A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent (...) logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent (...) setting. (shrink)

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion of (...) formal consistency. (shrink)

Paraconsistency is the study of logical systems with a non-explosive negation such that a pair of contradictory formulas (with respect to such negation) does not necessarily imply triviality, discordant to what would be expected by contemporary logical orthodoxy. From a purely logical point of view, the significance of paraconsistency relies on the meticulous distinction between the general notions of contradictoriness and triviality of a theory—respectively, the fact that a given theory proves a proposition and its negation, and the fact that (...) a given theory proves any proposition (in the language of its underlying logic). Aside from this simple rationale, the formal techniques and approaches that meet the latter definitional requirement are manifold. Furthermore, it is not solely the logical-mathematical properties of such systems that are open to debate. Rather, there are several foundational and philosophical questions worth studying, including the very question about the nature of the contradictions allowed by paraconsistentists. This entry aims to advance a brief account of some distinct approaches to paraconsistency, providing a panorama on the development of paraconsistent logic. (shrink)

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of (...) using the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic (...) is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively. (shrink)

This chapter contains sections titled: What is Paraconsistency? Motives for Paraconsistency The Sources of Trivialization A Natural Taxonomy for Paraconsistent Logics Paraconsistent Logics Current Issues.

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound (...) and complete three-sided sequent calculus for this expressively rich theory. (shrink)

This paper extends Ontological Density Theory by identifying the logical foundation upon which all density formation operates: paraconsistency. Paraconsistent logic—a formal system in which contradictory statements can both hold truth values without producing systemic collapse—is not a failure mode of human cognition but its natural operating environment. High-density entities do not function despite internal contradictions; they function through them. The paper proposes that human beings are socialized into paraconsistent space before they develop any capacity for critical reflection. Layer (...) 0 (pre-linguistic family immersion, ages 0-4) encodes contradiction tolerance at the somatic level. Subsequent layers of socialization reinforce and institutionalize this tolerance, producing adults who navigate fundamentally incoherent ontological systems as a matter of course. All high-density entities—religious, political, economic, national—are internally contradictory and many are mutually contradictory. This is not a defect. Contradiction is the fuel of density. A critical implication follows: the Enlightenment did not transcend this condition. It substituted the aesthetic of its densities while preserving identical epistemic architecture. Science, Nation, and Market replaced God, King, and Church while operating through the same paraconsistent logic. The priests were renamed experts. The miracles were renamed data. The faithful were renamed citizens and consumers. Humans remain permanently embedded in magical-paraconsistent space. Modernity changed the furniture, not the house. The paper further examines how densities under temporal pressure develop characteristic repair mechanisms: when material reality fails to align with ontological claims, entities patch the gap with additional contradictions rather than structural revision. The 'rules-based international order' is analyzed as an exemplary case of a high-density entity that achieves causal power precisely through definitional incoherence. Understanding paraconsistency as density's foundation is essential for analyzing institutional resilience, ideological capture, and the persistence of magical thinking in ostensibly rational societies. Keywords: paraconsistent logic, ontological density, socialization, magical thinking, Enlightenment, contradiction, institutional resilience, epistemic architecture, social ontology . (shrink)

The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical (...) logic. It is however not clear how paraconsistent logic can be seen as model-building. What exactly is modeled? In this paper I adopt the perspective of looking at a particular instance of paraconsistent logic—paranormal modal logic—which might be seen as a model of a specific kind of agent: inductive agents. After ntroducing what I call the highlevel and low-level models of inductive agents, I analyze the extent to which the above-mentioned idealizing features of model-building appear in paranormal modal logic and how they affect its philosophical significance. (shrink)

This article proposes The Paraconsistent as a philosophical-political category to name the subject who exists constitutively in ontological contradiction — not due to epistemic deficiency but by structural condition — and who from that position produces thought, knowledge and action without collapsing into either of its poles. Drawing on a critical revision of two dominant traditions for handling contradiction — presented here as interpretive models called the First Logos and the Second Logos — the article proposes the Third Logos (...) as a form of rationality especially adequate for contexts where contradiction is structural, persistent and irreducible. Logical colonialism — the imposition of coherence and non-contradiction criteria as conditions for recognizing knowledge, identity or decisions as valid — is identified as the object of liberation this philosophy proposes. The praxis operates in three simultaneous registers: pedagogical, technical and epistemic. (shrink)

Logics of Formal Inconsistency (LFIs) are usually considered a philosophically neutral logicwith respect to paraconsistency, in the sense that they provide a good basis to think in termsof dialetheias, i.e. true contradictions, or in terms of conflicting information, a notion weakerthan truth. In this article, I will show how this claim of neutrality fails in the face of the LiarParadox: in classical logic, the sentence A: “A is false.” implies a contradiction. By adoptinga paraconsistent logic, we avoid that contradictions (...) lead to triviality. LFIs, however, add aconsistency operator that recovers classical logic to propositions to which it applies. In thiscontext, the Liar Paradox arises once again by a type of Liar’s Revenge: now, we can constructthe sentence B: “B is only false.”, and that gives us triviality once again. With this result, weconclude that LFIs are not suitable logics to deal with semantic paradoxes. (shrink)

In this paper paraconsistent first-order logic LP^{#} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#} is discussed.Axiomatical system HST^{#}as paraconsistent generalization of Hrbacek set theory HST is considered.

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo, is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides (...) the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twiststructures, generalizing a known result on the representation of the algebraic counterpart of paraconsistent Nelson logic.

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the (...) importance of a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)

"Paraconsistent Belief Revision Based on a Formal Consistency Operator" delves into Belief Revision—a significant area of research in Formal Philosophy that uses logic to model the ways in which human and artificial agents modify their beliefs in response to new information and examines how these changes can be considered rational. -/- Originally authored as a PhD thesis (previously published in Portuguese), this work provides a novel epistemic interpretation of Paraconsistency through Paraconsistent Belief Revision systems. It explores the concept (...) of paraconsistency from the standpoint of epistemic attitudes of acceptance and rejection. -/- This work challenges the traditional notion that accepting a new belief requires retracting its negation from the current epistemic state. The author contends that such reflexive retraction goes against the principle of informational economy, which is a crucial aspect of rationality in the context of belief change. Consequently, the phenomenon of paraconsistency is further examined from this fresh perspective of belief change, shedding light on the complexities of the Logics of Formal Inconsistency (LFIs). These LFIs provide the foundational logic, offering a comprehensive framework for understanding and implementing paraconsistent principles within belief revision systems. -/- This thesis was supervised by Marcelo Esteban Coniglio and co-supervised by Márcio Moretto Ribeiro, as part of Rafael Rodrigues Testa's doctoral studies at the University of Campinas (Unicamp), Brazil. (shrink)

A logic is paraconsistent if it allows for non-trivial inconsistent theories. Given the usual definition of inconsistency, the notion of paraconsistent logic seems to rely upon the interpretation of teh sign '¬'. As paraconsistent logic challenges properties of negation taken to be basic in other contexts, it is disputable that an operator lacking those properties will count as real negation. The conclusion is that there cannot be genuine paraconsistent logics. This objection can be met from a (...) substructural perspective, since paraconsistent sequent calculi can be built from the same operational rules as classical logic but with slightly different structural rules. (shrink)

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to (...) philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we argue that an intuitive reading of the bivalued semantics for the logic mbC, a logic of formal inconsistency based on classical logic, fits in well with the basic ideas of an intuitive interpretation of contradictions. On this interpretation, the acceptance of a pair of propositions A and ¬A does not mean that A is simultaneously true and false, but rather that there is conflicting evidence about the truth value of A. (shrink)

PDK is a paraconsistent, dynamic reconstruction of Kant’s Categorical Imperative (CI). Its central move is to internalize universalizability not as a meta-level test but as a model update: an "everyone adopts M" operator that transforms the practice structure and then re-evaluates norms. Built on a four-valued (Belnap-Dunn) base with an LFI-style consistency test and neighborhood semantics for obligation, PDK tolerates genuine moral tensions without explosion while preserving disciplined deontic reasoning through consistency and feasibility guards. -/- Two CI tests are (...) formalized in the object language---no contradiction in conception and no contradiction in the will---and both are evaluated after update. A CI rule licenses duty only when both tests pass; autonomy appears as fixed-point stability of those tests under their own universalization. Technically, reduction schemata eliminate update operators into a static core; the paper proves soundness, establishes relative completeness for the propositional dynamic fragment, derives a finite model property and PSPACE-completeness for that fragment, and marks undecidability frontiers for first-order extensions. -/- An impossibility landscape explains why the guarded design is necessary: unguarded classical deontics plus a strong CI trivialize; no static surrogate exists for update; harmless commuting updates are vacuous; strong “ought implies can” fails under reflective resource limits; and update nesting yields a strict depth hierarchy. Case studies (lying promise, promise vs. rescue, self-defeating maxims, harmless beneficence, order sensitivity) illustrate the logic’s behavior. Philosophically, PDK isolates a logical core of transcendental normativity: update invariance and fixed-point stability, and, in this reconstruction, offers a novel structural reading of Kantian transcendentality as self-invariance under universalization. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, (...) further reflections on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs (...) recover the validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

Building on Nunes Filho's recent positioning of paraconsistent logic as a constitutive element of Latin American philosophy (RUDN Journal of Philosophy, 2025), this paper traces a continuation of that tradition into the contemporary problem of artificial intelligence alignment. We argue that the Latin American paraconsistent project — initiated by Miro Quesada's coining of the term in 1976 and formalized by Newton da Costa's C-systems — finds its natural twenty-first century extension in Florentin Smarandache's neutrosophic logic (1995), which generalizes (...) paraconsistency by introducing three independent dimensions of evidence: truth (T), indeterminacy (I), and falsity (F), with no sum constraint. We further contextualize this development within the broader Eastern European tradition of non-classical logic, from Vasiliev's non-Aristotelian logic (1911) and the Romanian school of Lukasiewicz–Moisil multi-valued algebras to Smarandache's emigration from Romania in 1988 and his subsequent founding of neutrosophy. We then show that contemporary AI alignment frameworks — Reinforcement Learning from Human Feedback, Constitutional AI, Direct Preference Optimization — operate under an implicit epistemological monism that mirrors precisely the classical-logic universalism the Latin American tradition critiqued. Anthropic's own documentation of Collective Constitutional AI confirms that contradictions among diverse constitutional principles are resolved by majority vote — what we term enforced convergence rather than alignment. We propose Pluriversal Alignment: a research program that operationalizes paraconsistent neutrosophic triplets as reward signals, constitutional evaluations, and policy outputs, allowing T+F>1 as a structural feature rather than an error. We close by arguing that the Latin American paraconsistent tradition, in convergence with its Russian and Eastern European counterparts, is uniquely positioned to contribute the formal apparatus that the decolonial critique of AI has named philosophically but not yet formalized. (shrink)

One tradition in relevant and paraconsistent logics has been to develop sys- tems intended for applications to arithmetic and computability theory. The aspiration, as in Meyer [38] and others, is to recover enough working mathe- maticsforrealcomputation, butwithoutthelimitativeresultsofTuring, Gödel, etc.; or more cautiously, as in Dunn [22], to respect relevance and with that be insulated against the possibility of a genuine inconsistency. We distill these goals into guiding questions, and study the options for logics within a range of relevant systems. (...) We focus on strong truth functional logics RM3and PAC [6] and their expansions, with application to inconsistent arithmetics [62, 63]. We argue that this approach, while having many virtues, does not fully answer our guiding questions. This points to weak relevant logics like Routley/Sylvan’s DKQ [54], Brady’s MCQ [14], and Logan and Boccuni’s DL2Qt,f c [31]. The recurring theme is that paraconsistent computability struggles with functional- ity [17, 41, 43]. A method for advancing on the ‘function problem’ is sketched with Kleene’s theorem as a worked example. (shrink)

In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once (...) the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on (...) classical logicians and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

In this paper we present an overview, with historical and critical remarks, of two articles by S. Jaśkowski ([20, 21] 1948 and [22, 23] 1949), which contain the oldest known formulation of a paraconsistent logic. Jaśkowski has built the logic – he termed discussive (D2) – by defining two new connectives and by introducing a modal translation map from D2 systems into Lewis’ modal logic S5. Discussive systems, for their formal details and their original philosophical justification, have attracted discrete (...) attention among experts. Indeed, in what follows, after having introduced Jaśkowski methodology of building D2 and his main philosophical motivations for providing such a system, we will explore some of the main contributions to the development of D2. (shrink)

Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...) some expressions is not uniquely defined. Other strategies for generalizing supervaluations are considered and some comparative facts are discussed. (shrink)

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2. This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)

In several papers [6–8], Beall argues that, since we can add to non-classical (including paraconsistent) arithmetics rules that restore classicality, we can effectively recover classical arithmetical reasoning in non-classical systems. According to Halbach and Nicolai [18], however, the move to non-classical arithmetic comes at the expense of proof-theoretic strength, undermining Beall’s claims. Then how can paraconsistent arithmetics be said to recover classical strength? It is not sufficient to prove classical arithmetical consequences in a fragment of the language, as (...) done e.g. by Friedman and Meyer [14], since this would yield strictly weaker theorems. In this paper, I provide a so-called classical recapture result for Zach Weber’s paraconsistent arithmetic $\textsf{subDLQ-A}$, based on the logic $\texttt{subDLQ}$ [43]. I reconstruct a notion of coding and recursion for this paraconsisent arithmetic, and show that the theory, if supplemented with additional forms of induction and classical axioms for identity, supports Gentzen’s classical lower bound proof for transfinite induction up to any ordinal less than $\varepsilon _{0}$. (shrink)

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...) both BLE and LET J. The meanings of the connectives of BLE and LET J, from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)

This paper is a sequel to “Subject Unicity and Self-Ascription: A Paraconsistent Formalization with σ-Lag” (hereafter “Subject Theory”, PhilPapers record CSUADU.). Preserving the value layer and rules of the previous work (X–σ, No3, SU-bridge), we extend the observational/representational layer into a topological–operational model. Specifically, we introduce a state space X, a decidable region O_+++ = { f_I>0, f_S>0, f_R>0 }, and a local orientation indicator R_sig = sign det[∇f_I, ∇f_S, ∇f_R], thereby relocating the judgment of the jouissance effect into (...) a topological space. Clinically, this means one reports only triggers/evidence, while the equality sign (=) is an event-type fixation permitted once only within a licensing window. The key indicators are: (i) a continuous quantity a_eff := Res_σ(Φ) ∈ ℝ_{≥0} representing the amount of σ-trace, (ii) R_sig ∈ {−1, 0, +1}, and (iii) the optional reinforcement by μ̄_123. Here, observational equivalence ≈_obs is evidenced by a_eff(x) > 0 and is kept strictly distinct from ontological equivalence ≡_onto. As a result, the structure remains discrete, while phenomenology is smoothly tracked via continuous quantities such as a_eff and κ. Lacan’s “phallus = imaginary” is re-formalized not as rhetoric but as an anti-scalarization rule: φ acts only as an inner rotation operator carried by the imaginary axis of quaternions (including slice invariance), forbidding any fall into the value layer. Fixation of fantasy is judged by the topological loop with R_sig = −1, and the promotion ‘≈ → =’ is permitted exactly once only within the AUG_eq subcategory. The subject–object a relation is read as a Möbius isomorph: ontologically equivalent yet phase-inverted on the observational layer, so ‘=’ is allowed only as an event after passing Gate(Δτ), thereby blocking explosion routes. Furthermore, consistency with the University discourse is exhibited by ∂(a_eff)/∂(s*) > 0 when x ∈ O_+++ and R_sig = −1, capturing the right-hand sensitivity (S2 → a) on the top line. Safety is secured by No3, SU, and the Reflexive Guards: global ‘=’ is prohibited; no direct updates to the value layer; and R_sig, μ̄_123, amp are used purely as trigger/evidence indicators. This design supplies a checklist-style clinical heuristic (Obs/σ/AUG logs, the condition R_sig = −1 ∧ a_eff > 0, and exactly one ‘=’ after gate approval) without compromising structural stability. In short, symptoms are not erased but operated—fixed as events precisely at the point where the same strip meets again, now inverted. 이 글은 「주체의 자기귀속과 단일성: σ-시차와 파라일관 논리의 형식화」(이하 「주체론」, PhilPapers record CSUADU.)의 후속이다. 전작 「주체론」의 값층·규칙(X–σ, No3, SU-브리지)을 그대로 유지한 채, 관측·표상 레이어를 위상-연산 모델로 확장한다. 구체적으로, 상태공간 X와 판정가능 영역 O_+++ = { f_I>0, f_S>0, f_R>0 } 및 국소 방향 판정자 R_sig = sign det[∇f_I, ∇f_S, ∇f_R]를 도입해, 주이상스 효과의 판정을 위상공간으로 이관한다. 이렇게 하면 임상에서는 증거·트리거만 보고하고, 등호(=)는 면허 윈도우에서만 1회 허가되는 사건형 고정으로 제한된다. 핵심 지표로는 (i) σ-흔적의 양을 나타내는 연속량 a_eff := Res_σ(Φ) ∈ ℝ_{≥0}, (ii) R_sig ∈ {−1, 0, +1}, (iii) 필요 시 보강되는 μ̄_123 등을 사용한다. 이때 관측-동치 ≈_obs는 a_eff(x) > 0에 의해 증거화되며, 존재론-동치 ≡_onto와 엄격히 구분된다. 덕분에 구조는 이산이되, 양상은 a_eff와 κ 같은 연속값으로 매끈하게 추적된다. 라캉의 "남근=허수"는 수사가 아니라 반(反)스칼라화 규칙으로 재정식화된다: φ는 사원수 허수 캐리어의 내적 회전 연산자(슬라이스 불변성 포함)로만 작동하며, 값층으로의 낙하를 금지한다. 환상의 교착은 R_sig = −1인 위상 고리로 판정되고, '≈ → =' 승격은 AUG_eq 하위 범주에서만 1회 허가된다. 또한 주체–대상 a 관계는 뫼비우스 동형으로 읽힌다: 존재론적으로는 동치이나 관측층에서는 위상이 반전되어, 등호는 오직 Gate(Δτ) 통과 시 사건형으로만 잠깐 가능하다(폭발 경로 차단). 더 나아가, 대학 담론과의 정합성은 x ∈ O_+++ · R_sig = −1일 때 ∂(a_eff)/∂(s*) > 0가 성립함을 통해 보인다(상단 S2 → a 채널의 우항 감도). 안전성은 No3·SU·Reflexive Guards로 고정된다: 전역 '=' 금지, 값층 직접 갱신 금지, 트리거/증거 전용 지표(R_sig, μ̄_123, amp). 이 설계는 임상에서 체크리스트형 휴리스틱(Obs/σ/AUG 로그, R_sig = −1 ∧ a_eff > 0 조건, 게이트 승인을 거친 단 1회의 '=')을 제공하면서도 구조적 안정성을 해치지 않는다. 요컨대, 증상은 지워지는 게 아니라 운용되며, 같은 띠지만 뒤집혀 만나는 그 지점에서 사건으로 고정된다. (shrink)

A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...) system with labels, signs, and suffixes is defined, extending the basic language $\mathscr{L}_{\mathbf{QB}}$ by quasiformulas (to express the denotations of predicates). The proposed logical system is paraconsistent since $\phi \wedge \neg\phi$ does not ``explode'' with arbitrary syntactic consequences. (shrink)

Review of the book "Paraconsistent Logic: Consistency, Contradiction, and Negation by Water Carnielli and Marcelo Coniglio.

Hal ini sering berpikir bahwa kemustahilan, ketidaklengkapan, Paraconsistency, Undecidability, Randomness, komputasi, Paradox, ketidakpastian dan batas alasan yang berbeda ilmiah fisik atau matematika masalah memiliki sedikit atau tidak ada dalam Umum. Saya menyarankan bahwa mereka sebagian besar masalah filosofis standar (yaitu, Permainan bahasa) yang sebagian besar diselesaikan oleh Wittgenstein lebih dari 80years yang lalu. -/- "Apa yang kita ' tergoda untuk mengatakan ' dalam kasus seperti ini, tentu saja, bukan filsafat, tetapi bahan baku. Jadi, misalnya, apa yang seorang matematikawan cenderung mengatakan (...) tentang objektivitas dan realitas fakta matematika, bukan filsafat matematika, tetapi sesuatu untuk pengobatan filosofis. " Wittgenstein PI 234 -/- "Filsuf terus melihat metode ilmu di depan mata mereka dan tak tertahankan tergoda untuk bertanya dan menjawab pertanyaan dalam cara ilmu tidak. Kecenderungan ini adalah sumber nyata metafisika dan memimpin filsuf menjadi gelap gulita. " Wittgenstein -/- Aku memberikan ringkasan singkat dari beberapa temuan utama dari dua siswa yang paling terkemuka perilaku zaman modern, Ludwig Wittgenstein dan John Searle, pada struktur Logis intensionality (pikiran, bahasa, perilaku), mengambil sebagai titik awal Penemuan fundamental Wittgenstein – bahwa semua masalah ' filosofis ' adalah sama — kebingungan tentang bagaimana menggunakan bahasa dalam konteks tertentu, sehingga semua solusi sama — melihat bagaimana bahasa dapat digunakan dalam konteks yang menjadi masalah sehingga kebenaranNya kondisi (kondisi kepuasan atau COS) jelas. Masalah dasar adalah bahwa seseorang dapat mengatakan apa-apa, tetapi orang tidak dapat berarti (negara yang jelas cos untuk) sembarang ucapan dan makna hanya mungkin dalam konteks yang sangat spesifik. -/- Saya membedah beberapa tulisan dari beberapa komentator utama pada isu ini dari sudut pandang Wittgensteinian dalam kerangka perspektif modern dari dua sistem pemikiran (Dipopulerkan sebagai ' berpikir cepat, berpikir lambat '), mempekerjakan meja baru intensionality dan baru sistem ganda nomenklatur. Saya menunjukkan bahwa ini adalah heuristik yang kuat untuk menggambarkan sifat sebenarnya dari hal ini ilmiah, fisik atau matematika masalah yang benar-benar terbaik didekati sebagai masalah filosofis standar bagaimana bahasa yang akan digunakan (permainan bahasa di Wittgenstein's terminologi). -/- Ini adalah pendapat saya bahwa tabel intensionality (rasionalitas, pikiran, pikiran, bahasa, kepribadian dll) yang fitur mencolok di sini menggambarkan lebih atau kurang akurat, atau setidaknya berfungsi sebagai heuristic untuk, bagaimana kita berpikir dan berperilaku, dan sehingga mencakup tidak hanya filsafat dan psikologi, tetapi segala sesuatu yang lain (sejarah, sastra, matematika, politik dll). Perhatikan terutama bahwa intensionalitas dan rasionalitas sebagai I (bersama dengan Searle, Wittgenstein dan lain-lain) melihatnya, mencakup baik sistem linguistik pertimbangan sadar 2 dan tidak disadari otomatis sistem prelinguistik 1 tindakan atau refleks. (shrink)

The main research goal of the work is to study the notion of co-topos, its correctness, properties and relations with toposes. In particular, the dualization process proposed by proponents of co-toposes has been analyzed, which transforms certain Heyting algebras of toposes into co-Heyting ones, by which a kind of paraconsistent logic may appear in place of intuitionistic logic. It has been shown that if certain two definitions of topos are to be equivalent, then in one of them, in the (...) context of a subobject classifier, there should be a neutral label for the generic subobject, or if the label "true" appears instead, it carries no additional properties or assumptions. It has been shown that a natural isomorphism occurring in one of the definitions of topos need not be an isomorphism of the corresponding algebraic structures on the sets, so that a co-Heyting algebraic structure can be defined on the set of characteristic morphisms, which moreover will also be natural. The analyzes suggest that the notion of co-topos may be considered correct. However, it should be strongly emphasized that although the possibility of defining the notion of co-topos has been shown, its further full consequences should be very carefully examined, which can severely limit its logical applications. (shrink)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new (...) proof of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

In celebration of Newton da Costa’s place in the history of paraconsistency, this paper considers the use and abuse of deliberate self-contradiction. Beginning with Parmenides, developed by Plato, and continued by Cicero, an ancient philosophical tradition used deliberately paraconsistent discourses to reveal the truth. In modern times, decisionism has used deliberate self-contradiction against Judeo-Christian revelation. • DOI:10.5007/1808-1711.2010v14n1p1.

Logic systems that can handle contradictions were being used for some time without having a general technical name. One of the main proposers of these systems, Newton da Costa, asked Francisco Miró Quesada to suggest him a name for those systems. In the historical letter that here we translate into English for the first time, Miró Quesada suggests three names to da Costa for this purpose: ‘ultraconsistent’, ‘metaconsistent’, and ‘paraconsistent’; explaining their pros and cons. Paper based on a letter (...) by Francisco Miró Quesada Cantuarias to Newton da Costa, edited, translated, and annotated by Luis Felipe Bartolo Alegre. (shrink)

'गोडेल के रास्ते' में तीन प्रख्यात वैज्ञानिकों ने अनिर्णय, अपूर्णता, यादृच्छिकता, गणनाऔरता और परासंगति जैसे मुद्दों पर चर्चा की। मैं Wittgensteinian दृष्टिकोण से इन मुद्दों दृष्टिकोण है कि वहाँ दो बुनियादी मुद्दों जो पूरी तरह से अलग समाधान है. वहाँ वैज्ञानिक या अनुभवजन्य मुद्दों, जो दुनिया के बारे में तथ्य है कि अवलोकन और दार्शनिक मुद्दों की जांच की जरूरत है के रूप में कैसे भाषा intelligibly इस्तेमाल किया जा सकता है (जो गणित और तर्क में कुछ सवाल शामिल हैं), (...) जो की जरूरत है एकटी कैसे हम वास्तव में विशेष संदर्भों में शब्दों का उपयोग देख कर फैसला किया. जब हम जो भाषा खेल हम खेल रहे हैं के बारे में स्पष्ट हो, इन विषयों को किसी भी अन्य की तरह साधारण वैज्ञानिक और गणितीय सवाल देखा जाता है. है Wittgenstein अंतर्दृष्टि शायद ही कभी बराबर किया गया है और कभी नहीं पार कर रहे हैं और के रूप में आज के रूप में प्रासंगिक हैं के रूप में वे 80 साल पहले थे जब वह ब्लू और ब्राउन पुस्तकें हुक्म दिया. अपनी असफलताओं के बावजूद-वास्तव में एक समाप्त पुस्तक के बजाय नोटों की एक श्रृंखला-यह इन तीन प्रसिद्ध विद्वानों के काम का एक अनूठा स्रोत है जो आधे से अधिक सदी से भौतिकी, गणित और दर्शन के खून बह रहा किनारों पर काम कर रहे हैं। दा कोस्टा और डोरिया Wolpert द्वारा उद्धृत कर रहे हैं (नीचे देखें या Wolpert पर मेरे लेख और Yanofsky 'कारण की बाहरी सीमा' की मेरी समीक्षा) के बाद से वे सार्वभौमिक गणना पर लिखा था, और उनके कई उपलब्धियों के बीच, दा कोस्टा में अग्रणी है paraconsistency. आधुनिक दो systems दृश्यसे मानव व्यवहार के लिए एक व्यापक अप करने के लिए तारीख रूपरेखा इच्छुक लोगों को मेरी पुस्तक 'दर्शन, मनोविज्ञान, मिनडी और लुडविगमें भाषा की तार्किक संरचना से परामर्श कर सकते हैं Wittgenstein और जॉन Searle '2 एड (2019). मेरे लेखन के अधिक में रुचि रखने वालों को देख सकते हैं 'बात कर रहेबंदर- दर्शन, मनोविज्ञान, विज्ञान, धर्म और राजनीति पर एक बर्बाद ग्रह --लेख और समीक्षा 2006-2019 3 एड (2019) और आत्मघाती यूटोपियान भ्रम 21st मेंसदी 4वें एड (2019) . (shrink)

We present a formal account of subjectivity without external foundations. Over an extended LP/FDE truth alphabet, we axiomatize a self-ascriptive relation R(x,x) and a Subject Unicity (SU) scheme. We separate the linguistic lag operator X from the intra-perspectival successor σ, redefine same-place equivalence (≈), and license the identity sign (=) only via explicit upgrade anchors at the fix layer (Augenblick). Under a no-third-channel guard that blocks explosion while preserving the contradiction value B, we prove that within each connected cover the (...) set of subject candidates A/≈ collapses to a single class. This distinction between coordinate identity and event identity prevents premature global identification while yielding a constructive criterion of identity at stabilization. Conceptually, the system couples Hegelian dialectics with Lacanian failure of subsumption: contradiction is treated not as error but as structural motor. Aligning Tarskian/Gödelian limits with a Lacanian “delegated deficit,” we accordingly read R(x,x). The σ-translation captures how contradiction (B) is conserved and truth (T) emerges post hoc, offering a logic-driven reconstruction of dialectical temporality and the singular emergence of the subject. 본 논문은 외부 준거 없이 닫히는 형식 체계 위에서 주체의 자기귀속 R(x,x)과 주체 단일성(SU)을 공리화한다. 언어적 시차 연산자 X와 관점 내부 후속자 σ를 분리하고, 동일장소 동치 ‘≈’와 등호 승격(앵커) 규칙을 도입해 동일성의 작동 조건을 제시한다. 확장 LP/FDE 값층에서 모순값 B를 보존하고 제3채널 금지(No3) 가드를 둘 때, 연결 성분/커버 내부에서 주체-후보 집합 A/≈가 단일 동치류로 붕괴함을 증명한다. 이는 좌표 동일화와 사건 동일화를 구분하여 과도한 전역 동일시를 차단하고, Augenblick(고정층)에서만 ‘=’이 면허됨을 보인다. 결과적으로 주체는 속성의 총합이 아니라 사후적 표지에 의해 고정되는 규칙적 자기지시로 나타난다. 본문은 헤겔적 변증법(모순의 내재적 운동)과 라캉적 포섭 실패를 접합해 모순을 결함이 아니라 구조적 동력으로 제시하고, 타르스키/괴델류 한계를 라캉의 ‘대리-결손’과 접속해 R(x,x)를 해석한다. σ-번역은 모순(B)의 보존과 진리(T)의 사후적 출현을 기술하며, 이를 통해 변증법적 시간성과 주체의 단독성이 파라일관 논리 장치로 재구성될 수 있음을 보인다. (shrink)

Dalam ' Godel ' s Way ' tiga ilmuwan terkemuka membahas isu seperti undecidability, ketidaklengkapan, kekasaran, komputasi dan paraconsistency. Saya mendekati masalah ini dari sudut pandang Wittgensteinian bahwa ada dua masalah dasar yang memiliki solusi yang sama sekali berbeda. Ada masalah ilmiah atau empiris, yang merupakan fakta tentang dunia yang perlu diselidiki masalah observationally dan filosofis mengenai bagaimana bahasa dapat digunakan secara jelas (yang mencakup pertanyaan tertentu dalam matematika dan logika), yang perlu diputuskan dengan mencarit bagaimana kita benar-benar menggunakan kata (...) dalam konteks tertentu. Ketika kita mendapatkan jelas tentang mana permainan bahasa yang kita bermain, topik ini dipandang sebagai pertanyaan ilmiah dan matematika biasa seperti orang lain. Wawasan Wittgenstein jarang sama dan tidak pernah melampaui dan seperti yang berkaitan dengan hari ini karena mereka 80 tahun yang lalu ketika dia mendikte buku Blue and Brown. Terlepas dari kegagalan-benar serangkaian catatan daripada buku selesai-ini adalah sumber yang unik dari pekerjaan tiga sarjana terkenal yang telah bekerja di tepi berdarah fisika, matematika dan filsafat selama lebih dari setengah abad. Da Costa dan Doria dikutip oleh Wolpert (Lihat di bawah atau artikel saya di Wolpert dan saya review yanofsky's ' The Outer batas dari alasan ') karena mereka menulis di Universal komputasi, dan di antara banyak prestasi, da Costa adalah pelopor dalam paraconsistency. -/- Mereka yang ingin komprehensif up to date kerangka perilaku manusia dari dua systEMS tampilan modern dapat berkonsultasi buku saya 'struktur Logis filsafat, psikologi, mind dan bahasa dalam Ludwig wittgenstein dan John Searle ' 2nd Ed (2019). Mereka yang tertarik pada tulisan saya lebih mungkin melihat 'berbicara monyet--filsafat, psikologi, ilmu, agama dan politik di planet yang ditakdirkan--artikel dan review 2006-2019 3rd ed (2019) dan bunuh diri utopian delusi di 21st Century 4th Ed (2019) . (shrink)

Dans 'Godel’s Way', trois éminents scientifiques discutent de questions telles que l’indécidabilité, l’incomplétude, le hasard, la calculabilité et la paraconsistence. J’aborde ces questions du point de vue de Wittgensteinian selon lesquelles il y a deux questions fondamentales qui ont des solutions complètement différentes. Il y a les questions scientifiques ou empiriques, qui sont des faits sur le monde qui doivent être étudiés de manière observationnelle et philosophique quant à la façon dont le langage peut être utilisé intelligiblement (qui incluent certaines (...) questions en mathématiques et en logique), qui doivent être décidés en regardant un comment nous utilisons réellement des mots dans des contextes particuliers. Lorsque nous obtenons clair sur le jeu de langue que nous jouons, ces sujets sont considérés comme des questions scientifiques et mathématiques ordinaires comme les autres. Les idées de Wittgenstein ont rarement été égalées et jamais dépassées et sont aussi pertinentes aujourd’hui qu’elles l’étaient il y a 80 ans lorsqu’il a dicté les Livres Bleus et Brown. Malgré ses défauts, vraiment une série de notes plutôt qu’un livre fini, c’est une source unique du travail de ces trois savants célèbres qui travaillent aux confins de la physique, des mathématiques et de la philosophie depuis plus d’un demi-siècle. Da Costa et Doria sont cités par Wolpert (voir ci-dessous ou mes articles sur Wolpert et mon examen de Yanofsky 'The Outer Limits of Reason') depuis qu’ils ont écrit sur le calcul universel, et parmi ses nombreuses réalisations, Da Costa est un pionnier dans la paraconsistence. -/- Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deux système peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 » 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (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)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking at (...) how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

In this paper, I survey the history of the Polish tradition of paraconsistency and its chronological development. I outline the features of this tradition to provide some insights into the more general notion of philosophical schools. The main features of the Polish tradition of paraconsistency are the continuation of research on a previous philosophical tradition and international collaboration.