Frege maintains that there are not two distinct acts, assertion and denial; rather, denying p is one and the same as asserting not-p. Wittgenstein appears not to recognise this identity in Frege, attributing to him the contrary view that a proposition may have one of two verbs, "is true" or "is false". This paper explains Wittgenstein’s attribution as a consequence of Frege’s treatment of content as theoretically prior to the act of judgment. Where content is prior to judgment, the (...) denial of p—what is rejected in asserting p—is distinct from the assertion of not-p. Wittgenstein’s own embrace of Frege’s identity is then considered, an embrace explained in part by his repudiation of Frege’s theoretical order. (shrink)

Rational dialetheism is the view that for some contradictions, it is rational to believe that they are true. The view, associated with the work of among others, Graham Priest, looks as if it must lead to absurd consequences, and the present paper is an unsuccessful attempt to find them. In particular, I suggest that there is no non-question-begging account of acceptance, denial and negation which can be brought to bear against the rational dialetheist. Finally, I consider the prospect (...) of attacking the position without trying to "refute" it, but even these approaches seem unpromising in the present case. If the drift of the paper is correct, the only strategy is to examine the paradoxes one by one, and show in each case that the best account is non-dialetheic. (shrink)

A comprehensive account of denial viewed not only psychoanalytically but also philosophically.

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)

At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial (...) or rejection, rather than vice versa. Some other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection. (shrink)

Negation, denial and falsity lie at the heart of debates about logic. We set out the classical account of the relationship between negation and denial, owing to Frege and Geach. We then challenge this on the basis that it does not permit an adequate account of falsity. A dialetheic alternative is minuted and criticised before a novel rejectivist account is proposed according to which falsity is the aim of the speech‐act of denial, whilst negation (...) embeds deniability into assertoric contexts. (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)

This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form (...) the topic of this paper are more intricate than previously realised, and that they are related in delicate and somewhat surprising ways. (shrink)

Here is one argument against realism. (1) Realists are committed to the classical rules for negation. But (2) legitimate rules of inference must conserve evidence. And (3) the classical rules for negation do not conserve evidence. So (4) realism is wrong. Most realists reject 2. But it has recently been argued that if we allow denied sentences as premisses and conclusions in inferences we will be able to reject 3. And this new argument against 3 generates a new (...) response to the antirealist argument: keep 1 and 2, avoiding 4 by rejecting 3. My aim in this paper is to see how much work in the fight against anti-realism this new response can really do. I argue that there is a powerful objection to the response: 2 is in tension with the claim that denied sentences can be premisses and conclusions in inferences. But I show that, even given this objection, the new response has an important role to play. (shrink)

In this paper, I will first draw attention to the central fact that Freud describes in his article on “Negation”; i.e., “recognition of the unconscious on the part of the ego is expressed in a negative formula.” Technically, such a negative formula is called denial. Second, I will ask whether such denials are accidental or necessary in the life of consciousness. To answer this question I will use the philosophical system of Hegel. I will make use of his (...) ideas at two levels of generality. At the first level of generality, I will analyze one of Hegel’s most famous and influential passages: “Lordship and Bondage.” Hegel presents this passage as a necessary moment in the development of consciousness. If we find in that passage a necessary denial, then we can argue that denial is not just a fact but is, at least in any philosophical anthropology akin to Hegel’s, a necessity. At the second level of generality, we will then quote two statements by Hegel, one about the nature of the will and one about the path to truth for consciousness. Both statements will be clarified by Hegel’s analysis of “Lordship and Bondage.” Both statements will be used to demonstrate that Hegel affirmed explicitly the necessity of negativity in the life of consciousness. (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)

We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that (...) this interaction is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely. (shrink)

Pam is an eighteen-year-old with a history of depression. She has been hospitalized for the past six months for severe weight loss and dehydration. When admitted, she was diagnosed with acute inflammation of the pancreas and gall bladder, but it became clear that these issues were secondary to a diagnosis of anorexia nervosa. Her weight upon admission was seventy-six pounds. Pam refuses to accept this diagnosis and will not cooperate with any provider who refers to “anorexia” or attempts to discuss (...) her eating disorder. As a pragmatic strategy for providing care, the medical team has largely avoided referring to anorexia or eating disorders when treating her. But Pam is not the only problem. Pam’s.. (shrink)

"Articulating a fresh vision for teaching, one that focuses on ensuring justice, believing people, and believing in people, this how-to offers evidence-based insights and draws from the author's own rich experiences as a professor to provide practical tips for reshaping syllabi, assessing student performance, and creating trust and belonging in the classroom"-Provided by publisher.

We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in (...) such a language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438–445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one’s theory a shrieking rule of the form A & ~A |- \bot, where \bot entails triviality. We argue, however, that the proposal doesn’t work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists—an extension of the logic commonly called LP. (shrink)

Proponents of “truth-value glut” responses to the paradoxes of self-reference, such as Priest [6, 7] argue that “truth-value gap” analyses of the paradoxes fall foul of the strengthened liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that the situation with these approaches has a pleasing symmetry: gap approaches take some denials to fail to be expressible (...) by negation, and glut approaches take some negations to not express denials. But in the light of this symmetry, considerations against a gap view point to parallel considerations against a glut view. Those who find some reason to prefer one view over another (and this is almost everyone) must find some reason to break this symmetry. (shrink)

This short paper has two loosely connected parts. In the first part, I discuss the difference between classical and intuitionist logic in relation to different the role of hypotheses play in each logic. Harmony is normally understood as a relation between two ways of manipulating formulas in systems of natural deduction: their introduction and elimination. I argue, however, that there is at least a third way of manipulating formulas, namely the discharge of assumption, and that the difference between classical and (...) intuitionist logic can be characterised as a difference of the conditions under which discharge is allowed. Harmony, as ordinarily understood, has nothing to say about discharge. This raises the question whether the notion of harmony can be suitably extended. This requires there to be a suitable fourth way of manipulating formulas that discharge can stand in harmony to. The question is whether there is such a notion: what might it be that stands to discharge of formulas as introduction stands to elimination? One that immediately comes to mind is the making of assumptions. I leave it as an open question for further research whether the notion of harmony can be fruitfully extended in the way suggested here. In the second part, I discuss bilateralism, which proposes a wholesale revision of what it is that is assumed and manipulated by rules of inference in deductions: rules apply to speech acts – assertions and denials – rather than propositions. I point out two problems for bilateralism. First, bilaterlists cannot, contrary to what they claim to be able to do, draw a distinction between the truth and assertibility of a proposition. Secondly, it is not clear what it means to assume an expression such as '+ A' that is supposed to stand for an assertion. Worse than that, it is plausible that making an assumption is a particular speech act, as argued by Dummett (Frege: Philosophy of Language, p.309ff). Bilaterlists accept that speech acts cannot be embedded in other speech acts. But then it is meaningless to assume + A or − A. (shrink)

A number of different kinds of negation and negation of negation are developed in Indian thought, from ancient religious texts to classical philosophy. The paper explores the Mīmāṃsā, Nyāya, Jaina and Buddhist theorizing on the various forms and permutations of negation, denial, nullity, nothing and nothingness, or emptiness. The main thesis argued for is that in the broad Indic tradition, negation cannot be viewed as a mere classical operator turning the true into the false, (...) nor reduced to the mainstream Boolean dichotomy: 1 versus 0. Special attention is given to how contradiction is handled in Jaina and Buddhist logic. (shrink)

The central characteristic of denials is that they perform a non-monotonic correction operation on discourse structure. A second characteristic is that they may be used to object to various kinds of information including presuppositions and implicatures. In this paper we first use standard DRT to capture these features, implement an earlier proposal of van der Sandt (1991) in DRT and point out a shortcoming of that approach. We then adopt Layered DRT. LDRT is an extension of standard DRT designed to (...) represent and interpret different types of information conveyed in a conversation by distributing them over separate layers of the same LDRS. We will then show how LDRT allows us to solve the problems of the classic monostratal system. The resulting system makes use of a directed reverse anaphora mechanism to locate, remove and negate the material objected to. (shrink)

A cognitive pragmatic approach is taken to some long-standing problem cases of negation, the so-called presupposition denial cases. It is argued that a full account of the processes and levels of representation involved in their interpretation typically requires the sequential pragmatic derivation of two different propositions expressed. The first is one in which the presupposition is preserved and, following the rejection of this, the second involves the echoic (metalinguistic) use of material falling in the scope of the (...) class='Hi'>negation. The semantic base for these processes is the standard anti-presuppositionalist wide-scope negation. A different view, developed by Burton-Roberts (1989a, 1989b), takes presupposition to be a semantic relation encoded in natural language and so argues for a negation operator that does not cancel presuppositions. This view is shown to be flawed, in that it makes the false prediction that presupposition denial cases are semantic contradictions and it is based on too narrow a view of the role of pragmatic inferencing. (shrink)

The central characteristic of denials is that they perform a non-monotonic correction operation on discourse structure. A second characteristic is that they may be used to object to various kinds of information including presuppositions and implicatures. In this paper we first use standard DRT to capture these features, implement an earlier proposal of van der Sandt in DRT and point out a shortcoming of that approach. We then adopt Layered DRT. LDRT is an extension of standard DRT designed to represent (...) and interpret different types of information conveyed in a conversation by distributing them over separate layers of the same LDRS. We will then show how LDRT allows us to solve the problems of the classic monostratal system. The resulting system makes use of a di- rected reverse anaphora mechanism to locate, remove and negate the material objected to. (shrink)

In this short paper, I compare and contrast the kind of symmetric treatment of negation favoured in different ways by Huw Price (in “Why ‘Not’?”) and by me (in “Multiple Conclusions”) with Robert Brandom’s analysis of scorekeeping in terms of commitment, entitlement and incompatibility. Both kinds of account are what Brandom calls a normative pragmatics. They are both semantic anti-realist accounts of meaning in the significance of vocabulary is explained in terms of our rule-governed (normative) practice (pragmatics). These accounts (...) differ from intuitionist semantic anti-realism by providing a way to distinguish the inferential significance of “A” and “A is warranted.” Although proof plays a central role, in neither accont is verification the primary bearer of meaning. Our accounts make these distinctions in terms of a subtle analysis of our practices. On the one hand according to Price and me, we assert as well as deny; on the other, Brandom distingushes downstream commitments from upstream entitlements and the notion of incompatibility definable in terms of these. In this paper I will examine a number connections between these different approaches, and end with a discussion of the kind of account of proof that might emerge from these considerations. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: "MP", Affirmation of the Consequent "AC") and denial problems (Denial of the Antecedent "DA", and Modus Tollens "MT"). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there (...) generally are reliable effects of a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...) the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there (...) generally are reliable effects of a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Suppose Alice asserts p, and the Caterpillar wants to disagree. If the Caterpillar accepts classical logic, he has an easy way to indicate this disagreement: he can simply assert ¬p. Sometimes, though, things are not so easy. For example, suppose the Cheshire Cat is a paracompletist who thinks that p ∨ ¬p fails (in familiar (if possibly misleading) language, the Cheshire Cat thinks p is a gap). Then he surely disagrees with Alice's assertion of p, but should himself be unwilling (...) to assert ¬p. So he cannot simply use the classical solution. Dually, suppose the Mad Hatter is a dialetheist who thinks that p ∧ ¬p holds (that is, he thinks p is a glut). Then he may assert ¬p, but it should not be taken to indicate that he disagrees with Alice; he doesn't. So he too can't use the classical solution. The Cheshire Cat and the Mad Hatter, then, have a common problem, and philosophers with opinions like theirs have adopted a common solution to this problem: appeal to denial. Denial, these philosophers suppose, is a speech act like assertion, but it is not to be understood as in any way reducing to assertion. Importantly, denial is something different from the assertion of a negation; this is what allows it to work even in cases where assertion of negation does not. Just as importantly, denial must express disagreement, since this is the job it's being enlisted to do. (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 paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The (...) main result of this paper is a theorem establishing the completeness of the system with respect to inquisitive semantics with weak negation. At the conclusion of the paper, the possibility of extending the framework to the level of first order logic is briefly discussed. (shrink)

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)

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)

This paper discusses the concept of nothing (nothingness) from the point of logic and ontology (metaphysics). It is argued that the category of nothing as a denial of being is subjected to various interpretations. In particular, this thesis concerns the concept of negation as used in metaphysics. Since the Leibniz question ‘Why is there something rather than nothing?’ and the principle of sufficient reason is frequently connected with the status of nothing, their analysis is important for the problem (...) in question. Appendix contains a short critical analysis of Heidegger’s famous statement Das Nichts nichtet. (shrink)

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and (...) structured objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality. (shrink)

Negation can be considered a shared social action that develops since early infancy with very basic acts of refusals or rejection. Inspired by an approach to the embodiment of concepts known as Multiple Representation Theories, the present paper explores negation as an embodied action that relies on both sensorimotor and linguistic/social information. Despite the different variants, MRT accounts share the basic ideas that both linguistic/social and sensorimotor information concur to the processes of concepts formation and representation and that (...) the balance between these components depends on the kind of concept, the context, or the performed task. In the present research we will apply the MRT framework for exploring negation in Italian sign language. The nature of negation in LIS has been explored in continuity with the co-speech gesture where negative elements are encoded through differentiated prosodic and gestural strategies across languages. Data have been collected in naturalistic settings that may allow a much wider understanding of negation both in speech and in spoken language with a semi-structured interview. Five LIS participants with age range 30–80 were recruited and interviewed with the aim of understanding the continuity between gesture and sign in negation. Results highlight that negation utterances mirror the functions of rejection, non-existence and denial that have been described in language acquisition both in deaf and hearing children. These different steps of acquisition of negation show a different balance between sensorimotor, linguistic and social information in the construction of negative meaning that the MRT is able to enlighten. (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)

A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences (...) in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth. (shrink)

The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic theory (...) of negation; stable negation in logic programming; antirealism and falsity; and negation, denial, and language change in philosophical logic. Suited to scholars and graduate students in the fields of philosophy, logic mathematics, computer science, and linguistics. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

The not-self teaching is one of the defining doctrines of Buddhist philosophical thought. It states that no phenomenon is an abiding self. The not-self doctrine is central to discussions in contemporary Buddhist philosophy and to how Buddhism understood itself in relation to its Brahmanical opponents in classical Indian philosophy. In the Pāli suttas, the Buddha is presented as making statements that seem to entail that there is no self. At the same time, in these texts, the Buddha is never presented (...) as saying explicitly that there is no self. Indeed, in the one discourse in which he is asked point blank whether there is a self, he refuses to answer. Thus, the suttas present us with a fundamental philosophical and interpretive problem: if the Buddha denies the existence of the self, why does he not state this denial explicitly? This paper resolves the problem by explaining why and how the Buddha can argue in a way that entails metaphysical anti-realism about the self while also refusing to state explicitly that there is no self. (shrink)

This book argues that the meaning of negation, perhaps the most important logical constant, cannot be defined within the framework of the most comprehensive theory of proof-theoretic semantics, as formulated in the influential work of Michael Dummett and Dag Prawitz. Nils Kürbis examines three approaches that have attempted to solve the problem - defining negation in terms of metaphysical incompatibility; treating negation as an undefinable primitive; and defining negation in terms of a speech act of (...) class='Hi'>denial - and concludes that they cannot adequately do so. He argues that whereas proof-theoretic semantics usually only appeals to a notion of truth, it also needs to appeal to a notion of falsity, and proposes a system of natural deduction in which both are incorporated. Offering new perspectives on negation, denial and falsity, his book will be important for readers working on logic, metaphysics and the philosophy of language. (shrink)

There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no formal argument (...) against intuitionism from the bilateralist perspective. Price gives an informal argument for classical negation based on a pragmatic notion of belief, characterised in terms of the differences they make to speakers' actions. The main part of this paper puts Price's argument under close scrutiny by regimenting it and isolating principles Price is committed to. It is shown that Price should draw a distinction between A or ¬A making a difference. According to Price, if A makes a difference to us, we treat it as decidable. This material allows the intuitionist to block Price's argument. Abandoning classical logic also brings advantages, as within intuitionist logic there is a precise meaning to what it might mean to treat A as decidable: it is to assume A ∨ ¬A. (shrink)

Hegel’s theory of dialectic has long been a source of both endless confusion and bitter debate. It has, for instance, been oversimplified and characterized as the mechanical movement from thesis to antithesis to synthesis. In a similar vein, some philosophers in the analytic tradition have reproached Hegel’s notion of dialectic, claiming that it amounts to an outright and absurd denial of the law of contradiction. The dialectic has, moreover, been co-opted and developed by some of Hegel’s most impassioned critics (...) such as Marx and Kierkegaard. One of the most controversial aspects of Hegel’s theory of dialectic has been his perplexing doctrine of determinate negation, which has proven to be difficult for even the most sympathetic interpreters to make sense of. Determinate negation is Hegel’s way of referring to the positive aspect of the dialectic which makes the conceptual movement a constructive one and not a purely destructive or negative one. Although Hegel discusses his notion of determinate negation at some length in the Phenomenology, interpreters have traditionally gone to the Science of Logic in order to illustrate this doctrine. In this essay by contrast, I would like to discuss this difficult and disputed concept of determinate negation by means of an example drawn from the “Consciousness” chapter of the Phenomenology of Spirit. At the transition from “Sense-Certainty” to “Perception,” the first two sections of that chapter, Hegel describes explicitly the aspect of determinate negation that the dialectic evinces at that point, and it is this transition and this uncharacteristic passage that I wish to examine in some detail. In the first section of this essay, I will discuss Hegel’s notion of dialectic generally in order to pinpoint the role of determinate negation in relation to the dialectic’s other aspects. Then in the second section, I will proceed to analyze his account of determinate negation specifically, drawing on various passages throughout the Hegelian corpus. I will give a brief account of “Sense-Certainty” in my third section in order to set the context for the transition to “Perception.” Finally, in the fourth section, I will analyze this transition to “Perception” in terms of the doctrine of determinate negation. (shrink)

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. (shrink)

This paper discusses the notion of disimagination a translation of the German word Entbildung, which was devised by Meister Eckhart as a reinterpretation of the Neoplatonic categories of abstraction (aphairesis) and negation (apophasis) in connection with Nishitani Keiji's standpoint of emptiness. Nishitani proposes a nonsubjective, nonrepresentational, and nonconceptual type of knowledge to avoid the problem of representation implied in the modern subjective self-consciousness that prevents our access to the reality of things. It is argued that what he calls a (...) knowing of non-knowing can be understood as a transposition of the problematics of aphairesis to a new context, that of the formless form. The ontology of images in the creative process, both cosmic and artistic, is examined from Nishitani's identification of likeness and suchness on the field of emptiness. It is suggested that the resulting denial of the traditional distinction between being and appearance approaches a critique closer to postfoundational metaphysics and, like disimagination, aims at an ascetic movement of self-negation and detachment from words and images that leads, in turn, to a creative and playful use of language free of representation. (shrink)