Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017

The project "Beyond Logic" is devoted to what hypothetical reasoning is all about when we go beyond the realm of "pure" logic into the world where logic is applied. As such extralogical areas we have chosen philosophy of science as an application within philosophy, informatics as an application within the formal sciences, and law as an application within the field of social interaction. The aim of the conference was to allow philosophers, logicians and computer scientists to present their work in connection with these three areas. The conference took place 22-27 May, 2017 in Cerisy-la-Salle at the Centre Culturel International de Cerisy. The proceedings collect abstracts, slides and papers of the presentations given, as well as a contribution from a speaker who was unable to attend

The Proscriptive Principle and Logics of Analytic Implication

The analogy between inference and mereological containment goes at least back to Aristotle, whose discussion in the Prior Analytics motivates the validity of the syllogism by way of talk of parts and wholes. On this picture, the application of syllogistic is merely the analysis of concepts, a term that presupposes—through the root ἀνά + λύω —a mereological background. In the 1930s, such considerations led William T. Parry to attempt to codify this notion of logical containment in his system of analytic implication AI. Parry’s original system AI was later expanded to the system PAI. The hallmark of Parry’s systems—and of what may be thought of as containment logics or Parry systems in general—is a strong relevance property called the ‘Proscriptive Principle’ (PP) described by Parry as the thesis that: No formula with analytic implication as main relation holds universally if it has a free variable occurring in the consequent but not the antecedent. This type of proscription is on its face justified, as the presence of a novel parameter in the consequent corresponds to the introduction of new subject matter. The plausibility of the thesis that the content of a statement is related to its subject matter thus appears also to support the validity of the formal principle. Primarily due to the perception that Parry’s formal systems were intended to accurately model Kant’s notion of an analytic judgment, Parry’s deductive systems—and the suitability of the Proscriptive Principle in general—were met with severe criticism. While Anderson and Belnap argued that Parry’s criterion failed to account for a number of prima facie analytic judgments, others—such as Sylvan and Brady—argued that the utility of the criterion was impeded by its reliance on a ‘syntactical’ device. But these arguments are restricted to Parry’s work qua exegesis of Kant and fail to take into account the breadth of applications in which the Proscriptive Principle emerges. It is the goal of the present work to explore themes related to deductive systems satisfying one form of the Proscriptive Principle or other, with a special emphasis placed on the rehabilitation of their study to some degree. The structure of the dissertation is as follows: In Chapter 2, we identify and develop the relationship between Parry-type deductive systems and the field of ‘logics of nonsense.’ Of particular importance is Dmitri Bochvar’s ‘internal’ nonsense logic Σ0, and we observe that two ⊢-Parry subsystems of Σ0 (Harry Deutsch’s Sfde and Frederick Johnson’s RC) can be considered to be the products of particular ‘strategies’ of eliminating problematic inferences from Bochvar’s system. The material of Chapter 3 considers Kit Fine’s program of state space semantics in the context of Parry logics. Recently, Fine—who had already provided the first intuitive semantics for Parry’s PAI—has offered a formal model of truthmaking (and falsemaking) that provides one of the first natural semantics for Richard B. Angell’s logic of analytic containment AC, itself a ⊢-Parry system. After discussing the relationship between state space semantics and nonsense, we observe that Fabrice Correia’s weaker framework—introduced as a semantics for a containment logic weaker than AC—tacitly endorses an implausible feature of allowing hypernonsensical statements. By modelling Correia’s containment logic within the stronger setting of Fine’s semantics, we are able to retain Correia’s intuitions about factual equivalence without such a commitment. As a further application, we observe that Fine’s setting can resolve some ambiguities in Greg Restall’s own truthmaker semantics. In Chapter 4, we consider interpretations of disjunction that accord with the characteristic failure of Addition in which the evaluation of a disjunction A ∨ B requires not only the truth of one disjunct, but also that both disjuncts satisfy some further property. In the setting of computation, such an analysis requires the existence of some procedure tasked with ensuring the satisfaction of this property by both disjuncts. This observation leads to a computational analysis of the relationship between Parry logics and logics of nonsense in which the semantic category of ‘nonsense’ is associated with catastrophic faults in computer programs. In this spirit, we examine semantics for several ⊢-Parry logics in terms of the successful execution of certain types of programs and the consequences of extending this analysis to dynamic logic and constructive logic. Chapter 5 considers these faults in the particular case in which Nuel Belnap’s ‘artificial reasoner’ is unable to retrieve the value assigned to a variable. This leads not only to a natural interpretation of Graham Priest’s semantics for the ⊢-Parry system S⋆fde but also a novel, many-valued semantics for Angell’s AC, completeness of which is proven by establishing a correspondence with Correia’s semantics for AC. These many-valued semantics have the additional benefit of allowing us to apply the material in Chapter 2 to the case of AC to define intensional extensions of AC in the spirit of Parry’s PAI. One particular instance of the type of disjunction central to Chapter 4 is Melvin Fitting’s cut-down disjunction. Chapter 6 examines cut-down operations in more detail and provides bilattice and trilattice semantics for the ⊢-Parry systems Sfde and AC in the style of Ofer Arieli and Arnon Avron’s logical bilattices. The elegant connection between these systems and logical multilattices supports the fundamentality and naturalness of these logics and, additionally, allows us to extend epistemic interpretation of bilattices in the tradition of artificial intelligence to these systems. Finally, the correspondence between the present many-valued semantics for AC and those of Correia is revisited in Chapter 7. The technique that plays an essential role in Chapter 4 is used to characterize a wide class of first-degree calculi intermediate between AC and classical logic in Correia’s setting. This correspondence allows the correction of an incorrect characterization of classical logic given by Correia and leads to the question of how to characterize hybrid systems extending Angell’s AC∗. Finally, we consider whether this correspondence aids in providing an interpretation to Correia’s first semantics for AC

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), Vol. IV

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) – but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions. This is an eclectic tome of 800 pages with papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory, information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics. It was my preoccupation and collaboration as author, co-author, translator, or cotranslator, and editor with many scientists from around the world for long time. Many topics from this book are incipient and need to be expanded in future explorations

Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society

Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud \ud \ud KEYWORDS: Emergence of Life and Human Consciousness;\ud Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud \u

Rethinking inconsistent mathematics

This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the rolee of logic and ethics in the practice of mathematics

Une Dialectica matérialiste

In this thesis, we give a computational interpretation to Gödel's Dialectica translation, in a fashion inspired by classical realizability. In particular, it can be shown that the Dialectica translation manipulates stacks of the Krivine machine as first-class objects and that the main effect at work lies in the accumulation of those stacks at each variable use. The original translation suffers from a handful of defects due to hacks used by Gödel to work around historical limitations. Once these defects are solved, the translation naturally extends to much more expressive settings such as dependent type theory. A few variants are studied thanks to the linear decomposition, and relationships with other translations such as forcing and CPS are scrutinized.Cette thèse fournit une interprétation calculatoire de la traduction dite Dialectica de Gödel, dans une démarche inspirée par la réalisabilité classique. On peut en particulier montrer que Dialectica manipule des piles de la machine de Krivine comme objets de première classe et que le principal effet de cette traduction consiste à accumuler ces piles à chaque utilisation de variables. La traduction d'origine souffre d'une certaine quantité de défauts dus aux hacks utilisés par Gödel pour contourner des limitations historiques. Une fois ces problèmes résolus, la traduction s'étend naturellement à des paradigmes beaucoup plus expressifs tels que la théorie des types dépendants. On étudie d'autres variantes par la suite grâce à la décomposition linéaire, ainsi que lien de parenté avec d'autres traductions tels que le forcing et les CPS

What the heck is Logic? Logics-as-formalizations, a nihilistic approach

Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse