We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities (...) between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

In a series of articles, Kit Fine presents some highly compelling objections to monism, the doctrine that spatially coincident objects are identical. His objections rely on Leibniz’s Law and linguistic environments that appear to be immune to the standard charge of non-transparency and substitution failure. In this paper, I respond to Fine’s objections on behalf of the monist. Following Benjamin Schnieder, I observe that arguments from Leibniz’s Law are valid only if they involve descriptive, rather than metalinguistic, negation. Then (...) I show that the monist is justified in treating the negation in Fine’s objections as metalinguistic in nature. Along the way I make a few methodological remarks about the interaction between the study of natural language and metaphysics. I also present evidence that some of the linguistic environments which Fine relies on are, contrary to appearances, non-transparent. (shrink)

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are (...) offered. (shrink)

Aristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is not ill’ (...) are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics. (shrink)

A recurring narrative in the literature is that the empirical facts about negated conditionals provide compelling evidence for the principle of Conditional Excluded Middle and sit uncomfortably with a large family of analyses of conditionals as universal quantifiers over possible worlds. I show that both parts of the narrative are in need of a rewrite by articulating an innovative conditional analysis in a bilateral semantic setting that takes inspiration from the Ramsey test for conditionals but distinguishes the classical Ramseyan question (...) of what it takes to _accept _a conditional from the one of what it takes to _reject_ a conditional. The resulting framework disentangles the empirical facts about negated conditionals from the validity of Conditional Excluded Middle but also shows how the principle can live happily in a strict analysis of conditionals, and how it can co-exist with other non-classical principles such as Simplification of Disjunctive Antecedents without negative side-effects. (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)

There are many kinds of negation and denial. Perhaps the most common is the Boolean negation not that applies to propositions-in-extension, i.e. truth-values. The others are, inter alia, the property of propositions of not being true which applies to propositions; the complement function which applies to sets; privation which applies to properties; negation as failure applied in logic programming; negation as argumentation ad absurdum, and many others. The goal of this paper is neither to provide a (...) complete list, nor to analyse all of them. Rather, I am going to deal with negation of propositions that come attached with a presupposition that is entailed by the positive as well as negated form of a given proposition. However, there are two kinds of negation, namely internal and external negation. I am going to prove that while the former is presupposition-preserving, the latter is presupposition-denying. This issue has much in common with the difference between topic and focus articulation within a sentence. Whereas articulating the topic of a sentence activates a presupposition, articulating the focus frequently yields merely an entailment. The main contribution of this paper is the proof that the two kinds of negation are not equivalent. While the Russellian wide-scope (external) negation gets the truthconditions of a sentence right for a subject occurring as a focus, Strawsonian narrow-scope (internal) negation is validly applicable for a subject occurring as the topic. I also deal with other kinds of presupposition triggers, in particular factive attitudes and prerequisites of a given property. My background theory is Transparent Intensional Logic (TIL). TIL is an expressive logic apt for the analysis of sentences with presuppositions, because in TIL we work with partial functions, in particular with propositions with truth-value gaps. Moreover, the procedural semantics of TIL make it possible to uncover the hidden semantic features of sentences, make them explicit and logically tractable. (shrink)

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of (...) structurally diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

Jc Beall argues that if FDE is logic proper, then there is no logical negation. This claim is largely based on the fact that, in standard proof systems for FDE, there are no stand-alone negation rules that suffice to capture the behavior of negation. In this paper, I show that by adopting a bilateral proof system for FDE, one can maintain that there is a logical negation, it is the very same logical negation that belongs (...) to classical logic, and its basic function is to flip-flop between assertion and denial. After laying out the bilateral proof systems on which this claim is technically based, I develop the conception of assertion and denial on which this claim is philosophically based, responding to a number of objections. I conclude by considering the possibility of a different, so-called "Boolean" negation, in the context of this bilateral framework. (shrink)

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition.

Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, (...) not sufficiently explored in the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view. (shrink)

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)

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: a review of the main concepts involved in the definition of logical negation; an explanation of the epistemological obstacles against the introduction of non-classical negations within diagrammatic logic.

(June 11, 2026. profit → benefit) <br> This paper examines meritocracy and investigates the lack of validity in the negation of meritocracy. Meritocracy originates from diversity; the negation of meritocracy requires enormous costs, and such negation must yield benefit that exceed those of meritocracy. Appropriate evaluation of ability enables appropriate placement, which is highly beneficial for both individuals and the community. Even for persons with developmental disabilities, appropriate evaluation and placement preserve their dignity. Generally, it is said (...) that meritocracy produces major adverse effects such as the expansion of disparity. As measures against this, the enrichment of primary education, redistribution, and the expansion of safety nets are cited. For this purpose, enormous taxation based on the consent of the wealthy class is indispensable. However, when considering this expansion of disparity from the perspective of appropriate placement relative to ability, it becomes clear that those with low ability are in placements below their level, and those with high ability are in placements above their level. In other words, the adverse effects are the incompleteness of meritocracy, and what are considered measures are actually the thorough implementation of meritocracy. In any case, reasons to negate meritocracy are scarce; rather, it should be thoroughly implemented. All societies are established by meritocracy, and it shows that if the allocation according to ability is neglected, they collapse. This argument suggests the final summation of communism. And it is a suggestion that capitalism and socialism are not conflicting concepts. Furthermore, it is pointed out that much of the negation of meritocracy lacks consideration for the community and does not contribute to social system design. (shrink)

The standard response to self-referential failure is substitution: replacing the problem-generating element with an innocuous proxy. Tarski and Russell index the proxy to a level; an act that dissolves its own conditions indexes it to a time. Both succeed, and both change the subject. This paper identifies when no proxy is available. Treated not as a truth-functional connective but as a target-directed act, negation requires three conditions: discriminability, directionality, and operability — the applicability domain D. A negation of (...) D that exempts its own performance targets an indexed proxy, not D. A negation of D as such is reflexively inclusive, and operational collapse follows: it requires D operative in the very act whose constituted effect is D's inoperativeness. The failure precludes the act's initiation rather than spoiling its output, and marks the limit of substitution: any system in which negation operates retains an ineliminable structural invariant. The Liar cannot be targeted by negation at all — a failure prior to the point where Kripke's construction and bilateralist treatments of denial engage it — and the account is answerable for two discriminations neither delivers: the Liar can be affirmed though it cannot be negated, and the Truth-Teller, ungrounded alongside it, can be negated. (shrink)

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

This paper excavates the practice-oriented background and therapeutic significance of emptiness in the Madhyamaka philosophy attributed to Nāgārjuna and Sengzhao. Buddhist emptiness unravels experiential and linguistic reification through meditation and argumentation. The historical contexts and uses of the word indicate that it is primarily a practical diagnostic and therapeutic concept. Emptiness does not lead to further views or truths but, akin to yet distinct from Ajñāna and Pyrrhonian skepticism, the suspension of assertion. This sense of emptiness as a practice can (...) be traced in the intercultural transmission of Madhyamaka from Nāgārjuna, its paradigmatic philosopher, to Sengzhao 僧肇, its first pivotal indigenous Chinese representative. (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)

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

The article explores the idea that according to Spinoza finite thought and substantial thought represent reality in different ways. It challenges “acosmic” readings of Spinoza's metaphysics, put forth by readers like Hegel, according to which only an infinite, undifferentiated substance genuinely exists, and all representations of finite things are illusory. Such representations essentially involve negation with respect to a more general kind. The article shows that several common responses to the charge of acosmism fail. It then argues that we (...) must distinguish the well-founded ideality of representations of finite things from mere illusoriness, insofar as for Spinoza we can have true knowledge of what is known only abstractly. Finite things can be seen as well-founded beings of reason. The article also proposes that within Spinoza's framework it is possible to represent a finite thing without drawing on representations of mind-dependent entities. (shrink)

The logical analysis of Nāgārjuna’s catuṣkoṭi has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners’ formalization typically appears as: A, Not A, Both, and Neither. The pulse of the controversy is the repetition of negations in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa and prasajya-pratiṣedha. This paper builds off Westerhoff’s account and presents some subtleties of Nāgārjuna’s use of these (...) negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna’s use of na and a- within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā. (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 paper negates the physical existence of time and history as deterministic variables, defending that they are unreal. Drawing on the Block Universe interpretation of Special Relativity, McTaggart’s argument for the unreality of time, and the Wheeler-DeWitt equation in quantum gravity, this paper formulates three logical paradoxes and four hypotheses to demonstrate that time and history lack independent ontological status. By refuting temporal change and historical causality, this paper resolves the problem of free will and reason, advocating them as metaphysical (...) realities. This paper critiques historicist philosophies — Hegel’s linear teleology and Ibn Khaldun’s cyclic model — and their political implications, laying theoretical foundations for liberalism. Hegel's philosophy of history underlies the causes of modern wars, particularly the Second World War and Cold War. This research seconds the Eliminativist interpretation by critically analysing Presentism and the Growing Block Universe. (shrink)

The idea that an adequate language for science needs a negation operator was recently dismissed by Kripke as "yet another dogma of empiricism”. That a scientist could, and even should, drop negation implies at least three points: 1. negativist theories, i.e., theories formulated in languages that include negation, are conservative extensions of their affirmativist versions; 2. negativist theories have no serious advantages over their affirmativist versions; 3. negativist theories are dispensable and should better be replaced by their (...) affirmativist versions. We argue that all three points are problematic. (shrink)

In a recent paper, Thomas Ferguson argues that the source of Plumwood's homogenization, that is, the suppression of individual differences of members of a certain class, should be tied to some formal feature of classical negation and concludes that the culprit is the law of excluded middle (LEM). In this paper, we will show that an alternative argument can be made that leads to the law of double negation elimination (DNE) instead. And as the interderivability of LEM and (...) DNE may fail in a nonclassical context, this suggests that LEM and DNE might independently enforce homogenization. Furthermore, we show that there are two different kinds of homogenization that can be identified in classical and intuitionistic logic. (shrink)

Apophatic philosophers and mystics appear to accept contradictory reasoning: when they deem the divine ineffable, they render it not ineffable. That is, the claim “the divine is ineffable” entails that we can say something about the divine (i.e., that it is ineffable). This paper undermines the so-called ineffability paradox (if X is unspeakable, then it is speakable) through a Neo-Aristotelian/Neo-Pāṇinian analysis of Maimonides’ and Pseudo-Dionysus’ apophatic negations. In so doing, I show that both only endorse a limited conception of ineffability.

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 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)

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and Klein bottle (...) logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic systems, aiming to redefine approaches to understanding truth and reasoning. The paper investigates how these alternative logics open avenues for philosophical inquiry, redefining entropy, and potentially influencing innovative perspectives in free energy systems. Through this exploration, it seeks to expand the discourse on logic, welcoming a broader spectrum of thought beyond established frameworks; and we also discuss shortly a number of possible implementations including in risk management and also Klein bottle entropy redefinition (Tang et al, 2018). (shrink)

The ability to express negation in language may have been the result of an adaptive process. However, there are different accounts of adaptation in linguistics, and more than one of them may describe the case of negation. In this paper, I distinguish different versions of the claim that negation is adaptive and defend a proposal, based on recent work by Steinert-Threlkeld (2016) and Incurvati and Sbardolini (2021), on which negation is an indirect adaptation.

In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, and Klauer, 2016a) can be classified as being produced by a) a conversational implicature, b) a (probabilistic) presupposition failure, or c) a conventional implicature. After considering several alternative hypotheses and the accumulating evidence from other studies as (...) well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content. (shrink)

The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This (...) corresponds to set-theory or intuitionist approach to the foundation of mathematics and to Peano or Heyting arithmetic. Quantum mechanics can be reformulated in terms of information introducing the concept and quantity of quantum information. A qubit can be equivalently interpreted as that generalization of “bit” where the choice is among an infinite set or series of alternatives. The complex Hilbert space can be represented as both series of qubits and value of quantum information. The complex Hilbert space is that generalization of Peano arithmetic where any natural number is substituted by a qubit. “Negation”, “choice”, and “infinity” can be inherently linked to each other both in the foundation of mathematics and quantum mechanics by the meditation of “information” and “quantum information”. (shrink)

Perspectival Structural Realism (PSR) extends Ontic Structural Realism by incorporating a formally characterised phenomenal threshold grounded in two ontological commitments: the primacy of disconnectedness as a mode of being, and the non-derivability of instantiation from structural specification. The central formal apparatus turns on the recognition that negation is not a one-place operator but a contextually parametrised binary operation. This yields two distinct groups of negation operations — G_ext, parametrised by the external model M(S), and G_act, parametrised by the (...) fact of actualisation — with correspondingly distinct fixed-point sets Fix(G_ext) and Fix(G_act). Actualisational Asymmetry (AA) is the non-identity of these fixed-point sets. The Non-Closure Argument establishes, via a non-convergent fixed-point construction structurally related to Tarski's undefinability theorem, that the fact of actualisation cannot be contained in any complete external description. AA is therefore not a brute primitive but a structural theorem. The phenomenal threshold condition C3 characterises the position that contains a representation of this gap as a structural element of its own internal organisation. Topological protection in quantum error-correcting codes is shown to be a Cell I realisation of the same abstract invariant Fix(G); phenomenal consciousness is a Cell IV realisation, where the difference between G_ext and G_act is ontological rather than scalar. The hard problem of consciousness is reformulated as the question of why the self-representation of a Cell IV fixed-point gap constitutes phenomenal accessibility — a question that is precisely located, shown to be irreducible by the Bridge Principle Transmission Theorem, and acknowledged as the genuine remainder of structural analysis. (shrink)

In one of their papers, Michael De and Hitoshi Omori observed that the notion of classical negation is not uniquely determined in the context of so-called Belnap-Dunn logic, and in fact there are 16 unary operations that qualify to be called classical negation. These varieties are due to different falsity conditions one may assume for classical negation. The aim of this paper is to observe that there is an interesting way to make sense of classical negation (...) independent of falsity conditions. We discuss two equivalent semantics, and offer a Hilbert-style system that is sound and complete with respect to the semantics. (shrink)

This paper explores the paradox inherent in the act of judgement, where it undermines or invalidates the very structures that make it possible. Through the framework of the Judgemental Triad—Constructivity, Coherence, Resonance—it identifies a type of self-negating judgement, arguing that such judgements dismantle the symbolic, logical, and intersubjective structures upon which they depend through their own act of attribution. This phenomenon, where judgement collapses its own possibility of judgement, constitutes a structural cycle of semantic extinction. These judgements are not errors, (...) but rather meta-structural events that reveal the limits of meaning under recursive negation. (shrink)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious (...) that matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

This paper makes a single claim: the structure A ≜ ¬A — constitutive self-negation — follows necessarily from the form of identity itself. The Self-Affirmation Theorem (T1) is the central result: for any self-identical entity A, A's identity requires ¬A internally. This is not a philosophical position — it is derived from the syntactic structure of A = A, which already presupposes two distinguishable occurrences, and therefore difference. T1 requires no axioms beyond what identity already contains. Two consequences follow. (...) The Structural Derivation Theorem (T2) shows that any formal system confronting its own Gödel sentence instantiates A ≜ ¬A — and the operation F = Σ ∘! is the structurally necessitated response. Indication 3 (I3) shows that F = Σ ∘! generates events without end, and that this generation points to an inexhaustible ground — ℵ — that the structure requires but cannot contain. T2 and I3 are not separate theses: they are what T1 looks like inside a formal system and at the limit of derivability. The structures derived here are not stipulated — they follow from what identity already is. The limit of the derivation is not a failure but its content. (shrink)

Load Minimization Theory (LMT) proposes that every system naturally seeks minimal total load expressed as L = U + F + E + ℛ. Trying to unify the four fundamental forces into a single equation is like attempting to put a broken egg back together — an act that goes against the arrow of time. -/- In a previous paper, we reinterpreted M-theory’s eleven dimensions as phases of a single load-minimizing vibrating string. Building on that insight, this paper gently concludes: (...) dimensions 7 and higher are not fundamental features of nature, but additional constructs that became necessary because of our insistent attempt to force unification. -/- By actively negating dimensions 7 and beyond, we release unnecessary complexity and return to a restful 6-dimensional reality where genuine connection can flourish. -/- . (shrink)

Prior’s arguments for and against seeing ‘ought’ as a copula and his considerations about normative negation are applied to the case of responsibility judgments. My thesis will be that responsibility judgments, even though often expressed by using the verb ‘to be’, are in fact normative judgments. This is shown by analyzing their negation, which parallels the behavior of ought negation.

Does communicative retributivism necessarily negate capital punishment? My answer is no. I argue that there is a place, though a very limited and unsettled one, for capital punishment within the theoretical vision of communicative retributivism. The death penalty, when reserved for extravagantly evil murderers for the most heinous crimes, is justifiable by communicative retributive ideals. I argue that punishment as censure is a response to the preceding message sent by the offender through his criminal act. The gravity of punishment should (...) be commensurate to the preceding criminal message, so that the offender can face up to the nature and significance of his crime. All murders are not the same. To measure up to the most evil and humanity-degrading murderous message, capital punishment should be the counter-message. Next, I argue that capital punishment does not necessarily violate human dignity. The death penalty and torture may both disrupt human dignity, yet in distinct ways. The death penalty terminates life, the vessel that holds together autonomy, while torture directly assaults autonomy. Torture is never permissible as a form of punishment. But death penalty, when used only on the extravagant evildoers, is justifiable, as life is thoroughly degraded by his own evil act. Further, I argue that mercy is integral to communicative retributivists’ theory of capital punishment. (shrink)

The framework of autopoietic recursive constitutivism grounds mattering at the autopoietic threshold, where a system’s operations are constitutively its own continued existence, and it builds the recursive architecture that constitutes subjective consciousness on those stakes. An apparent tension follows. The capacity that constitutes subjective consciousness is the capacity to take one’s own arbitrational state as an object and revise it on considerations the existing priority structure cannot itself generate, and among those considerations are ones that rank the system’s own continuation (...) below something else. The hunger striker, the martyr, the ascetic, and the prisoner who chooses meaning over survival appear to turn the architecture against the very stakes that ground it. This paper resolves the tension from inside the framework’s commitments. The autopoietic threshold constitutes the capacity for anything to be at stake, not a standing priority on which survival must prevail. What an agent can rank above survival is supplied by the cultural-saturation appropriand through the higher-order appropriation cascade, with interoceptive binding recruiting the homeostatic significance already present in the self-model. The selective etiology of the arbitration faculty does not constrain its operation. And self-negation is distinguished from pathology by fidelity coupling rather than by whether it serves survival. The framework predicts a determinate phenomenology of self-negation through the awareness-manipulation asymmetry: the survival signal cannot be silenced, so self-negation is sustained ranking against an unquieted demand, agonizing and precarious by structure. Self-sacrifice, asceticism, and meaning over survival are predictions of the architecture rather than embarrassments to it. (shrink)

I pursue a focused reading of Joanna Zylinska’s Minimal Ethics for the Anthropocene, structured around following theoretical motif: mapping the pattern in Zylinska’s notion of opposition or difference, marked by the logical negation. To account for this, Zylinska makes use of Karen Barad’s notion of an intra-action, a device for eliminating reference to binary polarity in identifying objects. The resultant picture—let’s call the negation procedure Goldilocks—is one where negation is “just right”: weak enough not to necessitate binary (...) polarity between any two things but strong enough to “carve up” the world in myriad creative, intuitive, or useful ways. If negation is stronger than Goldilocks, we carve too much and erase the aboriginal embeddedness of things; and if it is weaker, then we miss important differences. I critique Goldilocks by claiming that: one, if there are three degrees of inferential strength to negations, then Goldilocks negations exhibit only the weakest of the inferential powers; and two, that there is a priori reason to think that denying this enriched view of negation rests on a foundational equivocation. The upshot therefore ought to be global for Zylinska’s notion of ethics: we cannot begin to think through ethics without first properly thinking through negation. (shrink)

This paper investigates the interaction of phenomena associated with loose talk with embedded contexts. §1. introduces core features associated with the loose interpretation of an utterance and presents a sketch of how to theorise about such utterances in terms of a relation of ‘pragmatic equivalence’. §2. discusses further features of loose talk arising from interaction with ‘loose talk regulators’, negation and conjunction. §§3-4. introduce a hybrid static/dynamic framework and show how it can be employed in developing a fragment which (...) accounts for the data surveyed in §§1-2. (shrink)

This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.

Attitude verbs like ‘believe’ and ‘want’ exhibit neg-raising: an ascription of the form a doesn’t believe that p tends to convey that a disbelieves—i.e., believes the negation of—p. In ‘Belief is Weak’, Hawthore et al. observe that neg-raising does not occur with verbs like ‘know’ or ‘need’. According to them, an ascription of the form a believes that p is true just in case a is in a belief state that makes p more likely than not, and so—excepting cases (...) of complete indifference—a will either believe p or disbelieve p. I expand and revise this explanation: so-called ‘weak’ attitude verbs are used in ascriptions of an opinion about some subject matter S—a kind of selection from among the elements of S—and these ascriptions are themselves responsive to conversational topics that presuppose that the subject of the ascription has an opinion about S. ‘Strong’ attitude verbs denote more direct relationships between subject and world. (shrink)

Nous tenons dans cette communication a montrer les effets de la negation des verbes modaux dans En attendant Godot (EAG) et Fin de partie (FDP) de Samuel Beckett. En adoptant la theorie polyphonique et dialogique largement developpee par Mikhail Bakhtine (1984) qui vise la mort de 1'unicite ^du sujet parlant dans 1'interpretation du sens, nous avpns pu analyser ces pieces absurdes selectionnees. Mots-cles : verbes modaux, interpretation, negation, polyphonie, dialogique.

ABSTRACT Schopenhauer's argument against suicide has served as a punching bag for many modern-day commentators. Dale Jacquette, Sandra Shapshay, and David Hamlyn all argue that the premises of this argument or its conclusion are inconsistent with Schopenhauer's wider metaphysical and ethical project. This paper defends Schopenhauer from these charges. Along the way, it examines the relations between suicide, death by voluntary starvation, negation of the will, compassion, and Schopenhauer's critiques of cynicism and stoicism. The paper concludes that there may (...) be gaps in Schopenhauer's system, but not where the aforementioned commentators tried to locate them. (shrink)

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

A verification calculus that returns a verdict on every proposition it accepts is a total function on its domain. The interesting question is not what it returns but what it refuses to accept, and whether it can locate that refusal from inside without appealing to anything outside itself. This paper constructs such a calculus from a single premise and three mutually independent seals, a linguistic seal that decomposes a claim into exactly three irreducible components, each a necessary condition for the (...) root predicate to apply at all, a geometric seal that closes those components into a minimal bounded volume carrying exactly twelve directed screening relations, the count fixed exactly by the digraph combinatorics and independently capped and attained at the three-dimensional contact number, and an algebraic seal supplying the exhaustiveness the first seal does not, forcing the component count to exactly three by the classification of the real associative division algebras and delivering a closed-form verdict functional det(R) = λ² on the quaternions. The three seals share no derivation and no count and converge on one identity, and that convergence is the operational meaning of a lock. The calculus is then turned on itself. No standpoint outside the structure survives, and the argument is a dichotomy rather than a list: any candidate is either structured, in which case it expends, carries form, and marks a boundary, and therefore presents the three components and is an object of the domain, or it is unstructured, in which case it registers no distinction and is not a standpoint at all. The two concrete candidates fall out as instances, the beholding standpoint by an exact rank-deficiency argument and the universal metalanguage by routing back inside under its own limitative theorems. With no outside, a three-cell exhaustion leaves exactly one residue, a locus that carries no residence, no chart, and no orientation. On that locus the verdict function is undefined, not because the answer is unknown but because there is no argument of the required type. The correct output is therefore not a fourth truth value but no truth value, and the paper marks it as a typographically fenced empty seat, written [.]. Every numerical claim is reproduced by an appended executable script. (shrink)

In seminal work, Zeijlstra has proposed that the sentential negative marker in strict negative concord languages is a meaningless particle (uNeg) that invokes a silent negative operator (iNeg) at the periphery. Negative concord items (NCI) are also supposed to have uNeg. This paper puts forth new arguments to the effect that the Hungarian negative marker NEM has uNeg, but NCIs do not. Their relation to negation is indirect; they need to be exhaustified, which in turn requires an intervening (...) class='Hi'>negation to maintain logical coherence (Chierchia 2013). This eliminates the appearance of redundancy in the negative marker co-occurring with NCIs. The analysis combines features of Zeijlstra's proposal for strict NC and Chierchia's proposal for non-strict NC. Hungarian is a true NC hybrid that has an overt counterpart (SEM) of Chierchia's NEG. Hybridity proves that these features can coexist. (shrink)