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)

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)

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.

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)

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)

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.

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)

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)

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.

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)

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)

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)

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)

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)

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)

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.

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)

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 formalizing the problem of mental causation, we first prove rigorously that the premises of the problem are jointly incompatible. Before the background of the formalizations, we clarify and assess the anti-physicalist argument by Scott Sturgeon and the supervenience argument by Jaegwon Kim. We demonstrate that, contrary to what has sometimes been contended, the negation of the non-identity premise of Kim's version of the supervenience argument is not tantamount to the claim that all mental events are identical (...) to physical events, that a premise implicitly invoked by Kim is actually required for the validity of the first stage of his supervenience argument, that precisely this premise makes an epiphenomenalism with respect to mental events an impossible position, and that there are good reasons to believe in the falsity of this implicit premise which in turn shows that Sturgeon's critique of the supervenience argument is substantive. (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)

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.

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 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)

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)

A theory of substructural negations as impossibility and as unnecessity based on bi-intuitionistic logic, also known as Heyting-Brouwer logic, has been developed by Takuro Onishi. He notes two problems for that theory and offers the identification of the two negations as a solution to both problems. The first problem is the lack of a structural rule corresponding with double negation elimination for negation as impossibility, DNE, and the second problem is a lack of correspondence between certain (...) sequents and a characterizing frame property. While the identification of negation as impossibility and negation as unnecessity does solve Onishi’s problems, in general it nevertheless seems desirable to keep the two notions separate. The present paper addresses the first problem by introducing a reformulation of Onishi’s display sequent calculus in a language of sequents that incorporates Boolean negation. Instead of identifying negation as impossibility and negation as unnecessity, a notion of weak frame correspondence is defined. It is observed that DNE weakly corresponds with a certain frame property, and two structural sequent rules are presented that together also weakly correspond with that frame property and allow one to derive DNE. Moreover, the reformulated display calculus has an independent motivation by considerations on proof-theoretic semantics. (shrink)

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

In the following, limiting ourselves to two objects—the processes X and Y—we will compare three kinds of regularities in their specific manifestation in physics: interaction; causality; and functional dependence. In considering as objective all the regularities which are inherent in things and material processes themselves, and in considering causality and functional dependence merely as one-sided abstractions of interaction, which in its turn is an abstraction from the universal interconnection of things, we avoid such an arbitrary definition of causality as, for (...) instance, the possibility of exact prognosis which leads to the negation of causality. We also avoid placing functional dependence above causality. (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)

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)

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)

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)

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)

In print, the central objection to expressivism has been the Frege–Geach problem. Yet most cognitivists seem to be motivated by “deeper” worries, ones they have spent comparatively little time pursuing in print. Part of the explanation for this mismatch between motivation and rhetoric is likely that those deeper worries are largely metaphysical. Since expressivism is not a metaphysical view, it can be hard to see how to mount a relevant attack. The strategy in this chapter is to introduce claims (...) about thought and language, rather than metaphysics, that represent common intuitions about normative objectivity. It then argues that popular forms of expressivism cannot accommodate these claims if they are to solve the negation problem—an aspect of Frege–Geach. If successful, this shows that expressivism really does have a problem accommodating normative objectivity. But, significantly, it does so without requiring any assumptions about what expressivist metaphysics look like. (shrink)

Negation is widely thought to be uniquely captured by the usual extensional Boolean connective in the setting of classical logic. However, there has been recent interest in a modal approach to negation. This essay examines the problem of modal negation with an Husserlian phenomenological lens. I argue that the Husserlian approach to negation contains an ambiguity which points to a pluralism about negation. On this view, negation begins its life as a modal notion (...) with nonclassical properties, and the question of classical negation is a question of its demodalization. I reconstruct a phenomenological legitimation of the demodalization, but I remain skeptical about its wider prospects. Nevertheless, the phenomenological-modal approach to negation answers the skepticism about the very possibility of debates about negation and gives valuable insight into the fundamental nature of the problem. The argument should be of interest both to those who are specifically interested in Husserl's logic and the relationship of phenomenology to intuitionistic (and other nonclassical) logics, as well as to philosophers of logic more generally interested in obtaining different angles on the problem of negation from a systematic perspective. (shrink)

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. (...) Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nāgārjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nāgārjuna’s logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus ponens as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir’s proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Furthermore, I shall argue that the Collapse Argument has been misguided from the outset. The last chapter suggests a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse – as far as this is possible. (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.

This paper investigates a problem related to quantifiers which has some analogies to that of propositional completeness I give a definition of quantifier in many-valued logics generalizing the cases which already occur in first order many- valued logics. Though other definitions are possible, this particular one, which I call distribution quantifiers, generalizes the classical quantifiers in a very natural way, and occurs in finite numbers in every m-valued logic. We then call the problem of quantificationa2 completeness in m-valued (...) logic the problem of characterizing which are the quantifiers in a given language which can generate all other quantifiers in this language, using the connectives, as is the case, for example, of the universal and exis- tential quantifiers in classical logic, using negation. We are interested, in particular, in those many-valued quantifiers which closely mimic the behavior of existential an universal quantifiers in generating all other quantifiers using negation: these I call perfect quantifiers, as defined below. The main result of this paper is the characterization of all perfect quantifiers in 3-valued logics, which are complete if the logic is functionally complete. As a byproduct, we obtain the same result for the classical logic, which we include mainly for motivation. (shrink)

I examine the problem of dirty hands, suggesting that there is a possibility for the individual decision-maker to do bad to achieve good consequences. According to Consequentialism, because the consequences are what counts in morality, then there seems to be no phenomenon of dirty hands. I will first present what Jean-Paul Sartre meant by the problem of dirty hands, after which I will describe how contemporary philosophers have identified that problem. Finally, I will argue that Consequentialism does (...) not negate the phenomenon of dirty hands on the grounds that consequences determine the ethical nature of action. Statements of “good” “bad”, or “the best” consequences are subjective and ambiguous in which case the phenomenon of dirty hands exists. Thus, action that produces positive consequences may not be morally justified. (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)