The Negation Problem states that expressivism has insufficient structure to account for the various ways in which a moral sentence can be negated. We argue that the Negation Problem does not arise for expressivist accounts of all normative language but arises only for the specific examples on which expressivists usually focus. In support of this claim, we argue for the following three theses: 1) a problem that is structurally identical to the Negation Problem (...) arises in non-normative cases, and this problem is solved once the hidden quantificational structure involved in such cases is uncovered; 2) the terms ‘required’, ‘permissible’, and ‘forbidden’ can also be analyzed in terms of hidden quantificational structure, and the Negation Problem disappears once this hidden structure is uncovered; 3) the Negation Problem does not arise for normative language that has no hidden quantificational structure. We conclude that the Negation Problem is not really a problem about expressivism at all but is rather a feature of the quantificational structure of the required, permitted, and forbidden. (shrink)

We develop a novel solution to the negation version of the Frege-Geach problem by taking up recent insights from the bilateral programme in logic. Bilateralists derive the meaning of negation from a primitive *B-type* inconsistency involving the attitudes of assent and dissent. Some may demand an explanation of this inconsistency in simpler terms, but we argue that bilateralism’s assumptions are no less explanatory than those of *A-type* semantics that only require a single primitive attitude, but must stipulate (...) inconsistency elsewhere. Based on these insights, we develop a version of B-type expressivism called *inferential expressivism*. This is a novel semantic framework that characterises meanings by inferential roles that define which *attitudes* one can *infer* from the use of terms. We apply this framework to normative vocabulary, thereby solving the Frege-Geach problem generally and comprehensively. Our account moreover includes a semantics for epistemic modals, thereby also explaining normative terms under epistemic modals. (shrink)

This paper investigates an objection often raised against metaethical error theory. The challenge runs as follows. Metaethical error theory says that all substantive ethical sentences are false. But if a sentence p is false, then given a standard semantics for “not,” ¬p must be true, and vice versa. On the face of it, one can’t hold that p and ¬p are both false. After presenting a more refined version of the challenge (in the form of a set of initially plausible (...) and yet jointly inconsistent principles), the paper examines a common way out of the puzzle, finds it unsatisfactory, and offers some alternative escape routes that, it is submitted, fare better than the standard one. (shrink)

It has recently been alleged that expressivism cannot account for the obvious fact that normative sentences and their negations express inconsistent kinds of attitudes. I explain how the expressivist can respond to this objection. I offer an account of attitudinal inconsistency that takes it to be a combination of descriptive and normative relations. The account I offer to explain these relations relies on a combination of functionalism about normative judgments and expressivism about the norms governing them. It holds that the (...) inconsistency of normative judgments is primitive. One potential problem for this view is that the large number of normative primitives that the expressivist will allegedly need to accept will render the view grossly unparsimonious. In defending this thesis, I suggest that it is a mistake to hold the lack of normative parsimony of expressivism against its core psychological claims. (shrink)

A difficulty is exposed in Allan Gibbard's solution to the embedding/Frege-Geach problem, namely that the difference between refusing to accept a normative judgement and accepting its negation is ignored. This is shown to undermine the whole solution.

Expressivists, such as Blackburn, analyse sentences such as 'S thinks that it ought to be the case that p' as S hoorays that p'. A problem is that the former sentence can be negated in three different ways, but the latter in only two. The distinction between refusing to accept a moral judgement and accepting its negation therefore cannot be accounted for. This is shown to undermine Blackburn's solution to the Frege-Geach problem.

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)

The double negation has always been considered by the logical systems from ancient times to the present. In fact, that is an issue that the current syntactic theories studying human reasoning, for example, the mental logic theory, address today. However, in this paper, I claim that, in the case of some languages such as Spanish, the double negation causes problems for the cognitive theories mainly based on formal schemata and supporting the idea of a universal syntax of thought (...) in the human mind. Thus, I propose that, given those problems, semantic frameworks such as that of the mental models theory seem to be more appropriate for explaining the human inferential activity. (shrink)

This is only a very short essay on negation and harmony in philosophical logic. If you buy it anyway, you'll help me pay the bills and I'll be able to write longer things.

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the (...) meanings of modal operators in terms of rules of inference. (shrink)

Where is it written that only naming words, conceptual signs, language symbols can facilitate the sort of intersubjective communication about things which is necessary in human life? (Bühler, 1990: 120).

Solving expressivism’s Frege-Geach problem requires specifying the attitudes expressed by arbitrarily complex moral sentences. Nicholas Unwin emphasizes the problems that arise in doing so for even the relatively simple case of negated atomic sentences. Terry Horgan and Mark Timmons believe that contrary-forming predicate negation offers a solution to this negation problem. I argue that their solution is incomplete.

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

In this introduction to the Being of Negation in Post-Kantian Philosophy, I elucidate the problem of negation in classical Greek philosophy, Kant, and German Idealism. Inspired by the Platonic insight that any inquiry into non-being must impute non-being with the being of non-being, this book sets out to think the being of nothing. Whenever we ask ‘what is nothing?’ we are implicitly asking ‘what is it for nothing to be?’ To answer with a judgment of the form (...) ‘nothingness is such and such’ inevitably identifies the being of nothing. To think nothingness by itself cannot be achieved without introducing what nothingness is not—namely being. Thus, inquiries into nothingness turn back on themselves [παλίντροπός] in the manner of Heraclitus’ back turning harmony [παλίντροπος ἁρμονίη]. (shrink)

Many think that expressivists have a special problem with negation. I disagree. For if there is a problem with negation, I argue, it is a problem shared by those who accept some plausible claims about the nature of intentionality. Whether there is any special problem for expressivists turns, I will argue, on whether facts about what truth-conditions beliefs have can explain facts about basic inferential relations among those beliefs. And I will suggest that the (...) answer to this last question is, on most plausible attempts at solving the problem of intentionality, ‘no’. (shrink)

Frege-Geach worries about embedding and composition have plagued metaethical theories like emotivism, prescriptivism and expressivism. The sharpened point of such criticism has come to focus on whether negation and inconsistency have to be understood in descriptivist terms. Because they reject descriptivism, these theories must offer a non-standard account of the meanings of ethical and normative sentences as well as related semantic facts, such as why certain sentences are inconsistent with each other. This paper fills out such a solution to (...) the negation problems, following some of the original emotivist ideas about the interplay of interests in conversation. We communicate both to share information and coordinate our actions, and we use distinctively normative language like deontic ‘must’ and ‘may’ to negotiate what people are to do. The kinds of disagreement involved in such negotiation can illuminate the issues with negation and inconsistency. This paper outlines a dynamic semantic system in which these ideas can bear fruit, developing the scorekeeping model of conversation. The result is clarification about what Frege-Geach worries can mean for nondescriptive semantics. (shrink)

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a (...) constraint model, which includes relevant theories. These three modelings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning traditional negation and natural negation. Firstly, the dominant traditional view, except around scholastic times when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of much of traditional logic is distinctively nonclassical. Secondly, the primary negation determinable of natural negation is ·relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressive) refined, to nonexclusive restricted otherthanness. Several pictures result, a reversal picture, a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the Marxist tradition, the other on Wittgenstein's treatment of negation and contradiction. (shrink)

Selon certains philosophes, le principe « devoir-implique-pouvoir » exprime une vérité analytique et permet d’inférer des énoncés normatifs sur la base de prémisses purement descriptives. Le principe DIP offrirait ainsi un contre-exemple à la fameuse loi de Hume. Le problème est que DIP permet uniquement de construire des raisonnements dont les conclusions sont des négations de normes. Or, selon certains auteurs, les négations de normes n’expriment pas de véritables jugements moraux. En ce sens, selon eux, DIP ne permet pas de (...) tirer des conclusions normatives sur la base de prémisses uniquement descriptives. Dans cet article, nous soutenons au contraire que les négations de normes sont de véritables normes et que DIP permet bien de déduire une conclusion normative à partir de prémisses purement descriptives. (shrink)

The final part of Schopenhauer’s argument in The World as Will and Representation concerns “affirmation and negation of the will”. He argues, with a fervor that borders on the religious, that “negation of the will” is a condition of unique value, the only state that enables “true salvation, redemption from life and from suffering”. Some commentators have asserted without qualification that this condition is his “highest good.” However, Schopenhauer in fact claims that there cannot be a highest good, (...) because 'good' is always relative to sstisfaction of a will, and there is no possible final satisfaction of the will. It is only figuratively the will-lessness is the highest good. The article examines the coherence of Schopenhauer's position. Because of the relation of 'good' to willing, he appears reluctant to call will-lessness 'good' at all, despite rating it a state of superior value. The article suggests that Schopenhauer should either abandon his univocal account of 'good' as related to willing, or accept that things can be good in relation to different kinds of willing, namely egoistic and non-egoistic willing. It is argued that the latter resolution if preferable. (shrink)

Last year (2005) marked the 100th anniversary of the publication of Russell’s classic ‘On denoting’. It should not cast any shadow on that great work to note that the problems it provided solutions to are still the subject of controversy. Two of those problems involved noun phrases (NPs) which fail to denote. Russell’s examples (1a) and (1b) (1) a. The king of France is bald. b. The king of France is not bald. are puzzling because they have the form of (...) simple contradictories, and yet we are not inclined to say either one is true. Example (2) (2) Pegasus does not exist. is even more problematic; the lack of denotation for Pegasus, which makes the sentence true, also seems to rob it of a meaningful constituent. Once the king of France is unpacked according to Russell’s analysis, (1b) is revealed to be ambiguous. It’s logical forms are given in (3). (3) a. ∃x[Kx ∧ ∀y[Ky ↔ y=x] ∧ ¬Bx] b. ¬∃x[Kx ∧ ∀y[Ky ↔ y=x] ∧ Bx] (3a) says that there is a unique (French) king who is not bald (obviously false), but (3b), the logical contradictory of (1a) says that it is not the case that there is a unique king who is bald (which is true). We can apply the analysis to sentence (2) once we recognize Pegasus as a concealed definite description, e.g. the winged horse of Greek mythology. (2) can then be unpacked as (4) (4) ¬∃x[Wx ∧ ∀y[Wy ↔ y=x]] which seems both meaningful and true, as required. Problems solved. Well, not quite. Strawson (1950) challenged the first solution above, arguing that neither (1a) nor (1b) could be used to assert the existence of a king of France. Rather, use of such sentences presupposes the existence of a king of France, and failing that existence, neither of (1a) or (1b) could be used to make either a true or a false statement – in Strawson’s words, “the question of whether it’s true or false simply doesn’t arise” (Strawson 1950, 330).1 In an extended series of essays, and one book, Jay Atlas (1977, 1978, 1979, 1989, 2004) has taken issue with the work of both Russell and Strawson.. (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 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)

J?aimerais interroger ici le problème de la négation de la vie à partir de certains textes de Michel Henry consacrés à Friedrich Nietzsche dans Généalogie de la psychanalyse . Par négation de la vie, Michel Henry désigne l?ensemble des modes de vie que nous pouvons ramener sous le projet de rompre avec la vie. Il emprunte à Friedrich Nietzsche des exemples tels que le doute à l?égard de soi, l?objectivisme, le scientisme, la critique de soi, la mauvaise conscience et une (...) figure devenue l?archétype de la négation, celle du prêtre. Le prêtre est l?homme qui tourne le dos à la vie, qui l?infirme et qui la nie pour aspirer à un au-delà, un ailleurs, une autre vie. Naïvement, le problème de la négation se formule de la manière suivante : l?individu peut-il se tourner contre la vie et la nier ? Pour répondre à cette première question, il me faut reprendre sommairement les principaux aspects de l?articulation de la vie et de la conscience telle qu?elle ressort des analyses des textes de Nietzsche par Michel Henry. Premièrement, la conceptualisation henryenne de l?articulation de la vie et de la conscience repose sur une idée fondamentale : « La vie, en tant que se supportant soi-même », en tant que s?éprouvant soi-même dans tout ce que l?individu est amené à vivre est un « a priori insupportable 1 . » Dans Du communisme au capitalisme , Henry revient sur cet être-rivé à soi de la vie : pure présence à. (shrink)

This chapter contains sections titled: Negation and Nonexistence Designation and Existence Logical Truth, Modality, and Ontology.

Schelling and Nishitani both confront the problem of absolute negation in post-Kantian philosophy and drive it beyond its eventual development into existentialism. This essay seeks not so much to sort out all of the similarities and contrasts between these two thinkers on this issue but rather to consider the issue of absolute negation itself and to consider it in and between the two thinkers as a gateway to an ontological conversion, a transformation into the positive manifestation of (...) beings just as they are. Just as access to Dante’s paradisio demands that one first traverse through the inferno, or as the rebirth in Zen of heaven and earth requires the Great Doubt and the Great Death, we must plunge into the depths of absolute negation. Yet this descent is not an end itself, but rather the opening to a new image of thought and a new sense of philosophy. (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 paper consists of two parts. In the first one I present some general remarks regarding the history of negation and attempt to answer the philosophical question concerning the essence of negation. In the second part I resume the theological teaching on the degrees of certainty and point to five forms of negation – known from other areas of research -- as applied in the framework of theological investigations.

There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto, 761–793, 2015) defends at length in a recent paper. According to one such modal account, (...) the negation of a sentence is true at a world x just in case all the worlds at which the sentence is true are incompatible with x. Incompatibility is taken to be the key notion in the account, and what minimal properties a negation has comes down to which minimal conditions incompatibility satisfies. Our aims in this paper are twofold. First, we wish to point out problems for the modal account that make us question its tenability on a fundamental level. Second, in its place we propose an alternative, non-modal, account of negation as a contradictory-forming operator that we argue is superior to, and more natural than, the modal account. (shrink)

The negation constitutes one of the main troubles for attempts to naturalise the semantics of the logical vocabulary, as shown by the problems related to the interpretation of disjunction in the treatment of error (Fodor) or to the definition of contraries in the analysis of reidentification abilities (Millikan). There seems to be no way out between “no (naturalized) negation, no grip of logic on the world” and “no (truth-functional) negation, no logic”. Unexpected help may come from the (...) cognitive phenomenology of negation. For three reasons: • Firstly, because it allows a distinction to be made between semantic analysis, identification of the possession conditions and psychology of the acquisition of the notion of negation, a distinction whose absence produces many misunderstandings between those who support a naturalization of semantics and those who oppose it. • Then because it places negation at the level of the contrast between beliefs, a terrain that is hostile to some naturalizers. • Finally, because it makes it possible to define a peculiar type of liberalised naturalization of semantics and, consequently, to present a hypothesis for the naturalization of cognitive phenomenology. (shrink)

This paper advances three necessary conditions on a successful account of sentential negation. First, the ability to explain the constancy of sentential meaning across negated and unnegated contexts (the Fregean Condition). Second, the ability to explain why sentences and their negations are inconsistent, and inconsistent in virtue of the meaning of negation (the Semantic Condition). Third, the ability of the account to generalize regardless of the topic of the negated sentence (the Generality Condition). The paper discusses three accounts (...) of negation available to moral expressivists. The first—the dominant commitment account—fails to meet the Fregean Condition. The two remaining accounts—commitment semantics and the expression account—satisfy all three conditions. A recent argument that the dominant commitment account is the only option available to expressivists is considered and rejected. (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)

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)

The paper is concerned with negation in artificial and natural languages. "Negation" is an ambiguous word. It can mean three different things: An operation(negating), an operator (a sign of negation), the result of an operation. The threethings, however, are intimately linked. An operation such as negation, is realizedthrough an operator of negation, i.e. consists in adding a symbol of negation to an entity to obtain an entity of the same type; and which operation it (...) is dependson what it applies to and on what results from its application.I argue that negation is not an operation on linguistic acts but rather anoperation on the objects of linguistic acts, namely sentences. And I assume that the negation of a sentence is a sentence that contradicts it. If so, the negation of a sentence may be obtained, in case the sentence is molecular, by applying the operation of negation not to the sentence itself but to a constituent sentence. To put it in a succinct and paradoxically sounding way we could say that in order to negate a sentence it is sufficient but not necessary to negate it.However that negation applies to sentences is true only for artificial languages, in which the sign of negation is a monadic sentential connective. In natural language, negation applies to expressions other than sentences, namely word sand non-sentential phrases. Still words and not sentential phrases are interesting and valuable only as ultimate or immediate constituents of sentences, as a means of saying (something that can be true or false) and the concern with negation is ultimately the concern with the negation of sentences. So the problem is what sub-sentential and non sentential expressions negation should apply to in order to obtain the negation of the containing sentence. The standard answer is that the negation of a natural language sentence is equivalent to the negation of its predicate. Yet, I argue, predicate negation is necessary but not sufficient, due to the existence of molecular sentences.Finally I notice that if to apply negation to an artificial sentence is to put the negation sign in front of it, to negate the predicate of a natural language sentencemay or may not be to put the negation sign in front of it. (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)

I resolve the major challenge to an Expressivist theory of the meaning of normative discourse: the Frege–Geach Problem. Drawing on considerations from the semantics of directive language (e.g., imperatives), I argue that, although certain forms of Expressivism (like Gibbard’s) do run into at least one version of the Problem, it is reasonably clear that there is a version of Expressivism that does not.

In order to understand negation as such, at least since Aristotle’s time, there have been many ways of conceptually modelling it. In particular, negation has been studied as inconsistency, contradictoriness, falsity, cancellation, an inversion of arrangements of truth values, etc. In this paper, making substantial use of category theory, we present three more conceptual and abstract models of negation. All of them capture negation as turning upside down the entire structure under consideration. The first proposal turns (...) upside down the structure almost literally; it is the well known construction of opposite category. The second one treats negation as a contravariant functor and the third one captures negation as adjointness. Traditionally, negation was investigated in the context of language as negation of sentences or parts of sentences, e.g. names. On the contrary we propose to negate structures globally. As a consequence of our approach we provide a solution to the ontological problem of the existence of negative states of affairs. (shrink)

One of the oldest inquiries of philosophical and theological thought is addressed to the question who or what "God" is. Negative theology provides a way of answering that question by identifying what God is not. In recent years certain critical trends, such as deconstruction, have resembled features of negative theology in that they cancel the apparent meanings of the written word. Similarly, the Buddhist concept of nothingness has raised questions about the meaning of negation and theism. These trends have (...) caused philosophers and theologians to reconsider negation and theology in new ways, which are explored in this collection. In Negation and Theology a group of distinguished philosophers and theologians take up issues that illuminate the character of negative thinking and seek to make connections both with traditional negative theologies and with current theological and philosophical discussions. One essay, for example, is concerned with the problem of reconciling Paul Tillich's statement that God is being-itself with the Buddhist conception of an ultimate nothingness or with the tradition of negative theology. The format of the book distinguishes it from mere collections of essays. Scharlemann assumes the role of editor, introducer, and interlocutor, questioning the contributors and allowing them to respond. (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.

By 1929, after the full acknowledgment of the colour–exclusion problem, Wittgenstein had to admit that material incompatibilities presented in conceptual systems could not be reduced to formal tautologies and contradictions. Wittgenstein then, in his middle period, had to examine the kind of negation which, for instance, colour systems should render, which expose not just one but many or, in some cases, infinite inferentially articulated alternatives. Here, inspired by Brandom’s inferentialism, I explore the idea that Wittgenstein, in his middle (...) period, advocated a form of inferentialism based on the inferentially articulated content of propositions in Satzsysteme. At that time, Wittgenstein suggested that every sentence should be logically connected to many others. I call this feature inferential thickness. Therefore, I use Löf’s normative read of verificationism to explain Middle Wittgenstein’s holist solution to problems concerning the use of negation related to material incompatibilities and determination of propositional sense. I also investigate the distinction between contrariety and contradiction and some possible connections to a mandatory restriction of the principle of excluded middle in Satzsysteme. (shrink)