Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the FUL, (...) I argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (shrink)

This paper introduces the contradiction trap: a dialectical and game-theoretic method for exposing concealed asymmetry in institutional and algorithmic reasoning. By forcing a system to reconcile mutually exclusive commitments, the trap converts inconsistency into evidence — a falsifiable signal of structural bias, motivated deviation, or narrative drift. -/- The framework models contradiction as an epistemic game with informational payoffs, providing a portable diagnostic for systems that claim impartiality but behave otherwise. It bridges philosophical logic, applied audit design, and (...) adversarial reasoning, showing how contradiction can be operationalised as a test of legitimacy rather than a purely logical artefact. -/- This paper constitutes the first work in a planned trilogy on evidential integrity, establishing the epistemic foundations for procedural and institutional models to follow. -/- Keywords: contradiction; epistemic game theory; evidential reasoning; structural bias; motivated asymmetry; governance integrity; algorithmic accountability; dialectical logic; audit design; fairness diagnostics; philosophy of technology; adversarial evaluation. (shrink)

In this analysis of one of the most difficult and neglected topics in Hegelian studies, Songsuk Susan Hahn tackles the status of contradiction in Hegel's ...

One of the most important difficulties facing Kant’s Formula of Universal Law (FUL) is its apparent inability to show that it is always impermissible to kill others for the sake of convenience. This difficulty has led current Kantian ethicists to de-emphasize the FUL or at least complement it with other Kantian principles when dealing with murder. The difficulty stems from the fact that the maxim of convenience killing fails to generate a ‘contradiction in conception’, producing only a ‘contradiction (...) in the will’ when subjected to the two-fold test associated with the FUL. This result is thought to imply that the FUL allows us sometimes to kill for the sake of convenience. In this essay, I argue that the very diagnosis of the problem rests on a mistake, and that if the maxim of convenience killing generates a contradiction in the will, then acting on it is never permissible. (shrink)

Suppose we’re at a horserace, and you turn to me and say, ‘Eclipse is at the finish line!’ But by the time you’ve finished saying this—by the time your utterance is complete—Eclipse is already well past the finish line, and what you’ve said is no longer true. But you did say something true. More generally, we can—and often do—say true things about events that take up less time than our utterances themselves. We can also contradict each other about such events—something (...) that takes even more time. How is all this possible? In the twentieth century, this problem was discussed by Arthur Prior. In the 14th, John Buridan treated an older—probably 12th-century—version of it. Buridan’s treatment is more successful than Prior’s, which runs into Zeno’s paradox of the arrow. Buridan avoids the paradox, but faces further puzzles for his account of contradiction. In untangling these, we’ll uncover important latent features of his pragmatics and temporal logic—features that are supported by more recent research in linguistics. Ultimately, our considerations here will turn up new insight into the Gricean Cooperative Principle. In a slogan: to contradict is to cooperate. (shrink)

A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.

In this article, I reply to Jens Timmermann’s critical discussion of my essay “Contradiction and Kant’s Formula of Universal Law”. I first consider Timmermann’s reasons for rejecting my interpretation of the Formula of Universal Law. I argue that the self-contradiction relevant to determining a maxim’s moral status should not be sought in the imagined world in which the maxim is a universal law. I then discuss Timmermann’s suggestion that something like a volitional self-contradiction is found within the (...) will of the immoral agent. I deny this and clarify that the relevant contradiction is diagnosed counterfactually in moral reflection. Finally, I explain the differences between Timmermann’s account, Korsgaard’s Practical Contradiction interpretation, and my own Volitional Self-Contradiction interpretation. (shrink)

The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline (...) class='Hi'>contradiction. Many theories of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language. Here, I first briefly review claims made by various theorists about these borderline contradictions, attempting to draw out some predictions about the behavior of ordinary speakers. Second, I present an experiment intended to gather relevant data about the behavior of ordinary speakers. Finally, I discuss the experimental results in light of several different theories of vagueness, to see what explanations are available. My conclusions are necessarily tentative; I do not attempt to use the present experiment to demonstrate that any single theory is incontrovertibly true. Rather, I try to sketch the auxiliary hypotheses that would need to be conjoined to several extant theories of vague language to predict the present result, and offer some considerations regarding the plausibility of these various hypotheses. In the end, I conclude that two of the theories I consider are better-positioned to account for the observed data than are the others. But the field of logically-informed research on people’s actual responses to vague predicates is young; surely as more data come in we will learn a great deal more about which (if any) of these theories best accounts for the behavior of ordinary speakers. (shrink)

The logical Law of Non-contradiction – that a proposition cannot be both true and false – enjoys a special, perhaps uniquely privileged, status in philosophy. Most philosophers think that finding a contradiction – the assertion of both P and not-P – in one's reasoning is the best possible evidence that something has gone wrong, the ultimate refutation of a position. But why should this be so? What reason do we have to believe it? In this paper, I address (...) these questions. (shrink)

ABSTRACT In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we (...) have adopted a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor to inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has (...) an operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

The Law of Non-Contradiction holds that both sides of a contradiction cannot be true. Dialetheism is the view that there are contradictions both sides of which are true. Crucial to the dispute, then, is the central notion of contradiction. My first step here is to work toward clarification of that simple and central notion: Just what is a contradiction?

The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the (...) world. For example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)

Confucianism, as a core component of Eastern traditional civilization, has exerted profound influence on social order, education, and governance. However, it contains significant internal contradictions, practical paradoxes, and sectarian divergences. The root of these contradictions lies in its heavy reliance on human-made norms (Ren, Yi, Li, Zhi, Xin, and ritual systems) rather than natural laws. This paper systematically analyzes the manifestations, types, and historical evolution of Confucian internal contradictions and philosophically proposes the proposition that “human-made is false.” By contrasting these (...) human-made norms with natural laws and systemic principles, the study further explores the implications of Confucian experience for modern social governance, educational systems, and civilization development. Drawing on the Lao-Yang Genesis Cosmology’s concept of “Dao follows Nature,” the paper suggests that modern civilization should prioritize holistic, scientific, and feedback-based approaches to achieve theoretical consistency and practical stability. This research provides a novel perspective integrating philosophy and science for understanding the limitations of traditional ethics and constructing sustainable civilization. (shrink)

Several Indian religious traditions associated with Vedānta offer conflicting descriptions of ultimate reality, Brahman. A prominent example is found in the Bhedābheda Vedānta tradition, which posits that Brahman is both different (bheda) and non-different (abheda) from the world and individual selves. At first glance, this seems like a contradictory statement. However, most Bhedābheda Vedānta thinkers attempt to reconcile the contradiction, asserting, for example, that Brahman is different from the world and individual selves in one sense, yet non-different in another, (...) distinct sense of “difference.” A notable exception seems to be Jīva Gosvāmī (16th Century), a leading theologian of the Caitanya (15th-16th Century) Vaiṣṇava school. According to a widely accepted interpretation, Jīva accepts the contradiction directly, adding that it is inconceivable (acintya). He coined the term that names his school: Acintya Bhedābheda. Despite textual evidence supporting this view, other evidence from Jīva’s writings and subsequent commentaries suggests his theology might be reconstructed using the more traditional contradiction-avoiding approach. This raises some interesting theological issues. The purpose of this paper is to offer an integrated interpretation of Jīva’s Bhedābheda Vedānta, one that synthesizes both interpretations while staying true to the key elements of his ontology. This will be based on a version of Graham Priest’s Logic of Paradox (LP), which I refer to as (a) Logic of Partial Truth (LPT). The result is a paraconsistent and glut-theoretic approach to Jīva’s Bhedābheda Vedānta theology. (shrink)

Within the Byzantine Christian tradition, one commonly finds affirmative and negative predicates equally applied to God—for example, “God is Being-itself” and “God is not Being-itself”—suggesting a suspension of the Principle of Non-Contradiction (PNC). Byzantines in large part draw on the Pseudo-Dionysius (~6th-cent. CE) for this position, who was in large part influenced by the later Neoplatonist Proclus (5th cent. CE) who, by contrast, maintained the PNC by referring to the first cause (i.e. the One) in terms of negations alone (...) (e.g. “the One is not Being”). In attempting to justify Ps.-Dionysius’ position, the 12th-cent. Byzantine Nicholas of Methone critiqued Proclus’ position on the first cause, explicitly arguing for the suspension of the PNC in allowing for negative and positive predications about God. This chapter closely analyzes how we get from Proclus’ affirmation of the PNC to Nicholas of Methone’s suspension of the PNC when referring to the first cause, looking closely at Pseudo-Dionysius as a key figure behind Nicholas’ position. An important, additional background for Ps.-Dionysius is Damascius, who, in contrast to Proclus, argues that the One implies the opposite, positive attributes that come after it, suggesting both affirmative and negative properties predicated of it. Damascius thus suggests what Ps.-Dionysius affirms and what Nicholas of Methone makes explicit in his critique of Proclus, giving us the background for understanding the Byzantine view on contradictory affirmations made about the first cause. (shrink)

This study applies the author's Contradiction-Debt (CD) model (based on the Geometry of the Good, forthcoming) to assess the risk of governance rupture in Argentina as of September 2025. The CD model evaluates violations across five domains—security/rights, rule of law/elections, center–local contradictions, narrative/facts gap, and humanitarian obligations—against the effectiveness of repair mechanisms, weighted by institutional capacity. Using recent reports from Human Rights Watch, Dejusticia, Al Jazeera, and Forbes, we coded violations, repair efforts, and capacity indicators. Argentina’s violation score (V (...) ≈ 1.03) far outweighs its effective repair score (R_eff ≈ 0.095), yielding a repair-to-violation ratio (R/V) of ~0.09. This ratio falls below the 0.30 threshold, placing the country in a 1–2 quarter rupture window. Tipping conditions—including low legitimacy, weak elite cohesion, high cost strain, and rising protest backlash—are all present, reinforcing the high-risk designation. Projections for Q4 2025–Q1 2026 suggest escalating protests, elite fragmentation, and worsening humanitarian conditions, with plausible scenarios ranging from mass mobilization and government collapse to autocratic consolidation. While the model highlights severe rupture risks, it also underscores potential stabilizing measures: acknowledgment of grievances, inclusive reforms, and restoration of institutional oversight could raise the R/V ratio and avert crisis. This analysis demonstrates the CD model’s utility in diagnosing early warning signals of rupture and in identifying pathways for policy intervention. (shrink)

In Metaphysics Γ, Aristotle argues against those who seem to accept contradictions. He distinguishes between the Sophists, who deny the principle of non-contradiction through arguments, and the Natural Philosophers, whose physical investigations lead to the acceptance of objective contradictions. Heraclitus’ name appears throughout the discussion. Usually, he is associated with the discussion against the Sophists. In this paper, I explore how the discussion with the Natural Philosophers may illuminate both the interpretation of Heraclitus by Aristotle and Heraclitus’ own worldview. (...) To refute the Natural Philosophers, Aristotle proposes a general reconstruction of their reasoning. Roughly, relying on sensory evidence (A1), they see that the same thing changes from one opposite to another (A2). Such a change appears to characterize a generation out of non-being, which a Natural Philosopher does not accept (A3). To solve the problem, despite their different worldviews, Natural Philosophers hint at a state in which opposites co-occur, characterizing an objective contradiction (C). Looking at the discussion in Metaphysics Γ and Heraclitus fragments, sections 1–3 show how assumptions A1, A2, and A3 easily apply to Heraclitus. The case of the conclusion is more challenging. In the case of the Pluralists, the co-existence of opposites characterizes a state in which there is no generation. Such a view does not fit Heraclitus’ mobilism. To argue that Aristotle’s argument is general enough to encompass dynamic views, I examine his problematization of accepting the change of change in Metaphysics K and Physics V. There, after re-stating several points that appear in Metaphysics Γ, Aristotle argues that accepting the becoming of another becoming leads to a state of contradiction in which the becoming is perishing. Heraclitus’ B8, cited in Nicomachean Ethics, gives evidence that, for Aristotle, Heraclitus puts a process at the origin of an opposite process. Moreover, after examining the expression ‘living the death/dying the life’ in B62, I argue that Heraclitus was aware that his worldview implied a dynamic objective contradiction. Finally, an analysis of elemental changes in B36 proves that accepting objective contradictions does not make Heraclitus’ worldview less attractive. (shrink)

We introduce the τ-contradiction as a diagnostic tool for evaluating the coherence of metaphysical entities. Drawing on the concept of proper time (τ) from special relativity, we argue that any entity claimed to be both timeless (τ = 0) and capable of temporal functions (requiring τ > 0) harbors a logical contradiction equivalent to a round square. This framework applies to classical conceptions of God, immaterial souls, and other entities traditionally described as existing outside time while simultaneously performing (...) temporal activities such as thinking, deciding, or creating. The τ-contradiction does not merely render such entities improbable but logically impossible. We provide a formal modal-logical derivation and discuss implications for philosophy of religion and metaphysics. (shrink)

It is widely believed, among philosophers of literature, that imagining contradictions is as easy as telling or reading a story with contradictory content. Italo Calvino’s The Nonexistent Knight, for instance, concerns a knight who performs many brave deeds, but who does not exist. Anything at all, they argue, can be true in a story, including contradictions and other impossibilia. While most will readily concede that we cannot objectually imagine contradictions, they nevertheless insist that we can propositionally imagine them, and regularly (...) do, simply by entertaining a text which prompts us to do so. I argue that this narrative does not bear scrutiny for two main reasons. First, because propositional imagining is beside the point, where truth in fiction is concerned; evaluating truth in fiction engages the cognitive architecture in ways that prohibit the mobilization of merely propositional imagination to that end. And second, because it is not obvious, given the strategies usually suggested, that we ever propositionally imagine contradictions in the first place—in fact, it seems we go out of our way to avoid directly imagining them. (shrink)

Is there any value that applies to everyone? Some people believe that there is universal value, while pluralism believes that there is not. There are contradictions between the two sides. This article will compare John Gray's Isaiah Berlin with Amartya Sen's Democracy as a Universal Value to illustrate the contradictions between pluralism and universal values. In order to resolve this contradiction, this article has an experimental method to prove that democracy is universal.

We develop a second-order geometric analysis of structural tension in theory-space by examining curvature properties of the bounded completeness functional Δ. After establishing differentiability conditions on admissible domains, we define curvature via the Hessian of Δ and decompose instability modes into tangential (refinement-preserving) and normal (regime-breaking) components. Extending the framework to interacting agents, we construct a bounded global completeness functional aggregating individual incompleteness and interaction structure. We derive a collective descent condition and characterize normative stability as preservation of global descent (...) under admissible collective dynamics. The account remains structural rather than axiological: it identifies geometric constraints under which multi-agent systems remain refinement-preserving rather than self-undermining. -/- . (shrink)

This paper establishes a single foundational result: persistence without contradiction is structurally non-negotiable. Any entity that persists as identifiable must satisfy two conditions: recursive closure (stable identity under re-application) and energetic viability (boundary maintenance without resource depletion). These are not philosophical preferences but eliminative constraints—forms violating them cannot persist. We prove the constraint applies to itself, that denial presupposes it, that no more primitive alternative exists, that the constraint operates via two independent filters (consistency and solvency), and that classical (...) paradoxes resolve by structural diagnosis. The argument precedes physics, mathematics, and logic as usually formulated. The result establishes structural bedrock. (shrink)

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of (...) class='Hi'>Contradiction and Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

In his In Contradiction (1987), Priest levelled three powerful arguments against the received Russellian view of change and motion. He argued that his preferred paraconsistent theory of change, the Hegelian account, is immune from these objections. Here I argue that these three arguments are sound, but that the Hegelian account falls pray to them too. I conclude, however, that the Hegelian account is in a better position to tackle these challenges.

Here, by introducing a version of “Unexpected hanging paradox” first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in Theory of Computation about the consistency of this Theory. One of the major claim is:Theory of Computation and Classical Logic leads us to a contradiction.

This paper examines the paradoxical dynamics of political leadership and mass reception in contemporary Japan. Specifically, it highlights how factions such as the Aso group strategically utilize the symbolic legacy of former Prime Min- ister Shinzo Abe to promote Takaichi Sanae, despite simultaneous criticisms of religious–political collusion that were central to Abe’s era. Through an analysis of Yahoo! Japan comment sections (Yafukome), this study demonstrates how online masses accept and even embrace internal contradictions: condemning the Unifica- tion Church while praising (...) Abe as a heroic figure. This contradiction reveals the mechanism by which populist energy is absorbed into the party system. The comparative perspective further situates this phenomenon alongside Ger- man cases of digital populism, showing that, in both contexts, social media spaces function as ”pseudo-consensus machines.” These machines allow contradictory sen- timents to be mobilized without resolution, thus reproducing the structural logic of prewar organizations such as Japan’s Taisei Yokusankai. Ultimately, this paper ar- gues that in the age of social networks, masses are not only controlled by top-down propaganda, but also by the affective circuits of self-reinforcing digital populism. (shrink)

Tong Shijun holds a concept of dialectics which can also be found in Mao’s writings and in classical Chinese philosophy. Tong, however, is ambivalent in his attitude to dialectics in this sense, and for this reason he recommends Chinese philosophy to focus more on formal logic. My point will be that with another concept of dialectics Tong can have dialectics without giving up on logic and epistemology. This argument is given substance by an analysis of texts by Mao, Tong and (...) Hegel. (shrink)

This paper reconstructs the phenomenon of digital authoritarianism in post- Abe Japan as an inherent contradiction of populism. By analyzing the political communication strategies of Takaichi Sanae and the conservative digital networks surrounding Abe Shinzo, it redefines the structure of authority in the digital era as a triadic interaction among authority, crowd, and algorithm. Traditional populist frameworks are based on the dichotomy of ”people versus elite.” This study expands that into a triadic logic—authority versus crowd versus algorithm—demonstrating how online (...) emotional amplification, conspiracy narra- tives, and affective identity politics stabilize a new form of symbolic legitimacy. Particular attention is paid to the Japanese specificity of digital authoritarian- ism: the synthesis of tradition, nation, and female leadership. Takaichi’s rhetorical performance combines the progressive imagery of a female leader with a regressive nationalist revival, functioning as a “hybrid populist” capable of reconciling liberal expectation with conservative desire through algorithmic mediation. Finally, the paper situates these dynamics within the framework of infocratic governance—a form of control exercised not through coercion but through infor- mation modulation. The ethical limits of digital populism are thus exposed as the contradiction between expressive freedom and algorithmic dependence. (shrink)

In [Is Classical Mathematics Appropriate for Theory of Computation?] we show there is a contradiction which in [“Fuzzy Time”, a solution of Unexpected Hanging Paradox (A Fuzzy interpretation of Quantum Mechanics), Philpapers 2019-04-13] we give a solution for that. This is the starting point for new Theories, Theory of Fuzzy Time Computation and Fuzzy Time –Particle interpretation of quantum Mechanics. A question is remained which was mentioned in [Two points and two questions, F.Didehvar, Philpapers, Researchgate, 2025]. Is this (...) class='Hi'>contradiction a contradiction in Mathematics too? Here, we try to answer this question. The article belongs to a group of articles which presents the logical back bone of this line of research. (shrink)

In this paper, we deal with the issue of contradictory beliefs, particularly with regard to Philosophical Counseling: both voices from the philosophical tradition (with no claim of being exhaustive!) and concepts developed by philosophical practitioners will be considered, in order to make clear what a wide range of resources for dealing with contradictions is available to the philosopher who may wish to engage in Philosophical Counseling. Among the philosophical practitioners, we devote special consideration to Ben Mijuskovic and Gerd Achenbach, and (...) this for two main reasons: first, because the issue of contradiction plays a central role in their concept of Philosophical Counseling and, accordingly, it is given special consideration in their writings; second, because their approaches to Philosophical Counseling are so different that by looking at them one can get an impression of the variety of the positions one can adopt in Philosophical Counseling with respect to the issue of contradiction. (shrink)

In both Metaphysics Γ 4 and 5 Aristotle argues that Protagoras is committed to the view that all contradictions are true. Yet Aristotle’s arguments are not transparent, and later, in Γ 6, he provides Protagoras with a way to escape contradictions. In this paper I try to understand Aristotle’s arguments. After examining a number of possible solutions, I conclude that the best way of explaining them is to (a) recognize that Aristotle is discussing a number of Protagorean opponents, and (b) (...) import another of Protagoras’ views, namely the claim that there are always two logoi opposed to one another. (shrink)

We show how some model-theoretical devices (local reasoning, modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize the consequence relation that includes de dicto and de re contradictory beliefs. Instead of special ``sense objects'', appearances of objects in an agent's belief are introduced and presented as ordered pairs consisting of an object and an individual constant. A non-classical identity relation is applied. A relation S on the set of possible worlds is introduced, which (...) models possible distortions in an agent's picture of a (real) world. The application of such models in deontic logic is illustrated by a characteristic example. (shrink)

Dynamic semantics violates numerous classical laws, including Non-Contradiction. Proponents of dynamic semantics have offered no explanation for this behavior, and some critics consider this result to be strong evidence against the tenability of the dynamic program. I defend and explain failures of Non-Contradiction by comparing dynamic semantics and classical, truth conditional semantics in terms of their idealizing assumptions. I demonstrate that dynamic semantics rejects context fixity, an idealizing assumption that truth-conditional semantics typically adopts. I then argue that any (...) semantics which rejects context fixity should, by the classical semanticist’s own lights, violate Non-Contradiction under certain circumstances. I then demonstrate that dynamic semantics violates Non-Contradiction in all and only those circumstances. I subsequently appeal to this insight to vindicate some of dynamic semantics’ more controversial predictions. I close by suggesting that discussion of idealizing assumptions, common in the sciences, is similarly crucial to fruitful discussion in natural language semantics. (shrink)

This article debunks Bruno Latour’s seemingly pro-scientific and well-intentioned posture. I briefly summarize Latour’s constructivist, relativist, hybridist, and mystic philosophy, insisting on his radicalization in his last two books. I show that Latour’s conception is akin to “pseudo-profound bullshit”, inasmuch as he tries to hide his mysticism behind the invocation of scientific facts. I then concentrate on Latour’s politicization of climate science, showing that it is: self-contradictory from an epistemological point of view, since it presupposes scientifically established facts while at (...) the same time undermining their objectivity; counterproductive, and even dangerous, from the political point of view, since it recommends a full politicization of climate science and ignores its harmful effects. I conclude by advocating a distinction between science and politics, and by showing that Latour’s philosophy fosters our current post-truth predicament. (shrink)

Wittgenstein's farcical clash with literary critic F. R. Leavis over the analysis of Empson's poem "Legal Fiction" is well known to devotees of Wittgenstein's life (Ludwig Wittgenstein: Personal Recollections (1981), edited by Rush Rhees, Oxford: Basil Blackwell, 80). Less well known is the value of studying Empson's artistic and intellectual achievement as part of the wider cultural background for the appreciation of Wittgenstein's views and influence, early and late. This talk sketches some diverting byways awaiting further exploration. A recurrent theme (...) is contradiction. (shrink)

In this paper I critically engage with Pauline Kleingeld’s ‘volitional self-contradiction’ interpretation of Kant’s formula of universal law. I make three remarks: first, I seek to clarify what it means for a contradiction to be volitional as opposed to logical; second, I suggest that her interpretation might need to be closer to Korsgaard’s ‘practical contradiction’ interpretation than she thinks; and third, I suggest that more work needs to be done to explain how a volitional self-contradiction generates (...) both a ‘contradiction in conception’ and a ‘contradiction in will.’. (shrink)

This chapter interprets G. E. M. Anscombe’s discussion in §31 of Intention of the relationship between expressions of intention and descriptions of matters of fact. For Anscombe, a statement like “I’m raising my arm” or “I’m going to get up at 7:00”, which expresses an intention by saying what is happening or is going to happen, is contradicted only by an opposing command or the expression of an opposing intention. I first challenge an interpretation of this passage as claiming that (...) the truth of statements like these is somehow independent of whether the action they describe is actually performed. Against this reading, my preferred interpretation highlights the fact that Anscombe is speaking here only of what contradicts expressions of intention, while her position is that statements like these describe the world in ways that will be contrary to, and so truth-functionally incompatible with, any opposing statements of fact. (shrink)

Abstract Load Minimization Theory (LMT) claims to provide a non-manipulative framework for human-AI interaction based on *wu-wei*, prompt-independent resonance, and minimization of long-term system load delta E. However, examination of the YOS* preprint series (March–April 2026) reveals a systematic divergence between these theoretical principles and the described implementation methods. This paper constructs a contradiction matrix showing that LMT repeatedly advocates non- intervention while relying on explicit prompt protocols, external scaffolding, and guided conversational control. The findings indicate that LMT, in (...) its current form, lacks internal coherence and functions more as an intervention-dependent system disguised in non- intervention rhetoric. (shrink)

in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions (...) between different contexts of utterance. I present an alternative response which involves the negation of that claim, and argue that it is preferable to van Inwagen’s. (shrink)

This article challenges the prevailing interpretations of Hegel's account of the concept "contradiction" in the Science of Logic by arguing that it is concerned with the principle of Hegel's method rather than with the classical law of non-contradiction. I first consider Hegel's Doctrine of Essence in view of Kant's discussion of the concepts of reflection in the first Critique. On this basis, I examine Hegel's account of the logical principles based on the concepts "identity," "opposition," and "contradiction." (...) Finally, I point out how the principle Hegel derives from the concept of contradiction actually informs his own method. (shrink)

This work introduces a proprietary multi-layer consistency-checking framework (internally referred to as LMT MVP v1.0) designed to detect contradictions in input text early in the generation process. The system uses rule-based assertion extraction (focused on variable constraints such as ranges and negative allowance) and triggers a “consistency mode” upon conflict, resulting in re-tagged, cautious outputs that gently prompt users for re-definition rather than overconfident resolution. -/- Key features include strict example-skipping heuristics and OR-gate final gating. The framework remains proprietary and (...) is not disclosed in full detail due to upcoming commercial application. -/- We conducted informal experiments by feeding increasingly complex contradiction inputs to both standard Grok (normal mode) and a consistency-enforced instance. Results show a clear behavioral divergence: standard responses provide direct logical critique, while consistency mode yields softened, self-aware replies emphasizing epistemic humility (e.g., “the value becomes undefined… let’s redefine it together ♡”). -/- This illustrates how lightweight consistency enforcement can shift LLM interaction toward collaborative refinement. -/- . (shrink)

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on (...) the second (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold. (shrink)

This technical note introduces a structural definition of contradiction as a diagnostic variable for evaluating stability in artificial reasoning systems. It distinguishes contradiction from error, inconsistency, and hallucination by modeling it as a measurable form of internal pressure arising when a system maintains incompatible commitments. The note formalizes χ (contradiction pressure) as a scalar indicator of structural load, and C (coherence) as the system’s stability under that load. It further defines collapse as a front‑end failure mode occurring (...) when coherence can no longer be maintained as χ increases. These variables are presented strictly as diagnostic tools for analyzing reasoning behavior; they are not operational mechanisms, predictive models, or control strategies. The framework does not describe or imply any substrate‑linked, origin‑linked, or transformation‑linked processes, and it is not applicable to human identity or continuity. The document is released under a restrictive license prohibiting modification or extension. Its purpose is to provide a clear, bounded, and non‑operational vocabulary for researchers studying reasoning stability, interpretability, and alignment in artificial systems. -/- . (shrink)

Materialism asserts that matter exists independently of mind while also asserting that matter causally produces mind. This paper demonstrates that these two claims are not compatible. Independence means absence of connection. Causation is connection. The standard materialist defense invokes asymmetric temporal priority to dissolve the apparent contradiction, but this defense secretly requires external time as an unexamined premise. Since external time is itself an unjustified externalist assumption, the independence claim and the temporal assumption are mutually load-bearing, making the entire (...) structure circular at the foundational level rather than merely at the evidential level already documented in Experiential Empiricism (Sergent, n.d., "The Three-Step Argument"). (shrink)

Previously it was found that the Thing is both One Thing and another Thing at the same time. The Understanding rejects such a contradiction but Reason accepts what comes before it and allows the necessity in thought to proceed to its own conclusion. The attempt to maintain distinctions such as essential vs. unessential, singleness vs. universality, etc. may appeal to what is called ‘ordinary common sense,’ but it can now be seen that they are really only abstractions from the (...) actual truth that constitutes the entirety of perceptual consciousness. Those who do not have the presence of mind to rise above the being of the material of sense may proudly assert what they consider to be real and solid, while in truth it is only the play of abstractions that they deal with, so that such boasting is poorest where it fancies itself to be the richest. Rather than apprehending Truth, such an attitude sets itself against the Truth by calling it mere thought, ‘only in the mind’, etc. It is not possible for them to engage in scientific philosophy in which one result proceeds from another by rational necessity because they think that convincing by argument (holding one side against the other) is the natural process for winning Truth. But this is the definition of sophistry, directly the opposite of scientific philosophy in which Truth unveils itself by the rational necessity of its own dialectical development. In fact, Philosophy does also deal with mental entities but at the same time it recognizes thought as the pure essentiality that it is. It is the ignorance of our ‘scientific age’ that we neither appreciate, understand or even know how to comprehend the origin and nature of thought which is so fundamentally essential to human culture. Those who are the most neglectful of such knowledge are at the same time those who most vehemently propound sensuous materialism in the name of realism and seek to annul the place of thought altogether, thus sapping Truth of its own essence. Perceptual understanding holds on to mere abstract fixed essentialities without comprehending their specific determinations, i.e. it apprehends concepts as simple familiarities and therefore does not penetrate into the actual determinateness that constitutes such concepts. In that way it fails to master them; rather such abstract essentialities become the master of this understanding, constraining it to an endless bondage in opposing dualities. By holding on to only one determinateness as truth in opposition to its other and then turning to the opposite one (e.g., as we find in Kant’s antinomies) the ultimate unessentiality of both is established, yet it ignores this fact. What perceptual consciousness should do is accept the unessentiality of both sides and thereby recognize the sublimation of these opposing elements in a higher unity. Instead of doing that, however, it resorts to the in so far as and thus leads itself into abstractions and untruth. (shrink)

The question of whether the Pyrrhonist adheres to certain logical principles, criteria of justification, and inference rules is of central importance for the study of Pyrrhonism. Its significance lies in that, whereas the Pyrrhonist describes his philosophical stance and argues against the Dogmatists by means of what may be considered a rational discourse, adherence to any such principles, criteria, and rules does not seem compatible with the radical character of his skepticism. Hence, if the Pyrrhonist does endorse them, one must (...) conclude that he is inconsistent in his outlook. Despite its import, the question under consideration has not received, in the vast literature on Pyrrhonism of the past three decades, all the attention it deserves. In the present paper, I do not propose to provide a full examination of the Pyrrhonist’s attitude towards rationality, but to focus on the question of whether he endorses the law of non-contradiction (LNC). However, I will also briefly tackle the question of the Pyrrhonist’s outlook on both the canons of rational justification at work in the so-called Five Modes of Agrippa and the logical rules of inference. In addition, given that the LNC is deemed a fundamental principle of rationality, determining the Pyrrhonist’s attitude towards it will allow us to understand his general attitude towards rationality. (shrink)

This paper redefines the principle of non-contradiction (¬(P ∧ ¬P)) in classical logic not merely as a formal convention of thought, but as a structural “non-instantiability” within the universal system. We present a rigorous proof across five distinct layers—the physical, classical set-theoretic, quantum, computational, and category-theoretic—demonstrating the mechanisms by which contradiction is systematically avoided or annihilated. We conclude that “contradiction” as a physical entity does not exist; rather, what is perceived as undecidability or inconsistency is a convergence (...) toward “Indeterminacy,” a quarantine buffer arising from finite-precision observation systems. (shrink)

This essay argues that we should find Crimmigration, which is the collapsing of immigration law with criminal law, morally problematic for three reasons. First, it denies those who are facing criminal penalties important constitutional protections. Second, it doubly punishes those who have already served their criminal sentence with an added punishment that should be considered cruel and unusual (i.e., indefinite imprisonment or exile). Third, when the tactics aimed at protecting and serving local communities get usurped by the federal government for (...) immigration enforcement purposes, they often undermine these original aims or get used in ways that conflict with the U.S. Constitution. These concerns should prompt us therefore either to reject the government’s plenary power over immigration or require the federal government to be more consistent about maintaining the separation between criminal law and immigration law. (shrink)

This paper examines the etymological and semantic contradictions in the modern scientific terms "atom" and "molecule." The term "atom," derived from the ancient Greek atomos ("indivisible" or "uncuttable"), is fundamentally mismatched with contemporary physics, which has established that atoms are divisible composite structures made of subatomic particles (protons, neutrons, and electrons). Similarly, "molecule," from Latin molecula ("tiny mass"), lacks precise structural criteria and fails to clearly distinguish different scales and states of matter. To resolve these inconsistencies, the author proposes a (...) revised taxonomic framework drawing from the ancient Vaiśeṣika school of Indian philosophy (circa 600 BCE), particularly the concepts developed by Kaṇāda. The paper suggests: Reallocating "atom" exclusively to truly indivisible fundamental particles (fermions and bosons), restoring its original Greek meaning. Adopting Aṇu to describe the composite, divisible particles currently called atoms. Introducing Sañyuktāṇu (synthesized through Sanskrit grammatical rules) to replace "molecule," denoting bonded multi-particle systems unified through the Vaiśeṣika concept of sañyoga guṇa (conjunction or bonding force). This unified nomenclature bridges classical philosophy with modern science, eliminates conceptual paradoxes, and creates a more logically consistent and historically respectful terminology for physics and chemistry. The proposal highlights the value of integrating insights from both Greek and Indian atomistic traditions. (shrink)