibility argument against these assumptions, suggesting that no such variation is allowed by UG and that the same number, type and order (hierarchy) of functional projections holds across languages and clause types, despite apparent counterevidence. Specifically, he argues that in addition to the order of free functional morphemes ("particles" and auxiliaries) and of bound functional morphemes (affixes), there is a third type of different classes offunctional projections of AdvP.

Similarily to the proposal that has been made by Uwe Junghanns (2006), I do not adopt the specific approach to the grammar of adverbials that are associated with specific functional projections (cf. also ALEXIADOU 1997 for Greek).

Instead, and as opposed to Uwe Junghanns, I make the claim that sentential adverbs are base-generated as adjuncts
to an agreement phrase as opposed to VP-Adverbs that adjoin to VP in the base.

This vision is supported with respect to the different properties of Negation and Scope w.r.t. sentential adverbs (SA) and manner (lower) adverbs: The contrast of manner adverbs with respect to structural position and the SA is striking both with respect to lexicon (semantics) and to scope properties of negation.

First descriptive generalization + manner adverbs are subcategorized by the verbal projection (light vP) whereas the higher adverbs are subcategorized by the CP phase heading and dominating the higher sentential negation phrase that outscopes manner adverbs. If the negational scope outscopes the propositional phrase and thus also the higher sentential adverbs, it usually takes scope over the lower adverbs and thus has properties of focus (partial) and contrastive focus.

My proposal is the following: The fact that in most cases SAs do not meet scope conflicts (for the exceptions see JUNGHANNS, 2006) can be explained by the fact that sentential negation does not build a scope domain of SA, the latter being situated higher in the sentence structure. Whereas SAs usually and mostly do not affect the reading of the negated proposition - despite their apparent scope conflicts that are then resolved by covered movement after Speil-out out of the scope of sentential negation (cf. JUNGHANNS, 2006) - manner adverbs such as pekne 'nicely', vlEdne 'moderately', nah/as 'loudly', dobfe 'good', etc. strictly combine with constituent negation interpretations with different scope properties than the sentence negation has. As I already stated my proposal will be that the negation - besides its main property as operator responsible for binding the trace or variable of negated sentences - constitutes the focus domain of the lowest phrase, viz. VP-shell. The starting point of my analysis is then the assumption that the negation -like other scope taking items (e.g., the particle only, etc.) - can be a candidate for focalizers or focus sensitive particles in the sense of HAJlcovA (l995a,b).
I assume that the focus feature [FOC can be assigned to syntactic constituents that include SAs and manner adverbs. Because SAs must take scope over the whole proposition (they
take the proposition as their argument in complement position)
they have to stand higher than the NegP. Scope conflicts between a sentential negation and SAs as discussed in Junghanns are resolved or overcome in the non-overt part of syntax (traditionally called LF). After Speil-out, the SA, the offending item, leaves its base position to adjoin to CP (or in my version to AGRSP) from where it takes scope over the whole clause.

NEGACE A VETNA STRUKTURA V CESTINE (Negation and clause structure in Czech)

by Peter Kosta

In the article the structure of the negative clauses in Czech has been iscussed with respect to different types of... more In the article the structure of the negative clauses in Czech has been iscussed with respect to different types of clauses. We started from the typological observations conceming the possible means of expressing negation in the world languages as weil as their different structural.
Mostly,the negation is expressed by a bound morpheme (e.g. prefix or suffix), a negative auxiliary, a clitic like a head or an adverb. The most prominent negated sentences in Czech tumed out to be those in which a lexical independent functional projection with Neg as a head is assurned. Furthermore, some universal and specific properties of sentential negation as pposed to those of constituent negation were discussed. In the subsequent chapters, a closer look was taken at the negation related phenomena, namely Genitive of negation and negative pronouns (negative concord).

One crucial result of this article was that sentential negation must be located in the vicinity of the Accusative case checker, i.e. in some position above vP. The im of the subsequent section was to establish the precise position of negation in the clause. Doing so we established crucial differences between modal
and auxiliary verbs assuming that modal constructions are best analyzed as biclausal, consequently the negation occuring in the matrix or the complement clause has the properties of sentential negation. Finally, the last section focused on the
question of whether there is a NegP in Czech. The result of our investigation is the proposal that sentence negation is a proclitic heading of its own functional projection NegP.

What is Wrong with Classical Negation?

by Nils Kürbis

The focus of this paper are the meaning-theoretical arguments against classical logic that Dummett bases on... more The focus of this paper are the meaning-theoretical arguments against classical logic that Dummett bases on consideration about the meanings of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett’s outlook on the theory of meaning. In particular, I shall grant Dummett his general bias towards verificationism or justificationism, encapsulated in the slogan ‘meaning is use’. The second general assumption I see no need to question is Dummett’s particular breed of molecularism. Some of Dummett’s assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inferences in the Dummettian framework.

Negation: A Problem for the Proof-Theoretic Justification of Deduction

by Nils Kürbis

I won the Jacobsen Essay Price of the University of London for this essay!

Adynaton and Material Exclusion

by Francesco Berto

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and... more Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one.

Strong Paraconsistency and Exclusion Negation

by Francesco Berto

How to Sell a Contradiction: The Logic and Metaphysics of Inconsistency

by Francesco Berto

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the... more There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry.

Meaning, metaphysics, and contradiction

by Francesco Berto

Modus Tollens, Modus Shmollens: Contrapositive reasoning and the pragmatics of negation

by Gaelle Villejoubert

Bonnefon, J. F., & Villejoubert, G. (2007). Modus Tollens, Modus Shmollens: Contrapositive reasoning and the pragmatics of negation. Thinking & Reasoning, 13, 207–222. doi: 10.1080/13546780601069488.

The utterance of a negative statement invites the pragmatic inference that some reason exists for the proposition it... more The utterance of a negative statement invites the pragmatic inference that some reason exists for the proposition it negates to be true; this pragmatic inference paves the way for the logically unexpected Modus Shmollens inference: ‘‘If p then q; not-q; therefore, p.’’ Experiment 1 shows that a majority of reasoners endorse Modus Shmollens from an explicit major conditional premise and a negative utterance as a minor premise: e.g., reasoners conclude that ‘‘the soup tastes like garlic’’ from the premises ‘‘If a soup tastes like garlic, then there is garlic in the soup; Carole tells Didier that there is no garlic in the soup they are eating.’’ Experiment 2 shows that this effect is mediated by the derivation of a pragmatic inference from negation. We discuss how theories of conditional reasoning can integrate such a pragmatic effect.

Negación Pictórica y Animal

by Axel Barceló

De l’origine de la négativité chez Heidegger et Hegel

by Olivier Huot-Beaulieu

Ithaque (Revue de philosophie de l'Université de Montréal), no. 6, Printemps 2010.

Le tome 68 de l’Édition intégrale des œuvres de Martin Heidegger, qui met en scène un important épisode de son... more Le tome 68 de l’Édition intégrale des œuvres de Martin Heidegger, qui met en scène un important épisode de son explication avec Hegel, a relativement peu été commenté jusqu’à ce jour. Cet article se veut une analyse approfondie de la première moitié du texte, intitulée La négativité. Heidegger y traque l’origine de la négativité hégélienne et en vient à proposer lui-même un concept de « néant » qu’il juge plus originaire que celui de son prédécesseur.

On the syntactic derivation of negative sentence adverbials

by Paul Rowlett

Journal of French Language Studies 3.1: 39–69. Published in 1993.