There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: R.S. (...) Cohen et al. (Eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies fo Abner Shimony, Vol. 2, Kluwer Academic Publishers, Great Britain, 1997, pp. 177–190]. Unlike some others in the literature, these notions apply not only to certain nice sets, but to general sets in Rn and other appropriate spaces. We consider some motivations for these concepts and the logical relations between them. It has been argued that d.m.z. is especially appropriate for physical applications, and on Rn with the standard measure, it is strictly stronger than r.a. [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382]. Here we show that this is the only implication that holds among our three decidabilities in that setting. Under arbitrary measures, even this implication fails. Yet for intervals of non-zero length, and more generally, convex sets of non-zero measure, the three concepts are equivalent. (shrink)

Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates (...) Sommerer and Ott's (1996) claim of uncomputable behavior in a system with riddled basins of attraction. Furthermore, it clarifies speculations that the stability of the solar system (and similar systems) may be undecidable, for the invariant tori established by KAM theory form sets that are not d-. (shrink)

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...) be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

Transfinite ordinal numbers enter mathematical practice mainly via the method of definition by transfinite recursion. Outside of axiomatic set theory, there is a significant mathematical tradition in works recasting proofs by transfinite recursion in other terms, mostly with the intention of eliminating the ordinals from the proofs. Leaving aside the different motivations which lead each specific case, we investigate the mathematics of this action of proof transforming and we address the problem of formalising the philosophical notion of elimination which characterises (...) this move. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics (...) education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic multi-objective programming problem (...) at end of this paper. (shrink)

FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...) linear operational rules and only two branching structural rules, the latter expressing a generalized rule of bivalence. This system naturally leads to defining an infinite hierarchy of tractable depth-bounded approximations to FDE. Namely, approximations in which the number of nested applications of the two branching rules is bounded. (shrink)

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.

I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural (...) numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals. (shrink)

(...) However, whether we chose a weak or strong approximation, the set would not make any sense at all, if (once more) this choice would not be justified in either temporal or spatial sense or given the context of possible applicability of the set in different circumstances. This would obviously represent a dualism in itself as we would (for instance) posit and apply a full identity-equality-equivalence of x and y when applying Newtonian physics to certain observations we make (it would (...) be the case of neural correlates), and we would posit and apply a non - identity-equality-equivalence of x and y when applying Quantum mechanics to other observations. Following this dualism in and of theories, the same sate would need to be slightly modified: U2:(x~y)∪(x≈y); U3:(x~y)∩(x≈y); U4a:(x~y)⊆(x≈y) vs. U4b:(x~y)⊇(x≈y). (shrink)

Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception (...) of set and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable. (shrink)

By formalizing some classical facts about provably total functions of intuitionistic primitive recursive arithmetic (iPRA), we prove that the set of decidable formulas of iPRA and of iΣ1+ (intuitionistic Σ1-induction in the language of PRA) coincides with the set of its provably ∆1-formulas and coincides with the set of its provably atomic formulas. By the same methods, we shall give another proof of a theorem of Marković and De Jongh: the decidable formulas of HA are its provably ∆1-formulas.

Artificial Psychology (AP) is a highly multidisciplinary field of study in psychology. AP tries to solve problems which occur when psychologists do research and need a robust analysis method. Conventional statistical approaches have deep rooted limitations. These approaches are excellent on paper but often fail to model the real world. Mind researchers have been trying to overcome this by simplifying the models being studied. This stance has not received much practical attention recently. Promoting and improving artificial intelligence helps mind researchers (...) to find a holistic model of mental models. This development achieves this goal by using multiple perspectives and multiple data sets together with interactive, and realistic models. In this book, the methodology of approximate inference in psychological research from a theoretical and practical perspective has been considered. Quantitative variable-oriented methodology and qualitative case-oriented methods are both used to explain the set-oriented methodology and this book combines the precision of quantitative methods with information from qualitative methods. This is a book that many researchers can use to expand and deepen their psychological research and is a book which can be useful to postgraduate students. The reader does not need an in-depth knowledge of mathematics or statistics because statistical and mathematical intuitions are key here and they will be learned through practice. What is important is to understand and use the new application of the methods for finding new, dynamic and realistic interpretations. This book incorporates theoretical fuzzy inference and deep machine learning algorithms in practice. This is the kind of book that we wished we had had when we were students. This book covers at least some of the most important issues in mind research including uncertainty, fuzziness, continuity, complexity and high dimensionality which are inherent to mind data. These are elements of artificial psychology. This book implements models using R software. (shrink)

In this paper, we defined (I,T) − standard neutrosophic rough sets based on an implicator I and a t-norm T on I; lower and upper approximations of standard neutrosophic sets in a standard neutrosophic approximation are defined. Some properties of (I,T) − standard neutrosophic rough sets are investigated. We consider the case when the neutrosophic components (truth, indeterminacy, and falsehood) are totally dependent, single-valued, and hence their sum is ≤ 1.

Multi-space is the notion combining different fields in to a unifying field, which is more applicable in our daily life. In this paper, we introduced the notion of multi-soft space which is the approximated collection of the multi-subspaces of a multi-space . Further, we defined some basic operations such as union, intersection, AND, OR etc. We also investigated some properties of multi-soft spaces.

Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...) verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)

Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. Let R be a subring of Q with or without 1. By H_{10}(R), we denote the problem of whether there exists an algorithm which for any given Diophantine equation with integer coefficients, can decide (...) whether or not the equation has a solution in R. We prove that a positive solution to H_{10}(R) implies that the set of all Diophantine equations with a finite number of solutions in R is recursively enumerable. We show the converse implication for every infinite set R \subseteq Q such that there exist computable functions \tau_1,\tau_2:N \to Z which satisfy (\forall n \in N \tau_2(n) \neq 0) \wedge ({\frac{\tau_1(n)}{\tau_2(n)}: n \in N}=R). This implication for R=N guarantees that Smoryński's theorem follows from Matiyasevich's theorem. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have a rational solution is not recursive. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have only finitely many rational solutions is not recursively enumerable. These conjectures are equivalent by our results for R=Q. (shrink)

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some (...) theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft (...) class='Hi'>sets; LA-semihypergroups; single valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called (...) lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed. (shrink)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...) Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

(English then french abstract) -/- This article, which can be read by non-psychoanalysts, intends to browse in four stages through the issue offered to our thinking : two (odd-numbered) stages analyzing the argument that provides its context, and two (even-numbered) of propositions presenting our views on what could be the content of the analytic discourse in the coming years. After this introduction, a first reading will point by point but informally review the argument of J.-P. Journet by showing that each (...) of its clauses may generate a “bifurcated” comment able to serve or go against the analytic discourse. Hence the interest of the “differential diagnosis” mentioned in our title, which makes glimpse the traps that the homonymy may set to this speech. Then, to prepare a second scan which sticks neither to the analytical doxa, nor to the even authoritative opinions of our tenors and seniors, it will be proposed two attempts at redefinitions (“apophatic” and “recursive”) of what psychoanalysis is, as well as methodological tools operating downstream from these redefinitions to thwart the obstacles of “external” and “internal” homonymy (starting from a syllogism which can make consensus).The third stage will precisely be made of our second scan of the issue, whose elements will be reviewed and analyzed more methodically :“external differential diagnosis” between the analytic discourse and psychology, philosophy, sociology, and modern science, and “internal differential diagnosis” on the entanglement between theoretical advances of psychoanalysts and the repeated survival of fantasmatic elements...Finally, a fourth part will present propositions and perspectives resulting from these analysis (principle of economy as to the source of psychoanalytical theorizations; dialogue with the other fields, but without compromising; specific relations with the discourse of science), all this leading to an invitation, beyond disputes, to renew the content of the analytic discourse on some points... -/- --------------------------------------------------------------------- -/- Cet article, qui se veut lisible aux non-analystes, se propose de parcourir en quatre temps la problématique offerte à notre réflexion : deux temps (de rang impair) d'analyse de l'argument qui en fournit le contexte, et deux (de rang pair) de propositions présentant nos vues sur ce que pourrait être la teneur du discours analytique dans les prochaines années. Après cette introduction, un premier parcours réexaminera point par point mais informellement l'argument de J.-P. Journet en montrant que chacune de ses propositions peut donner lieu à un commentaire “bifide” à même de servir ou de desservir le discours analytique. D'où l'intérêt du “diagnostic différentiel” évoqué dans notre titre, qui fait entrevoir les pièges que l'homonymie peut tendre à ce discours.Puis, pour préparer un second balayage qui ne s'en tienne ni à la doxa analytique, ni aux opinions même autorisées de nos ténors et seniors, il sera proposé deux tentatives de redéfinitions (“apophatique” et “récursive”) de ce qu'est l'analyse, ainsi que des outils méthodologiques fonctionnant en aval de ces redéfinitions pour déjouer les embûches de l'homonymie “externe” et “interne” (à partir d'un syllogisme pouvant faire consensus). Le troisième temps sera fait justement de ce second balayage de la problématique, dont les éléments seront reconsidérés et analysés plus méthodiquement : “diagnostic différentiel externe” entre le discours analytique et les discours psychologique, philosophique, sociologique et celui de la science moderne ; et “diagnostic différentiel interne” portant sur l'intrication entre avancées théoriques des analystes et survivance à répétition d'éléments fantasmatiques...Enfin une quatrième partie exposera propositions et perspectives résultant de ces analyses (principe d'économie quant à la source des théorisations analytiques ; dialogue avec les autres champs, mais sans compromissions ; relations spécifiques avec le discours de la science), l'ensemble débouchant sur une invitation, au delà des différends, à renouveler sur certains points la teneur du discours analytique... (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

In this paper Johan Dahlbeck sets out to propose a pedagogy of “as if,” seeking to address the educational paradox of how students can be influenced to approximate a life guided by reason without assuming that they are already sufficiently rational to adhere to dictates of practical reason. He does so by outlining a fictionalist account, drawing primarily on Hans Vaihinger's systematic treatment of heuristic fictions and on Spinoza's ideas about how passive affects can be made to strengthen reason. (...) Dahlbeck suggests that such an account can help us overcome the problem of assuming that reason needs to be enlisted as an instrument in the educational endeavor to live according to the guidance of reason. The reason this is so is that fictions can use passive affects that are prosocial and that thereby strengthen the sense of community necessary for laying a cooperative foundation for successful joint striving. Dahlbeck suggests further that exemplary teachers are crucial to this endeavor insofar as they can offer educational fictions as imaginative and temporary placeholders for the truth, allowing students to act “as if” they were already guided by reason. (shrink)

The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single (...) valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; fuzzy measure; clustering algorithm; and many more. (shrink)

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real (...) world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. (shrink)

In this paper, a special type of polysemantic words, that is, words with multiple meanings for the same part of speech, are analyzed under the name of neutrosophic words. These words represent the most dif cult cases for the disambiguation algorithms as they represent the most ambiguous natural language utterances. For approximate their meanings, we developed a semantic representation framework made by means of concepts from neutrosophic theory and entropy measure in which we incorporate sense related data. We show the (...) advantages of the proposed framework in a sentiment classification task. (shrink)

Causation is a macroscopic phenomenon. The temporal asymmetry displayed by causation must somehow emerge along with other asymmetric macroscopic phenomena like entropy increase and the arrow of radiation. I shall approach this issue by considering ‘causal inference’ techniques that allow causal relations to be inferred from sets of observed correlations. I shall show that these techniques are best explained by a reduction of causation to structures of equations with probabilistically independent exogenous terms. This exogenous probabilistic independence imposes a recursive (...) order on these equations and a consequent distinction between dependent and independent variables that lines up with the temporal asymmetry of causation. (shrink)

Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation. This interpretation is equivalent to the interpretation by meanings of sentences if the object language is so interpreted. The added formula provides a truth predicate for the constructed language. The so obtained theory of truth satisfies the norms presented in Hannes Leitgeb's paper 'What (...) Theories of Truth Should be Like (but Cannot be)'. (shrink)

In clinical medicine, a diagnosis can offer an explanation of a patient's symptoms by specifying the pathology that is causing them. Diagnoses in psychiatry are also sometimes presented in clinical texts as if they pick out pathological processes that cause sets of symptoms. However, current evidence suggests the possibility that many diagnostic categories in psychiatry are highly causally heterogeneous. For example, major depressive disorder may not be associated with a single type of underlying pathological process, but with a range (...) of different causal pathways, each involving complex interactions of various biological, psychological, and social factors. This paper explores the implications of causal heterogeneity for whether psychiatric diagnoses can be said to serve causal explanatory roles in clinical practice. I argue that while they may fall short of picking out a specific cause of the patient's symptoms, they can nonetheless supply different sorts of clinically relevant causal information. In particular, I suggest that some psychiatric diagnoses provide negative information that rules out certain causes, some provide approximate or disjunctive information about the range of possible causal processes, and some provide causal information about the relations between the symptoms themselves. (shrink)

Purpose ‐ The purpose of this paper is to explore the "resource curse" problem as a counter-example of creative performance and innovation by examining reliance on capital and physical resources, showing the gap between expectations and ex-post actual performance that became clearer under conditions of economic turmoil. Design/methodology/approach ‐ The analysis uses logistic regressions with dichotomous response and predictor variables on structured tables of count data, representing firm performance as an outcome of capital resources, physical resources and innovation where appropriate. (...) Findings ‐ Key findings relevant to economic and business practice follow. First, a typical characteristic of successful Vietnamese firms in the transition period is their reliance on either capital resources or physical asset endowments. Second, poor performers exhibit evidence of over-reliance on both capital and physical assets. Third, firms that relied on both types of resources tended to downplay creative performance. Some evidence suggests that firms face more acute problem caused by the law of diminishing returns in troubled times. Fourth, the "innovation factor" has not been tapped as a source of economic growth. Research limitations/implications ‐ This study has some limitations. The size of the survey sample is approximately 150 firms, while the potential sample of > 300 should be possible in the future. When the size increases, the research could be expanded to include further variables that will help investigate more deeply into the related issues and business implications. With regard to the implications of the study, the absence of innovations has made the notion of "resource curse" identical to "destructive creation" implemented by ex-ante resource-rich firms, and worsened the problem of resource misallocation in transition turmoil. The Vietnamese corporate sector's addiction to resources may contribute to economic deterioration, through a downward spiral of lower efficiency leading to consumption of more resources. Practical implications ‐ Insights obtained from this study could save transition economies' resources which have almost always been considered sine qua non before any critical major policymaking, while this is not necessarily true, and in many cases, even counterproductive. Originality/value ‐ Original data set on Vietnam stock market are collected, processed, prepared and used by the authors. Original design by the authors for regression equations with dichotomous predictor variables: dependence on endowed physical assets, reliance on capital resources and significant signs of creative performance/innovations. Original idea of viewing "resource curse" as absence of innovation and due to uncreative "destructive creation" of poor-performing commercial operations by resource-rich firms is used in the paper. We have searched the literature in business research and found that the empirical results have not been previously reported. (shrink)

Abstract : Background: Vegetable agriculture is very important to human continued existence and remains a key driver of many economies worldwide, especially in underdeveloped and developing economies. Objectives: There is an increasing demand for food and cash crops, due to the increasing in world population and the challenges enforced by climate modifications, there is an urgent need to increase plant production while reducing costs. Methods: In this paper, Lemon classification approach is presented with a dataset that contains approximately 2,000 images (...) belong to 3 species at a few developing phases. Convolutional Neural Network (CNN) algorithms, a deep learning technique extensively applied to image recognition was used, for this task. The results: found that CNN-driven lemon classification applications when used in farming automation have the latent to enhance crop harvest and improve output and productivity when designed properly. The trained model achieved an accuracy of 99.48% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of self-reference.

Abstract: Tomatoes are part of the major crops in food security. Tomatoes are plants grown in temperate and hot regions of South American origin from Peru, and then spread to most countries of the world. Tomatoes contain a lot of vitamin C and mineral salts, and are recommended for people with constipation, diabetes and patients with heart and body diseases. Studies and scientific studies have proven the importance of eating tomato juice in reducing the activity of platelets in diabetics, which (...) helps in protecting them from developing deadly blood clots. A tomato classification approach is presented with a data set containing approximately 5,266 images with 7 species belonging to tomatoes. The Neural Network Algorithms (CNN), a deep learning technique applied widely in image recognition, is used for this task. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of (...) Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

According to some, the current political fracture is best described as political polarization – where extremism and political separation infest an entire whole population. Political polarization accounts often point to the psychological phenomenon of belief polarization – where being in a like-minded groups tends to boost confidence. The political polarization story is an essentially symmetrical one, where both sides are subject to the same basic dividing forces and cognitive biases, and are approximately as blame-worthy. On a very different account, what's (...) going on is best described propaganda – where a discrete set of bad actors have manipulated some part of the media environ-ment. The propaganda story is usually told as a highly asymmetrical story, where only some media consumers are under the spell of the propagandists. Which is right? I consider two analyses of the 2016 American election: Robert Talisse's polarization-style account in Overdoing Democracy, and Benkler et. al.'s propaganda-style account in Network Propaganda. I suggest that the propaganda account has better empirical support. I also offer a diagnosis of the appeal of the polarization story. Those who accept a polarization account are often political centrists, who accuse those at the political extremes of motivated reasoning – of believing what they find comfortable. Such centrists also tend to treat political extremism as the product of the irrational belief polarization, arising from living in like-minded groups. But, I argue, these arguments are too quick. First, we can’t dismiss a group as irrational merely be-cause they are likeminded. The existence of like-minded group can be explained in terms of irrational belief polarization, but it can also be explained by rational convergence on the truth. Second, belief polarization is not always irrational, such as when its emotional effects are used to repair impaired self-confidence. Third, political centrists are also subject to similar debunking argument. When we accept a polarization account, we get to feel the comfort of being “above it all”. Political centrists are just as plausibly subject to the irrational effects of living in like-minded groups. Belief polarization isn’t just for extremists. (shrink)

How confident does the history of science allow us to be about our current well-tested scientific theories, and why? The scientific realist thinks we are well within our rights to believe our best-tested theories, or some aspects of them, are approximately true.2 Ambitious arguments have been made to this effect, such as that over historical time our scientific theories are converging to the truth, that the retention of concepts and claims is evidence for this, and that there can be no (...) other serious explanation of the success of science than that its theories are approximately true. There is appeal in each of these ideas, but making such strong claims has tended to be hazardous, leaving us open to charges that many typical episodes in the history of science just do not fit the model. (See, e.g., Laudan 1981.) Arguing for a realist attitude via general claims – properties ascribed to sets of theories, trends we see in progressions of theories, and claimed links between general properties like success and truth that apply or fail to apply to any theory regardless of its content – is like arguing for or via a theory of science, which brings with it the obligation to defend that theory. I think a realist attitude toward particular scientific theories for which we have evidence can be maintained rationally without such a theory, even in the face of the pessimistic induction over the history of science. The starting point at which questions arise as to what we have a right to believe about our theories is one where we have theories and evidence for them, and we are involved in the activity of apportioning our belief in each particular theory or hypothesis in accord with the strength of the particular evidence.3 The devil’s advocate sees our innocence and tries his best to sow seeds of doubt. If our starting point is as I say, though, the innocent believer in particular theories does not have to play offense and propose sweeping views about science in general, but only to respond to the skeptic’s challenges; the burden of initial argument is on the skeptic.. (shrink)

Many of the moral and political disputes that loom large today involve claims (1) in the register of respect and offense that are (2) linked to membership in a subordinated social group and (3) occasioned by symbolic or expressive items or acts. This essay seeks to clarify the nature, stakes, and characteristic challenges of these recurring, but often disorienting, conflicts. Drawing on a body of philosophical work elaborating the moral function of etiquette, I first argue that the claims at issue (...) implicate a communicative apparatus of the same basic kind—a system that I term the “etiquette of equality.” That regime, I suggest, can serve a kindred function of facilitating the expression of morally appropriate attitudes. I also argue, however, that the etiquette of equality exhibits three problematic features that counsel ambivalence about its mounting significance: (1) the costly overdetermination of relevant signals; (2) a recursive tendency toward inflation in respect’s demands; and (3) a related set of incentives for testing, and then affirming, a group’s status through the assertion and symbolic remediation of dignitary harm. The upshot is a better understanding of the trade-offs and predicaments we face in a vital area of public life. (shrink)

Abstract cantaloupe and honeydew melons are part of the muskmelon family, which originated in the Middle East. When picking either cantaloupe or honeydew melons to eat, you should choose a firm fruit that is heavy for its size, with no obvious signs of bruising. They can be stored at room temperature until you cut them, after which they should be kept in the refrigerator in an airtight container for up to five days. You should always wash and scrub the rind (...) of your melon before you cut it to remove any dirt or bacteria on the outside. In this paper, cantaloupe classification approach is presented with a dataset that contains approximately 1,312 of Cantaloupes and honeydews. Convolutional Neural Network (CNN) algorithms, a deep learning technique extensively applied to image recognition was used, for this task. The results found that CNN-driven classification applications when used in farming automation have the latent to enhance crop harvest and improve output and productivity when designed properly. The trained model achieved an accuracy of 99.74% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

This paper concerns “human symbolic output,” or strings of characters produced by humans in our various symbolic systems; e.g., sentences in a natural language, mathematical propositions, and so on. One can form a set that consists of all of the strings of characters that have been produced by at least one human up to any given moment in human history. We argue that at any particular moment in human history, even at moments in the distant future, this set is finite. (...) But then, given fundamental results in recursion theory, the set will also be recursive, recursively enumerable, axiomatizable, and could be the output of a Turing machine. We then argue that it is impossible to produce a string of symbols that humans could possibly produce but no Turing machine could. Moreover, we show that any given string of symbols that we could produce could also be the output of a Turing machine. Our arguments have implications for Hilbert’s sixth problem and the possibility of axiomatizing particular sciences, they undermine at least two distinct arguments against the possibility of Artificial Intelligence, and they entail that expert systems that are the equals of human experts are possible, and so at least one of the goals of Artificial Intelligence can be realized, at least in principle. (shrink)

I spell out and update the individuality thesis, that species are individuals, and not classes, sets, or kinds. I offer three complementary presentations of this thesis. First, as a way of resolving an inconsistent triad about natural kinds; second, as a phylogenetic systematics theoretical perspective; and, finally, as a novel recursive account of an evolved character. These approaches do different sorts of work, serving different interests. Presenting them together produces a taxonomy of the debates over the thesis, and isolates (...) ways it has been productive. This goes to the larger point of this paper: a defense of the individuality thesis in terms of its utility, and an update of it in light of recent theoretical developments and empirical work in biology. (shrink)

The scientific realism debate has now reached an entirely new level of sophistication. Faced with increasingly focused challenges, epistemic scientific realists have appropriately revised their basic meta-hypothesis that successful scientific theories are approximately true: they have emphasized criteria that render realism far more selective and, so, plausible. As a framework for discussion, I use what I take to be the most influential current variant of selective epistemic realism, deployment realism. Toward the identification of new case studies that challenge this form (...) of realism, I break away from the standard list and look to the history of celestial mechanics, with an emphasis on twentieth century advances. I then articulate two purely deductive arguments that, I argue, properly capture the historical threat to realism. I contend that both the content and form of these novel challenges seriously threaten selective epistemic realism. I conclude on a positive note, however, arguing for selective realism at a higher level. Even in the face of threats to its epistemic tenet, scientific realism need not be rejected outright: concern with belief can be bracketed while nonetheless advocating core realist tenets. I show that, in contrast with epistemic deployment realism, a purely axiological scientific realism can account for key scientific practices made salient in my twentieth century case studies. And embracing the realists favored account of inference, inference to the best explanation, while pointing to a set of the most promising alternative selective realist meta-hypothesis, I show how testing the latter can be immensely valuable to our understanding of science. (shrink)

This is a sketch of the basis and role of consciousness and the minimally required elements and constraints of any setting that may produce consciousness. It proposes that consciousness (as we know it) is a biologically-mediated product of evolved recursive and hierarchically nested representational systems that obey information theoretic principles and Bayesian (probabilistic) feedback and feedforward predictive modeling processes.

The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a quantum theory of space-time and therefore focus on loop quantum gravity. We conceive atoms of space, represented in terms of nodes linked by edges in a graph, as the primitive ontology of the theory and show how a non-local law in which (...) a universal and stationary wave-function figures can provide an order of configurations of such atoms of space such that the classical space-time of general relativity is approximated. Although there is as yet no fully worked out physical theory of quantum gravity, we regard the Bohmian approach as setting up a standard that proposals for a serious ontology in this field should meet and as opening up a route for fruitful physical and mathematical investigations. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)