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)

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)

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)

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).

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)

Critical theory of technology (CTT) and postphenomenology (PostPhen) complement each other finely. Yet whereas CTT runs the risk of negating the interwovenness of humans and technology, a problem partly resolved by PostPhen, PostPhen itself threatens to neglect its very own base, i.e., the condition of technology and society being first and foremost human endeavors. This paper suggests not to decry these two approaches but to add a third component in order to compensate for their deficiencies. That third partner consists (...) of a new-fledged version of philosophical anthropology elaborated on the basis of the media theory of Marshall McLuhan. I am here mainly concerned with how such an approach can supplement CTT, which it does by offering an account of technological mediation that harbors not only a relational-ontological but also—in contrast with PostPhen—a substantivist-ontological aspect, and in addition a proper theory of technological blindness, much needed to make sense of perceptive biases and meaning-constituting activities in everyday life. I will illustrate these issues by way of what I dub ‘the Mailman Problem’: a sketch of a very mundane instance of “deworlding” that is, however, not perceived as such. (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)

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)

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)

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.

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)

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen (2008) argues that this view - call it logical inferentialism - is undermined by some "very little known" considerations by Carnap (1943) to the effect that "in a definite sense, it is not true that the standard (...) rules of inference" themselves suffice to "determine the meanings of [the] logical constants" (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that "no ordinary formalization of logic ... is sufficient to `fully formalize' all the essential properties of the logical constants" (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists - as proposed by Timothy Smiley and Ian Rumfitt - seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too. (shrink)

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.

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.

The philosophical manifestos of the past few decades involving attempts to go beyond constructs, discourses, and structures to the things themselves and a return to ontology and materialism often address the problems of the Anthropocene. Criticism of anthropocentrism and the introduction of the nonhuman into the focus of philosophy opened up new perspectives in solving the problems of idealism. This escape from the discursive aspect and the human factor, which is intended to break out philosophical projects to the outside, to (...) what is on the other side of culture and language, to the planet, to matter, is accompanied by sequences of negations. Exploring the outer edge of philosophy, the periphery of culture, dark and marginal subjects, these authors try to construct a kind of anti-discourse, a nonphilosophy. In order to unlock the nonthinkable, what is being proposed to us is an exploration of objects that philosophical thought has heretofore ignored. The path to the nonhuman and nonthinkable lies through nonphilosophy. This article attempts to analyze such negations. It analyzes the function of negation by turning to psychoanalytic theory, in which the examination and modification of negation is one of the key themes. The principal mechanism of analysis is the modified logic of the psychoanalyst Jean Michel Vappereau. But the classical modifications of negation of Sigmund Freud and Jacques Lacan are also considered. The article’s central question—how does one interpret the negation in a human’s turning to the nonhuman, of philosophy to nonphilosophy, of an act of thought to the nonthinkable—is resolved in two ways, which constitute the two sections of the article. The results of the analysis open up obscure ways of interpreting such philosophical manifestos. (shrink)

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 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.

Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to identify (...) truth-value gaps. Method A consists in collecting both truth judgments and, independently, falsity judgments. The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent. We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value. (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 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.

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen argues that this view—call it logical inferentialism—is undermined by some “very little known” considerations by Carnap (1943) to the effect that “in a definite sense, it is not true that the standard rules of inference” themselves suffice (...) to “determine the meanings of [the] logical constants” (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that “no ordinary formalization of logic [... ] is sufficient to ‘fully formalize’ all the essential properties of the logical constants” (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap’s problem. And although bilateral solutions for classical inferentialists—as proposed by Timothy Smiley and Ian Rumfitt—seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too. (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.

The aim of this paper is to show that the binary notions of reality and negation play an important role in the philosophical agenda of Kant, Maimon and Fichte. The paper has three sections. The first section illustrates the metaphysical significance of Kant’s introduction of the quantitative opposition between reality and negation, which informs the phenomena-noumena distinction and the attribution of intensive magnitude. The second section argues that Maimon’s speculative appropriation of differentials took up Kant’s conception of real (...) opposition between reality and negation but fundamentally revised the theory of space and time to dissolve the problem of applicability in Kant, leading to the consequence of obliterating the pure categories. The third section shows how Fichte inherited the Kantian-Maimonian quantitative opposition of reality and negation in his characterization of the interdetermination between the I and the Not-I and how he developed an immanent account of the relational categories such as causality and substantiality on that basis. (shrink)

The aim of this paper is to show that the binary notions of reality and negation play an important role in the philosophical agenda of Kant, Maimon and Fichte. The paper has three sections. The first section illustrates the metaphysical significance of Kant’s introduction of the quantitative opposition between reality and negation, which informs the phenomena-noumena distinction and the attribution of intensive magnitude. The second section argues that Maimon’s speculative appropriation of differentials took up Kant’s conception of real (...) opposition between reality and negation but fundamentally revised the theory of space and time to dissolve the problem of applicability in Kant, leading to the consequence of obliterating the pure categories. The third section shows how Fichte inherited the Kantian-Maimonian quantitative opposition of reality and negation in his characterization of the interdetermination between the I and the Not-I and how he developed an immanent account of the relational categories such as causality and substantiality on that basis. (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)

Among the many fundamental problems Wittgenstein discussed, two are especially relevant for evolutionary theory. The first one is the problem of negation and its relation to the intentionality of thought. Its resolution answers the question of how thought can anticipate reality though what is thought may not exist, and explains how empirical propositions are distinguishable from mathematical, logical, and conceptual (or what are traditionally called metaphysical) propositions. The second is the problem of the grounds of sensory experience. (...) Wittgenstein’s resolution of this problem is revolutionary since he showed that first-person, present-tense expressions (these are sentences by which we express what goes on in our mind) have no grounds at all, clarifying why we should abandon (all variants of) representative idealism. In combination with the resolution of the first problem, it enables us to develop new explanations about how during the course of development and evolution the mind evolves and evolved. (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)

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)

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)

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)

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)

I address the problem of how Socrates can claim his elenchus, or refutation, establishes the falsehood of his interlocutor's initial claim, when all it seems to do is show that the initial claim is inconsistent with other beliefs that the interlocutor expresses in the argument. ;To address this problem, I first uncover its fundamentals, including its central issue and main assumptions. This is an epistemological problem, the central issue of which is how Socrates thinks he and the (...) interlocutor are justified in thinking that the auxiliary premises in his elenctic arguments are true. If they have the requisite justification for the auxiliary premises, then they have the requisite justification that the interlocutor's initial claim is false. Second, I argue that the main assumptions of the problem are justified and thereby argue that there is a legitimate problem that needs to be solved. Third, I argue that this problem has not been adequately solved. Fourth, I argue for my own original solution. ;My solution is that in cases within the scope of the problem, Socrates and the interlocutor agree to the auxiliary premises under two important conditions: they both aim to acquire truth and avoid error,1 and they both say what they really think. When they agree under these conditions, Socrates thinks they secure from each other corroborative agreement: they both check with each other that their judgements about that to which they agree have objectivity. Socrates' fundamental epistemic intuition is that agreement under these conditions amounts to something regarding justification for that upon which they agree; we can't expect to make any philosophical progress at all unless we thought that our agreements under these conditions stood for something. ;This solves the problem because Socrates and the interlocutor disagree about the initial claim, but they have corroborative agreement to the auxiliary premises, which gives both Socrates and the interlocutor the requisite justification for them. Since the auxiliary premises imply the negation of the initial claim, both Socrates and the interlocutor can justifiably think that the elenctic argument establishes the falsehood of the initial claim. ;1This condition is similar to one proposed by Keith Lehrer , 130), as are other insights that provided inspiration for the solution presented here. (shrink)

In a series of studies children show increasing mastery of irregular plural forms (such as mice) simply by producing erroneous over‐regularized versions of them (such as mouses). We explain this phenomenon in terms of successive approximation in imitation: Children over‐regularize early in acquisition because the representations of frequent, regular plural forms develop more quickly, such that at the earliest stages of production they interfere with children's attempts to imitatively reproduce irregular forms they have heard in the input. As the strength (...) of the representations that determine children's productions settle asymptotically, the early advantage for the frequent regular forms is negated, and children's attempts to imitate the irregular forms they have observed become more likely to succeed (a process that produces the classic U‐shape in children's acquisition of plural inflection). These data show that children can acquire correct linguistic behavior without feedback in a situation where, as a result of philosophical and linguistic analyses, it has often been argued that it is logically impossible for them to do so. (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)

Michel Henry’s critique of barbarism,1 understood as a flight from life, almost immediately raises the question of how life’s tendency to negate itself is then to be overcome. Undoubtedly, such a question refers to ethics. Although Henry not only provides an analysis of civilization and its malaise, but also targets the level of the individual through the concept of despair inspired by Kierkegaard, there is no systematic treatment of ethics to be found in his phenomenology of life.2,3 In light of (...) the diagnosis of barbarism, it is therefore necessary to investigate what ethics would be contained in, or follow from, Henry’s phenomenology. And if the essence of life is to be found in immanent affectivity, the questions thus become: is there an “ethics of affectivity” and, if so, which are its main aspects? The purpose of this article is to give an overview of ethics from the standpoint of Henry’s radical phenomenology and to discuss some of the main problems it implies. The opposition of barbarism and culture is essential in order to understand Henry’s distinction between ethos and normative ethics, but it is only intelligible if one refers to immanent affectivity as the key-concept of his phenomenology. As we will see, it is the lack of recognition of immanent life as fundamental phenomenality that makes barbarism possible, a recognition that is therefore central to phenomenology of life as ethics and to the concept of “second birth.” However, since phenomenology is, as theory, tied to intentionality, how can it become indicative of that which escapes intentionality, and how can it provide a truth-criterion for propositions that refer to affectivity as invisible? As the access to the transcendental becomes both an ethical and a theoretical problem, it is necessary to investigate how a radicalised reduction can be performed with regard to three interrelated aspects that are central to human life and therefore to ethics: community, personhood, and action. The analysis of action in particular shows Henry’s reductive move at work, while also facing the problem of articulating transcendence with immanence. His radicalised concept of personhood reveals the same features as those contained in his approach to action: they both combine affectivity and intentionality, but limit the reality of personhood and action to their affective core. (shrink)

This study, under the title of an explanation of the New Nyäya views on negation, deals with the Navya-nyäya as a whole. The peculiarity of their theory of negation is that one can see the absence of an object in a given place. It includes the Sanskrit texts and translations of the Abhäva-väda of Gangesa and the Nañ-väda of Raghunätha. Though written for both Sanskritists and philosophers, the frequent use of Sanskrit terms almost requires that the reader be (...) a Sanskritist--though by keeping in mind the translations, previously given, it could be valuable. This is not an exposition of logic for beginners, but an exposition for scholars of a particular system. Renditions into modern logic are given throughout. Chapter headings include: On Cognition; The Content of Cognition and the Meaning Problem; On Relation; The Counterpositive of an Absence; The Ontological Status of Content-ness; The Relational Adjuncts; The Limitors and Quantificational Logic; Circularity; On Negation.--P. J. H. (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 lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.4 (2003) 559-560 [Access article in PDF] Elmar J. Kremer and Michael J. Latzer, editors. The Problem of Evil in Early Modern Philosophy. Toronto: University of Toronto Press, 2001. Pp. vi + 179. Cloth, $60.00. What can be added to classical defenses of the problem of evil? Did Voltairenotrelieve us from taking seriously the theodicies of early modern thinkers in Candide (...) when Pangloss avers that spectacles exist because noses were made to support them? Do we not rightfully regard Malebranche's ingenious appeal to God's simplicity and uniformity to explain malformed offspring as little more than a curiosity? Yet, the editors of this volume claim that the "theodicy problem was no mere idle puzzle of dogmatics, but a problem of immense social significance, a problem which cut to the heart of the philosophical and theological projects of the very best minds of the age" (5). Several essays in this volume bear out the editors' claim, and to a modern reader, show how the problem of evil was intricately woven into the philosophical ideas of early modern thought.The problem of evil is especially acute for many of the seventeenth-century authors surveyed in this volume who held that God is the total and efficient cause of the universe. God's constant involvement in physical events meant that defects, deformities, and natural disasters fell into the framework of the traditional problem of evil. Hence, physical evil became the preoccupation of natural philosophers and theologians alike. We learn that Leibniz, Malebranche, and Spinoza chose to limit God's will rather than His wisdom, whereas Descartes opted to limit God's wisdom. The odd man out is Bayle who crafted a third position that emphasized God's benevolence at the expense of His wisdom and will.The essays found in this volume are just a sampling of views in the period, but it is more than a good start. Freddoso's essay on Francisco Suarez sets the tone for the problem of explaining the causal origin of human evil. Freddoso shows how Suarez distinguished concurrent from original causes in order to credit God for His supreme causal role yet absolved Him of blame for the existence of moral defectiveness. Latzer, in his essay on Rene Descartes, perhaps overstates the case in attributing to Descartes a theodicy grander than that of Leibniz, but he draws on the Fourth Meditation account of error to provide a plausible and nuanced reconstruction of his views on evil.There are two essays on Baruch Spinoza. Hunter's essay lays out an argument for Spinoza as a radical Christian reformer touching on Spinoza's views on providence. Nadler notes in his essay that Spinoza ought to have rejected the whole question of theodicy as incoherent, but shows how the matter is a good deal more complicated. Nadler then introduces us to the Medieval Jewish tradition, from which Spinoza is said to have drawn his views leading to a denial of personal immortality. [End Page 559]Moreau's essay on Nicholas Malebranche is rich in historical context and philosophical interpretation. Malebranche is shown to be a critical and original thinker on the problem of evil. Moreau lauds Malebranche's philosophical and moral courage in his bold assertion that physical evil is not a negation but rather a real phenomenon requiring explanation.Larivière and Lennon argue that Bayle held a third position rarely seen in the period: that God's benevolence trumps considerations of both His wisdom and will. Bayle develops a "moral solution" to the problem of evil wherein God's benevolence requires that humans possess an autonomy of conscience whose exercise makes error and heresy morally possible and justifiable.The final three essays in the volume rightly focus on aspects of Leibniz's response to the problem of evil. Kremer shows how, in the case of Leibniz's treatment of the fate of infants who die unbaptized, Leibniz abandons the Augustinian approach to the problem of evil and calculates the fate of all creatures on the basis of what produces... (shrink)

In 2004, Garrett Cullity made a significant contribution to the literature on what the world’s relatively affluent owe to the world’s relatively poor through the publishing of The Moral Demands of Affluence. In this discussion note, I draw attention to a logical problem in Cullity’s master argument in favor of the view that affluent individuals are justified in spending monetary resources on themselves at a level that lies well above what Peter Singer finds justified. The proposition I defend is (...) that the premises leading to Cullity’s conclusion about the moderate, and not extremely demanding, nature of his position are inconsistent. These premises license any conclusion, including the negation of the one preferred by Cullity. (shrink)

Various philosophers have long since been attracted to the doctrine that future contingent propositions systematically fail to be true—what is sometimes called the doctrine of the open future. However, open futurists have always struggled to articulate how their view interacts with standard principles of classical logic—most notably, with the Law of Excluded Middle. For consider the following two claims: Trump will be impeached tomorrow; Trump will not be impeached tomorrow. According to the kind of open futurist at issue, both of (...) these claims may well fail to be true. According to many, however, the disjunction of these claims can be represented as p ∨ ~p—that is, as an instance of LEM. In this essay, however, I wish to defend the view that the disjunction these claims cannot be represented as an instance of p ∨ ~p. And this is for the following reason: the latter claim is not, in fact, the strict negation of the former. More particularly, there is an important semantic distinction between the strict negation of the first claim [~] and the latter claim. However, the viability of this approach has been denied by Thomason, and more recently by MacFarlane and Cariani and Santorio, the latter of whom call the denial of the given semantic distinction “scopelessness”. According to these authors, that is, will is “scopeless” with respect to negation; whereas there is perhaps a syntactic distinction between ‘~Will p’ and ‘Will ~p’, there is no corresponding semantic distinction. And if this is so, the approach in question fails. In this paper, then, I criticize the claim that will is “scopeless” with respect to negation. I argue that will is a so-called “neg-raising” predicate—and that, in this light, we can see that the requisite scope distinctions aren’t missing, but are simply being masked. The result: a under-appreciated solution to the problem of future contingents that sees and as contraries, not contradictories. (shrink)

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)

Since Fodor 1970, negation has worn a Homogeneity Condition to the effect that homogeneous predicates, ) denote homogeneously—all or nothing —to characterize the meaning of – when uttered out-of-the blue, in contrast to –:The mirrors are smooth. The mirrors are not smooth. The mirrors circle the telescope’s reflector. The mirrors do not circle the telescope’s reflector. It has been a problem for philosophical logic and for the semantics of natural language that – appear to defy the Principle of (...) Excluded Middle while – do not—Smooth ¬Smooth Circle ¬Circle. An impoverished logical form – has been the occasion to embellish all else—Boolean algebra, lexical presuppositions, Strongest Meaning Hypothesis, trivalence, supervaluation, double strengthening, etc., enriching the semantics and pragmatics with what remains a special theory of negation, which may be dismissed when the logical syntax and semantics of negation reflects that negated sentences are also tensed sentences. (shrink)

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.

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)