Paraconsistent Research Articles

Rev. of Taking Children: A History of American Terror by Laura Briggs

Adoption & Culture Vol. 10, Issue 2 (2022) Copyright © 2022 by The Ohio State University Reviews Rev. of Taking Children: A History of American Terror LAURA BRIGGS, U of California P, 2020 240 pp. $24.95 (hardback) ISBN: 9780520343672; and Legitimating Life: Adoption in the Age of Globalization and Biotechnology SONJA VAN WICHELEN, Rutgers UP, 2019 207+xii pp. $34.95 (paperback) ISBN: 9781978800519 By John McLeod When I first accessed my adoption records six years ago and read through the paperwork with a tremulous eye, I learned a great many things about the earliest days of my life in 1969. Among the surprises that lay in wait was my designation, in one formal document, as “illegitimate.” This was not necessarily news: we had always known I was conceived and born to a single mother. Rather, the surprise was the use of this word in a quasi-official capacity, on a formal document, as an explanatory lever that was already crafting my adoptability in principle and cleaving me from my birthmother. It was a salutary lesson, post-dated forty-five years or so, of the social and discursive constitution of adoption’s validity, which is always needed for its contracting. There may never be in essence an unimpeachable reason for rendering a child adoptable, but the adoption machine both requires and produces reasons, upheld by national and international institutions, in order to legitimate its objectives. Discourses of legitimation often cloak vested interests in the guise of what’s “natural” or “best,” but can never fully conceal the politics they work so hard to hide. “Fine word—legitimate!” spits Edmund acidly in Shakespeare’s King Lear (1606), keenly aware of the confection of his branded baseness. To be sure, the base fiction of my illegitimacy was certainly required to uphold the “humanitarian” placing of me in acceptable new company as the certified son of upwardly-mobile, heterosexual, married white parents. With a paradoxical logic so often definitive of adoption’s design, these very dynamics of legitimation made me a problem to be solved and provided the ready-made solution. The adoption machine both designated me as illegitimate and rescued https://orcid.org/0000-0002-2802-3525 2 ADOPTION & CULTURE 10.2 me from shame by legitimating me via a sanctioned family unit. The plague of custom did its work, readily assisted by the laws and moral precepts of the time. In different ways, and for different reasons, Laura Briggs and Sonja van Wichelen concern themselves with with the legitimation work required to enable both the surrendering of children and the resolving of adoption contracts. Each focuses on the organizations—ranging from governments and judiciaries to adoption agencies to biomedical institutions—that concretize and realize the wider discursive construction , always highly political, of a child’s vulnerability to being taken. Briggs addresses vulnerable racialized and minoritized communities in the US and Latin America whose children have been forcibly removed thanks to the actions of welfare officers, the police and medical professionals, Homeland Security, and more besides, as part of the aggressive manipulation of judicial process at both state and federal levels by politicians and their powerful supporters. Van Wichelen explores the international legal conventions, policies, professions, and agencies that direct and deliver the transcultural adoption of children today usually by white adopters in the Global North. Both are conscious of the indebtedness of contemporary child surrender and adoption contracts to the dismal history of inequality, oppression, and family-breaking in which minoritized and marginalized peoples have severely suffered. For Briggs, in the US today the brutal taking of children from asylum seekers and precarious migrants at the southwest border has deep roots in the nation’s longstanding assault on family relations suffered especially by Native Americans, African Americans, and Latinx peoples. Van Wichelen’s inquiry into contemporary adoption in an international frame repeatedly points to the complicity of contemporary adoption practice in the neocolonial dispensation of the global world system, thinly veiled by a residual investment in a freshly laundered humanitarianism that has yet to be fully shaken off. While very different books for several reasons, when read together Briggs’s and van Wichelen’s work combine to offer a laser-sharp critique...

The doctrine of kenosis as the basis of Buddhist-Christian dialogue in the works of the philosophers of the Kyoto school

The article is devoted to the consideration of one of the episodes of the Buddhist-Christian dialogue, which was actively held in the last decades of the 20th century. The immediate cause of the discussion was the work of the Japanese thinker Abe Masao (1915–2006) “Kenotic God and Dynamic Sunyata”, where Abe compared the Buddhist concept of emptiness and the Christian idea of kenosis, “the self-emptying of God”. Abe Masao was one of the representatives of the Kyoto School of Philosophy, which existed in Japan since the beginning of the 20th century, and the idea of comparing the concepts of emptiness and kenosis was also considered by other members of this philosophical community. The philosophers of the Kyoto School developed methods of interpreting kenosis using the paradoxical Mahayana logic of “simultaneous identification and differentiation” (soku-hi). This logic can be described by the formulas: “A is not A, and therefore A” or “A is if and only if A is not A”. The first paradoxical logic of soku-hi was formulated by D. T. Suzuki (1870–1966). Nishida Kitaro (1870–1945), the founder of the Kyoto School of Philosophy, and his followers used this idea in comparative studies of the basic concepts of Buddhism and Christianity. In conclusion, one of the ways of perception of Christianity by Japanese thinkers through the prism of Buddhist philosophical approaches is shown.

Algebra-valued models for LP-set theory

In this paper, we explore the possibility of constructing algebra-valued models of set theory based on Priest's Logic of Paradox. We show that we can build a non-classical model of ZFC which has as internal logic Priest's Logic of Paradox and validates Leibniz's law of indiscernibility of identicals. This is achieved by modifying the interpretation map for $\in$ and $=$ in our algebra-valued model. We end by comparing our model constructions to Priest's model-theoretic strategy and point out that we have a tradeoff between desirable model-theoretic properties and the validity of ZFC and its theorems.

Should God believe the Liar? A non-dialetheist paraconsistent approach to God’s Omniscience

In this paper, we discuss a family of arguments that show the inconsistency of the concept of omniscience, which is one of the central attributes of the theistic God. We introduce three member of this family: Grim’s Divine Liar Paradox, Milne’s Paradox and our own Divine Curry. They can be seen as theological counterparts of well-known semantic paradoxes. We argue that the very simple dialetheist response to these paradoxes doesn’t work well and then introduce our own response based on a framework that we call Logic of Impossible Truths (LIT). LIT is a non-dialetheist paraconsistent logic designed to represent divine ominiscience and to preserve the transparency of the truth predicate and which semantics rests on the concept of situation. Since some rules of classical logic are not valid in LIT, we are in a position to block the derivation of the paradoxes. Thus, LIT offers a way out of the dilemma of accepting that there are true contradictions (dialetheism) or giving up the idea that there is an all-powerful, omniscient and perfectly good being (atheism).

Il paradosso del mentitore

The liar paradox is an ancient logical paradox (revisited by modern thinkers) which links truth with falsehood and falsehood with truth, and is based on a self-referential mechanism. It has been discussed by a variety of authors, from Aristotle to Bateson. The solution to that paradox, however, can be found by having recourse to Ludwig Wittgenstein’s philosophy, and by, so to speak, getting out of language (because true and false are words which belong to our language) to attain reality. This can be expressed through Wittgenstein’s idea that no proposition can say of itself whether it is true or false. However, experience is also expressible in words – and one can think of propositions which cannot be confirmed or disproved according to experience. Studying the paradox, therefore, leads one to Gödel’s theorem which offers a mathematical demonstration of the existence of undecidable propositions.

Why classical logic is privileged: justification of logics based on translatability

In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages.

Neural Network Explainable AI Based on Paraconsistent Analysis: An Extension

This paper explores the use of paraconsistent analysis for assessing neural networks from an explainable AI perspective. This is an early exploration paper aiming to understand whether paraconsistent analysis can be applied for understanding neural networks and whether it is worth further develop the subject in future research. The answers to these two questions are affirmative. Paraconsistent analysis provides insightful prediction visualisation through a mature formal framework that provides proper support for reasoning. The significant potential envisioned is the that paraconsistent analysis will be used for guiding neural network development projects, despite the performance issues. This paper provides two explorations. The first was a baseline experiment based on MNIST for establishing the link between paraconsistency and neural networks. The second experiment aimed to detect violence in audio files to verify whether the paraconsistent framework scales to industry level problems. The conclusion shown by this early assessment is that further research on this subject is worthful, and may eventually result in a significant contribution to the field.

Characterization and classification of numerical data patterns using Annotated Paraconsistent Logic and the effect of contradiction

This work describes the development of a computational mathematical model that uses Annotated Paraconsistent Logic - APL and a concept derived from it, the effect of contradiction, to identify patterns in numerical data for pattern classification purposes. The APL admits paraconsistent and paracomplete logical principles, which allow the manipulation of inconsistent and contradictory data, and its use allowed the identification and quantization of the attribute related to the contradiction. To validate the model, series of Raman spectroscopies obtained after exposure of proteins, lipids and nucleic acids, collected from cutaneous tissue cell samples previously examined for the detection of cancerous lesions, identified as basal carcinoma, melanoma and normal, were used. Initially, the attributes related to contradiction, derivative and median obtained from spectroscopies were identified and quantified. A machine learning process with approximately 31.6% of each type of samples detects a sequence of spectroscopies capable of characterizing and classifying the type of lesion through the chosen attributes. Approximately 68.4% of the samples are used for classification tests. The proposed model identified a segment of spectroscopies where the classification of test samples had a hit rate of 76.92%. As a differential and innovation of this work, the use of APL principles in a complete process of training, learning and classification of patterns for numerical data sets stands out, with flexibility to choose the attributes used for the characterization of patterns, and a quantity of samples of about one third of the total required for characterization.

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language (sec. 2–5). Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.

Weakly Free Multialgebras

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in exploring the foundations of multialgebras applied to the study of logic systems. It is well known from universal algebra that, for every signature \(\Sigma\), there exist algebras over \(\Sigma\) which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of \(\Sigma\)-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of \(\Sigma\)-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor \(\mathcal{U}\), from the category of \(\Sigma\)-multialgebras to Set, does not have a left adjoint. In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that \(\mathcal{U}\) does not have a left adjoint.

Managerial sensemaking of tensions in sustainability: Empirical evidence from Chinese and New Zealand business partnerships

In this paper we examine sustainability tensions among firms in business partnerships, and how managers make sense of them. To achieve this, 33 in-depth individual interviews alongside one informal group discussion were carried out at 16 relatively large, Chinese and New Zealand firms in business partnerships. We found that the New Zealand-based firms face complex and multiple sustainability tensions. We show that managers at Chinese and New Zealand firms tended to apply three kinds of logics: paradoxical, dichotomous, and business. Paradoxical logic is the type most commonly adopted. We also argue that how managers make sense of tensions in sustainability may not be influenced by their cultural values and norms. We offer scholarly and practical implications in identifying tensions in sustainability. Looking beyond traditional cultural roots helps practitioners recognise that tensions do exist when addressing divergent sustainability issues, creating more difficulty and challenges for these companies to manage them simultaneously.

Self-reflexive cognitive bias

Cognitive scientists claim to have discovered a large number of cognitive biases, which have a tendency to mislead reasoners. Might cognitive scientists themselves be subject to the very biases they purport to discover? And how should this alter the way they evaluate their research as evidence for the existence of these biases? In this paper, we posit a new paradox (the ‘Self-Reflexive Bias Paradox’), which bears a striking resemblance to some classical logical paradoxes. Suppose that research R appears to be good evidence for the existence of bias B, but if B exists, then R would have been subject to B. Thus, it seems sensible for the researcher to reject R as good evidence for the existence of B. However, rejecting R for this reason admits the existence of B. We examine four putative cognitive biases and criticisms of them, each of which seem to be subject to self-reflexivity. In two cases, we argue, paradox is avoidable. In the remaining two, we cannot find a way to avoid the paradox, which poses a practical obstacle to scientific inquiry and results in an intriguing theoretical quandary.

Metainferences from a Proof-Theoretic Perspective, and a Hierarchy of Validity Predicates

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic, 49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy, 110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc.

Consistency and Decidability in Some Paraconsistent Arithmetics


 
 
 The standard style of argument used to prove that a theory is unde- cidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent. In a non-paraconsistent set- ting, this amounts to an assumption that the theory is non-trivial, but these diverge when theories are couched in paraconsistent logics. Furthermore, there are general methods for constructing inconsistent models of arithmetic from consistent models, and the theories of such inconsistent models seem likely to differ in terms of complexity. In this paper, I begin to explore this terrain, working, particularly, in incon- sistent theories of arithmetic couched in three-valued paraconsistent logics which have strong (i.e. detaching) conditionals. 
 
 

Type Theory with Opposite Types: A Paraconsistent Type Theory

Abstract A version of intuitionistic type theory is extended with opposite types, allowing a different formalization of negation and obtaining a paraconsistent type theory ($\textsf{PTT} $). The rules for opposite types in $\textsf{PTT} $ are based on the rules of the so-called constructible falsity. A propositions-as-types correspondence between the many-sorted paraconsistent logic $\textsf{PL}_\textsf{S} $ (a many-sorted extension of López-Escobar’s refutability calculus presented in natural deduction format) and $\textsf{PTT} $ is proven. Moreover, a translation of $\textsf{PTT} $ into intuitionistic type theory is presented and some properties of $\textsf{PTT} $ are discussed.

China’s Inclusive Public Finance System: Based on an Examination of Irregular Revenue

China’s achievement of miraculous economic growth is a theoretical proposition that calls for an explanation. The key to understanding the logic of China’s economic reform is a rational explanation of the logical paradox between irregular local finance and the incentive compatibility of central and local governments. Based on the fact that autonomous local financial resources have long been dependent on irregular fiscal revenue, this paper constructs an inclusive public financial system analysis framework from the dual perspectives of the central and local government. This analytical framework offers an explanation of the long-standing implicit fiscal decentralization contract in which irregular fiscal revenue is the carrier in the reform process, together with a description of the central-local interaction process and institutional space underlying the behavioral motivations of central finance tolerance and local financial autonomy. It demonstrates the logical consistency of irregular fiscal revenue, central and local incentive compatibility, economic growth and market-oriented reform. The inclusive public finance system, which takes into account both local dynamism and central control, provides the important institutional logic that has enabled China to reach the dual goals of economic growth and market-oriented reform.

LOGICS OF FORMAL INCONSISTENCY ENRICHED WITH REPLACEMENT: AN ALGEBRAIC AND MODAL ACCOUNT

AbstractIt is customary to expect from a logical system that it can bealgebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa’s paraconsistent calculi, algebraic equivalents for such systems have been sought. It is known, however, that these systems are not self-extensional (i.e., they do not satisfy thereplacement property). More than this, they are not algebraizable in the sense of Blok–Pigozzi. The same negative results hold for several systems of the hierarchy of paraconsistent logics known asLogics of Formal Inconsistency(LFIs). Because of this, several systems belonging to this class of logics are only characterizable by semantics of a non-deterministic nature. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization ofLFIs, by extending with rules severalLFIs weaker than$C_1$, thus obtaining the replacement property (that is, suchLFIs turn out to be self-extensional). Moreover, these logics become algebraizable in the standard Lindenbaum–Tarski’s sense by a suitable variety of Boolean algebras extended with additional operations. The weakestLFIsatisfying replacement presented here is calledRmbC, which is obtained from the basicLFIcalledmbC. Some axiomatic extensions ofRmbCare also studied. In addition, a neighborhood semantics is defined for such systems. It is shown thatRmbCcan be defined within the minimal bimodal non-normal logic$\mathbf {E} {\oplus } \mathbf {E}$defined by the fusion of the non-normal modal logicEwith itself. Finally, the framework is extended to first-order languages.RQmbC, the quantified extension ofRmbC, is shown to be sound and complete w.r.t. the proposed algebraic semantics.

Paraconsistent Annotated Logic Algorithms Applied in Management and Control of Communication Network Routes.

This paper presents a computational method based on non-classical logic dedicated to routing management and information stream control in communication networks. Paraconsistent logic (PL) was used to create an algorithmic structure whose main property is to accept contradiction. Moreover, a computational structure, the denominated paraconsistent data analyzer (PDAPAL2v), was constructed to perform routing management in communication networks. Direct comparisons of PDAPAL2v with a classical logic system that simulates routing conditions were made in the laboratory. In the conventional system, the paraconsistent algorithms were considered as binary logic gates, and in the tests, the same adjustment limits of PDAPAL2v were applied. Using a database with controlled insertion of noise, we obtained an efficacy of 97% in the detection of deteriorated packets with PDAPAL2v and 72% with the conventional simulation system. Functional tests were carried out, showing that PDAPAL2v is able to assess the conditions and degradation of links and perform the analysis and correlation of various inputs and variables, even if the signals have contradictory values. From practical tests in the laboratory, the proposed method represents a new way of managing and controlling communication network routes with good performance.

The Birth of Dialetheism

The aim of this paper is to lay bare the roots of dialetheism in discussions about dialectics and dialectical logic at the time of the first development of paraconsistent logics. In other words, this essay is the attempt to write the first step of a history of dialetheism. I consider, first, the logico-philosophical terrain in which dialetheism was born: the discussions on what was called at that time ‘dialectical logic’ and its relation to paraconsistent logic. Second, I highlight what I define a dialectical turn in Richard Routley’s thought. Third, I consider Graham Priest’s arrival to Australia, which goes hand in hand with the beginning of a longstanding collaboration and friendship with Routley, and provides the conditions for the introduction of the new word at the beginning of the 1980s. I conclude with some reflections about what happens when a new word enters the philosophical world: what is made possible by the new presence? But also: what can get lost, and how can what was lost be recuperated?

Normalisation for Some Quite Interesting Many-Valued Logics

In this paper, we consider a set of quite interesting three- and four-valued logics and prove the normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3⊃. Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation.