Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In (...) this paper, we propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

This paper explains what an infinite regress argument is. Part 1 contains some examples of infinite regress arguments. Part 2 presents a schema for all such arguments an defines an infinite regress argument as one that approximates to the schema. Part 3 tests the schema on the examples. Part 4 contrasts my account of infinite regress arguments with that given by Passmore and shows that Passmore's theory succumbs to objections. Part 5 distinguishes an infinite regress argument from an infinite regress (...) and defines an infinite regress. Part 6 explains the dyslogistic force of 'infinite regress'. (shrink)

In this book, the authors introduce the linguistic set associated with a linguistic variable and the structure of matrices, which they define as linguistic matrices. The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The first chapter is introductory, in which we introduce all the basic concepts of linguistic variables and the associated linguistic set to make this book self-contained. (...) Chapter two introduces linguistic matrices and develops basic properties associated with them, like types of matrices, transpose of matrices and diagonal matrices. Most of the properties enjoyed by real or complex matrices are satisfied by these linguistic matrices. Chapter three deals with operations on the linguistic matrices. (shrink)

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. This book will be highly useful to social scientists who wish (...) to work with multi expert models. (shrink)

In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution.

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts of the (...) nature of vagueness and definiteness. (shrink)

This paper outlines a critique of the use of the genetic variance–covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations – contrary to what assumed by most practicing biologists. I suggest that the search for (...) a general solution to the difficult problem of identifying causal structures given observed correlation’s has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners. (shrink)

Puisque nous n'avons pu trouver un fondement logique à la dialectique, nous avons alors compris que la dialectique était historique. Il ne restait plus alors qu'à trouver la culture d'origine que nous avons localisée en Perse. -/- Since we could not find a logical foundation for the dialectic, we then understood that the dialectic was historical. All that remained was to find the culture of origin, which we located in Persia.

In this book authors for the first time introduce the notion of super interval matrices using special intervals. The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes.

In this article, we shall define the addition and multiplication of two neutrosophic fuzzy matrices. Thereafter, some properties of addition and multiplication of these matrices are also put forward.

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

The objective of this paper is to study algebraic properties of neutrosophic matrices, where a necessary and sufficient condition for the invertibility of a square neutrosophic matrix is presented by defining the neutrosophic determinant. On the other hand, this work introduces the concept of neutrosophic Eigen values and vectors with an easy algorithm to compute them. Also, this article finds a necessary and sufficient condition for the diagonalization of a neutrosophic matrix.

Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...) and well-ordering -- and implying an ordinal re-creation of the continuum. During the last hundred years, the mainstream set-theoretical research -- all insights and adjustments due to Kurt G\"odel's revolutionary insights and discoveries notwithstanding -- has compliantly centered its efforts on ad hoc axiomatizations of Cantor's intuitive transfinite design. We demonstrate here that the ontological and epistemic sustainability} of this design has been irremediably compromised by the underlying peremptory, Reductionist mindset of the XIXth century's ideology of science. (shrink)

The thesis of the paper maintains it is impossible to disregard a change in the statue of analytical psychology involving the notion of psychoid and its correlation to quantum physics, being psyche not separable from matter. This change finds its most accomplished and impressive epicentre in C.G. Jung and W. Pauli’s theory of synchronicity, in which the Jungian Self becomes the psyche’s quantum psychoid regulatory center, in a Spiritual sense.

Here we present an experimental model to be applied to the storage and retrieval of information based on an associative information system’s sensory and motor state change data, aiming to represent the dynamics of a dynamic perceptual system. The model and database implementation use a universal information storage structure holding both data and metadata within the same structure. This model is characterized by the emphasis on associative information about the represented system derived from raw data, which are in their turn (...) produced by the associative system’s interactions with the environment. Instead of defining objects using descriptive relations, this model stores relations between occurents where the represented system is not replicated in its various components, but defined by its relations when they occur. This model therefore represents the dynamics and interaction of systems such as human perception, rather than imposing artificial boundaries and qualities. In essence, the model is an alternative to perceptual knowledge accumulation, which, as we show, can be applied to a database design. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

Trivalence is quite natural for deontic action logic, where actions are treated as good, neutral or bad.We present the ideas of trivalent deontic logic after J. Kalinowski and its realisation in a 3-valued logic of M. Fisher and two systems designed by the authors of the paper: a 4-valued logic inspired by N. Belnap’s logic of truth and information and a 3-valued logic based on nondeterministic matrices. Moreover, we combine Kalinowski’s idea of trivalence with deontic action logic based on (...) boolean algebra. (shrink)

The authors propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. The cycle basis corresponds to a fundamental null-space basis of the adjacency matrix. This problem is meant to model sparse null-space basis computations occurring in a variety of settings. An O(n3/2) bound is achieved on the nullspace basis size (i.e., the number of nonzero entries in the basis), and an O(n log n) bound on the size in the special case of grid graphs.

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

Although Strawson’s main aim in “On Referring” was to argue that definite descriptions can be used referentially – that is, “to mention or refer to some individual person or single object . . . , in the course of doing what we should normally describe as making a statement about that person [or] object” (1950, p. 320) – he denied that definite descriptions are always used referentially. The description in ‘Napoleon was the greatest French soldier’ is not used referentially, says (...) Strawson, since it is used not to mention an individual, but only “to say something about an individual already mentioned” (p. 320). This is an example of what we may call a predicative use of a definite description, though such uses might be better illustrated by considering the false sentence.. (shrink)

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...) where a reasoner fulfills all the alethic norms and could be used as a standard of rationality (as they are, in fact, used in some of these approaches). I propose a function α, which accepts a set of beliefs as inputand returns a numeric alethic value. Then I use this function to define a notion of alethic maximality that is satisfiable by finite reasoners (reasoners with cognitive limitations) and does not present problems with blindspots. Function α may also be used in alethic norms and evaluation methods (comparative and non-comparative) that may be applied to finite reasoners and do not present problems with blindspots. A result of this investigation isthat the project of providing purely alethic norms is defective. The use of function α also sheds light on important epistemological issues, such as the lottery and the preface paradoxes, and the principles of clutter avoidance and reflection. (shrink)

In this paper I explore Kant’s critical discussions of the topic of miracles (including the important but neglected fragment from the 1780s called “On Miracles”) in an effort to answer the question in the title. Along the way I discuss some of the different kinds of “laws” in Kant’s system, and also the argument for his claim that, even if empirical miracles do occur, we will never be in a good position to identify instances of them. I conclude with some (...) tentative remarks about the notorious suggestion that intelligible finite agents, too, might have some sort of influence over the laws of nature. The goal throughout is to show that exploring Kant’s answer to a traditional question in philosophical theology can deepen our understanding of his metaphysics and epistemology of nature generally. (shrink)

Mereotopology faces problems when its methods are extended to deal with time and change. We offer a new solution to these problems, based on a theory of partitions of reality which allows us to simulate (and also to generalize) aspects of set theory within a mereotopological framework. This theory is extended to a theory of coarse- and fine-grained histories (or finite sequences of partitions evolving over time), drawing on machinery developed within the framework of the so-called ‘consistent histories’ interpretation (...) of quantum mechanics. (shrink)

Can the theory that reality is a simulation be tested? We investigate this question based on the assumption that if the system performing the simulation is nite (i.e. has limited resources), then to achieve low computational complexity, such a system would, as in a video game, render content (reality) only at the moment that information becomes available for observation by a player and not at the moment of detection by a machine (that would be part of the simulation and whose (...) detection would also be part of the internal computation performed by the Virtual Reality server before rendering content to the player). Guided by this principle we describe conceptual wave/particle duality experiments aimed at testing the simulation theory. (shrink)

Understanding Hume’s theory of space and time requires suspending our own. When theorizing, we think of space as one huge array of locations, which external objects might or might not occupy. Time adds another dimension to this vast array. For Hume, in contrast, space is extension in general, where being extended is having parts arranged one right next to the other like the pearls on a necklace. Time is duration in general, where having duration is having parts occurring one aft (...) er another like the notes of a song. Hume’s diff erent view stems from his empiricism, his reliance on experience and observation as the foundation of our concepts. Nothing in our experience suggests a single vast array of locations. Rather, we simply notice that bodies are similar insofar as they have lengths that can be compared. Likewise, nothing in our experience suggests a single dimension of time. Rather, we simply notice that diff erent successions are similar insofar as they have durations that can be compared. Th eorizing that these observations show there to be a single multidimensional array goes well beyond the evidence for Hume. As a skeptic, he fi nds himself unable to assent to theories that stray too far beyond the deliverances of the senses. For Hume, the ideas of space and time are each a general idea of simple—partless— objects arrayed in a certain manner. He argues that the structures of the ideas of space and time refl ect the structures of space and time. Th erefore, space and time are not infi - nitely divisible, and they are ways simple objects are arrayed. Consequently, there is no such thing as empty space nor time without change. (shrink)

Bilattices, introduced by Ginsberg as a uniform framework for inference in artificial intelligence, are algebraic structures that proved useful in many fields. In recent years, Arieli and Avron developed a logical system based on a class of bilattice-based matrices, called logical bilattices, and provided a Gentzen-style calculus for it. This logic is essentially an expansion of the well-known Belnap–Dunn four-valued logic to the standard language of bilattices. Our aim is to study Arieli and Avron’s logic from the perspective of (...) abstract algebraic logic . We introduce a Hilbert-style axiomatization in order to investigate the properties of the algebraic models of this logic, proving that every formula can be reduced to an equivalent normal form and that our axiomatization is complete w.r.t. Arieli and Avron’s semantics. In this way, we are able to classify this logic according to the criteria of AAL. We show, for instance, that it is non-protoalgebraic and non-self-extensional. We also characterize its Tarski congruence and the class of algebraic reducts of its reduced generalized models, which in the general theory of AAL is usually taken to be the algebraic counterpart of a sentential logic. This class turns out to be the variety generated by the smallest non-trivial bilattice, which is strictly contained in the class of algebraic reducts of logical bilattices. On the other hand, we prove that the class of algebraic reducts of reduced models of our logic is strictly included in the class of algebraic reducts of its reduced generalized models. Another interesting result obtained is that, as happens with some implicationless fragments of well-known logics, we can associate with our logic a Gentzen calculus which is algebraizable in the sense of Rebagliato and Verdú . We also prove some purely algebraic results concerning bilattices, for instance that the variety of distributive bilattices is generated by the smallest non-trivial bilattice. This result is based on an improvement of a theorem by Avron stating that every bounded interlaced bilattice is isomorphic to a certain product of two bounded lattices. We generalize it to the case of unbounded interlaced bilattices. (shrink)

Some contemporary semantic views defend an asymmetry thesis concerning defi-nite descriptions and indexicals. Semantically, indexicals are devices of singular refer-ence; they contribute objects to the contents of the speech acts made with utterances including them. Definite descriptions, on the other hand, are generalized quantifiers, behaving roughly the way Russell envisaged in “On Denoting”. The asymmetry thesis depends on the existence of a sufficiently clear-cut distinction between semantics and pragmatics, because indexicals and descriptions are often used in ways that apparently contradict (...) the asymmetry thesis; the semantics/pragmatics distinction is invoked to see behind the appearances. The paper critically examines arguments by Schiffer against the asymmetry thesis, based on referential uses of incomplete descriptions. (shrink)

Berkeley was a philosopher who wrote about such diverse topics as natural philosophy, political philosophy, mathematics, economy, and theology. Within this broad range of interests, his concern about the infinite spirit stands out; thus, the aim of this paper is to trace the origins of Berkeley´s conception of God, an issue which is already prefigured in the Philosophical Commentaries. The importance of knowing and analyze the notes that make up the Commentaries lies in that they make it possible to understand (...) not only how the incipient immaterialist philosophy was established, but above all –being purpose of this paper– what features and role God acquired within it. (shrink)

D O N A L D D AV I D S O N’S “ Meaning and Truth,” re vo l u t i o n i zed our conception of how truth and meaning are related (Davidson    ). In that famous art i c l e , Davidson put forw a rd the bold conjecture that meanings are satisfaction conditions, and that a Tarskian theory of truth for a language is a theory of meaning for that language. (...) In “Meaning and Truth,” Davidson proposed only that a Tarskian truth theory is a theory of meaning. But in “Theories of Me a n i n g and Learnable Languages,” he argued that the finite base of a Tarskian theory, together with the now familiar combinatorics, would explain how a language with unbounded expre s s i ve capacity could be learned with finite means ( Davidson    ). This certainly seems to imply that learning a language is, in p a rt at least, learning a Tarskian truth theory for it, or, at least, learning what is specified by such a theory. Davisdon was cagey about committing to the view that meanings actually a re satisfaction conditions, but subsequent followers had no such scru p l e s . We can sum this up in a trio of claims: Davidson’s Conjecture () A theory of meaning for L is a truth-conditional semantics for L. () To know the meaning of an expression in L is to know a satisfaction condition for that expression. () Meanings are satisfaction conditions. For the most part, it will not matter in what follows which of these claims is at stake. I will simply take the three to be different ways of formulating what I will call Davidson’s Conjecture (or sometimes just The Conjecture). Davidson’s Conjecture was a very bold conjecture. I think we are now in a.. (shrink)

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

This study focuses on the essential difference between Kant’s and Husserl’s transcendental Idealism. In fact, Husserl describes in the «Cartesian Meditations» his own ontological thesis as a «transcendental idealism», in which all sorts of entities have to be constituted by an activity of the transcendental subjectivity, so that we have to regard pure consciousness as the ontological origin of all entities in the world. But this study is interested in the two opposite signications of the Kantian copernican inversion. On the (...) one hand, the Copernican inversion has the same sense as the phenomenological reduction, which implies that Husserl can’t agree with Kant’s presupposition of absolute things in themselves; on the second hand, it involves a relativistic and anthropologistic orientation, so that the aprioristic structures of given objects are founded on the universal structures of finite subjectivity, on pure forms and faculties of human consciousness. At the opposite, Husserl enounces a methodological prescription for any phenomenological elucidation: it is not allowed to presuppose in phenomenology any given faculty or given nature of transcendental subjectivity. This prescription has important consequences on which this study focuses. First the ontological difference between intuitus originarius and intuitus derivatus, in nite and nite type of intuition, doesn’t have any validity: the difference between factual and rational truths only depends on the essence of the truth itself, and doesn’t have its foundation on the ontological difference between creative and receptive sort of intuition. Secondly, this first thesis admits an immediate application on the level of subjective constitution of objects: the modality in which an object appears to the subjectivity doesn’t depend on the universal structure of finite subject, but is exclusively founded on the essence of the object itself, so that it is impossible to consider the aprioristic constitutive structure as a merely subjective structure. Thirdly, in this transcendental phenomenology everything has to be constituted by subjectivity: the aprioristic character of the pure forms of sensibility is not founded on the structure of finite subjectivity, but rather on the essential connection between sensual material and form; so that it is not allowed to presuppose any facticity of time and space; the pure forms of sensibility have to be constituted by a special type of synthesis that we have to elucidate in opposition to other types of higher levels. The profound signication of Husserl’s anticopernican inversion is that the field of transcendental phenomenology consists of the essential form of an eidos ego, which is «more objective than any objectivity», as Levinas said; and that transcendental phenomenology is completely dominated by the principium reddendae rationis. (shrink)

Context sensitivity is one of the distinctive marks of human intelligence. Understanding the flexible way in which humans think and act in a potentially infinite number of circumstances, even though they’re only finite and limited beings, is a central challenge for the philosophy of mind and cognitive science, particularly in the case of those using representational theories. In this work, the frame problem, that is, the challenge of explaining how human cognition efficiently acknowledges what is relevant from what is (...) not in each context, has been adopted as a guide. By using it, we’ve been able to describe a fundamental tension between context sensitivity and the mental representations used in cognition theories. The first chapter discusses the nature of the frame problem,as well as the reasons for its persistence. In the second and third chapters, the problem is used as a measure tool in order to inquiry a few representational approaches and check how well suited they are to deal with context dependencies. The problems found are then correlated with the frame problem. Throughout the discussion, we try to show that 1) none of the evaluated approaches is capable of dealing with context sensitivity in a proper manner, but 2) that’s not a reason to think that the frame problem constitutes an argument against representational approaches in general, and 3) that it constitutes a fundamental conceptual tool in contemporary research -/- A sensibilidade ao contexto é uma das marcas distintivas da inteligência humana. Compreender o modo flexível como o ser humano pensa e age em função de um número potencialmente infinito de circunstâncias, ainda que munido de recursos finitos e limitados, é um desafio central para a filosofia da mente e para a ciência cognitiva, em particular aos que fazem uso de teorias representacionalistas. Nesse trabalho, adotou-se como fio condutor o modo como isso se manifesta no "frame problem": a dificuldade em explicar como a cognição humana reconhece, de maneira eficiente, o que é ou não relevante em cada contexto. A partir dele, buscou-se caracterizar uma tensão fundamental entre a sensibilidade ao contexto e o uso de representações mentais em teorias da cognição. O primeiro capítulo discute a natureza do frame problem, bem como as razões de sua resiliência. No segundo e terceiro capítulos, faz-se uso do problema como métrica para investigar o quão adequado é o tratamento das dependências contextuais no âmbito de várias abordagens representacionais. No decorrer da discussão, realiza-se um esforço argumentativo para mostrar que 1) nenhuma das estratégias abordadas é capaz tratar adequadamente da sensibilidade ao contexto, mas que 2) apesar disso, o frame problem não constitui argumento fatal para teorias representacionalistas em geral, e que 3) ele constitui uma ferramenta conceitual fundamental para pesquisas contemporâneas. (shrink)

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces are (...) introduced. The notion of a linguistic special subset of doubly non-commutative topological spaces of linguistic topological spaces is introduced in this book. (shrink)

The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data (...) structures, pairs of terms syntax, semantics for example. These sequences then combine with the help of simple generalizations of the usual abstraction and application operations. This theory, which I call Lambda Grammars and which is closely related to the independently formulated theory of Abstract Categorial Grammars (de Groote, 2001; de Groote, 2002), in fact is an implementation of Curry’s ideas: the level of tectogrammar is encoded by the sequences of lambda-terms and their ways of combination, while the syntactic terms in those sequences constitute the phenogrammatical level. In de Groote’s formulation of the theory, tectogrammar is the level of abstract terms, while phenogrammar is the level of object terms. (shrink)

It is commonly held that nature is knowable in itself and that death has no explanatory priority in knowing nature. I reject both claims as they undermine an account of the unity of human life, failing, respectively, to thematize the limitations of finite understanding and to acknowledge what’s most certain about finite existence. I use Kant’s idea of the thing in itself and Heidegger’s idea of death to solve two structurally analogous antinomies these failures leave intact. I conclude (...) that to think these ideas is to represent the telos that unifies our living as, respectively, finite knowers and finite beings. (shrink)

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with (...) a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture (...) of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in (...) semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic semirings and can be used in Neutrosophic matrices and vectors. (shrink)

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding as (...) inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)

A mesure qu'ils avancent dans leur œuvre de prospection, les sémioticiens s'aperçoivent que tout est communication, la langue bien sûr, mais aussi les images, les sons, les objets, les gestes, et que tous ces phénomènes constituent des systèmes de signes qui doivent être étudiés en ramenant chaque message aux codes qui en régissent l'émission et la compréhension. Comprendre les systèmes de signes impose toutefois d'envisager les codes comme des structures, puis de recouvrir à des structures toujours plus vastes, dans un (...) mouvement de régression vers la matrice originelle de toute communication possible, vers un prétendu Code des Codes qui devrait représenter la détermination " naturelle " précédant toute culture. Mais si la sémiotique s'engageait dans cette voie, elle ne pourrait qu'aboutir à la " source " de toute structure possible, forcément non structurée, à ce qu'Umberto Ecco appelle la structure absente. Son livre, tout en refusant ce Code des Codes, essaie de montrer que tout acte communicatif est dominé par la présence massive de codes socialement et historiquement déterminés. La sémiotique découvre ainsi dans la dialectique entre code et message les rapports entre l'univers de signes et l'univers des idéologies, qui se reflètent dans les modes communicatifs préconstitués, et elle relie le monde des choses au monde de la culture, qui formalise les choses non pas pour les reconnaître comme elles sont mais afin de les transformer. Après avoir étudié dans L'œuvre ouverte (1965) les structures des langages expérimentaux de l'art contemporain, Umberto Ecco traite ici l'ensemble des problèmes sémiotiques et ce livre constitue à la fois sa contribution à la recherche en cours et le panorama actuellement le plus vaste et le plus complet sur les préalables constitutifs à toute sémiotique et sur l'état présent du structuralisme. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

Qu’est-ce qui justifie des normes comme « Tu ne tueras point » ou «Nul ne peut être soumis à la torture »? -/- C’est autour de cette question fondamentale que se sont constituées les trois grandes théories morales : l’éthique des vertus (inspirée d’Aristote), l’éthique des devoirs (mise en forme par Kant) et l’éthique des conséquences (matrice de l’utilitarisme). Qu’est-ce qui distingue ces trois approches ? Y a-t-il des raisons décisives d’en préférer une ? -/- Dans ce livre, Ruwen Ogien (...) et Christine Tappolet montrent que, pour trancher ce débat, il faut clarifier les deux concepts-clés de l’éthique et analyser leurs relations : les normes (qui posent des obligations, des interdictions, des permissions) et les valeurs (qui disent ce qui est bien ou désirable). -/- Ils proposent une hypothèse simple, mais iconoclaste : si pour justifier les normes, il faut nécessairement faire appel à des valeurs, c’est que, contre Kant et Aristote, il faut être conséquentialiste. (shrink)

The aim of this article is to show that, just like in recent years Cobreros, Égré, Ripley and van Rooij provided a non-transitive counterpart of classical logic (meaning by this that all classically acceptable inferences are valid, but Cut and other metainferences are not) the same can be done for every Tarskian logic, with full generality. In order to establish this fact, we take a semantic approach, by showing that appropriate structures can be devised to characterize a non-transitive counterpart of (...) every Tarskian logic, starting from the logical matrices that are usually taken to render them. (shrink)

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By applying these (...) data, one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind. (shrink)

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and (...) sub-attributes. For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented themasPlithogenicAttributiveSubjectivelyWholeHyper-Super-Soft-Matrix(PASWHSS-Matrix)andPlithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. (shrink)

Il deismo unisce all’attestazione di una “religione naturale” e alla difesa della tolleranza religiosa la critica all’autorità ecclesiastica e il rifiuto di ogni rivelazione divina, secondo un orientamento metodologico di chiara matrice lockiana. Tutti aspetti rinvenibili in questo libro in cui sono tradotti per la prima volta in italiano due pamphlet di Anthony Collins, seguiti in Appendice dalle lettere che John Locke gli scrisse a testimonianza della profonda amicizia tra i due. Il primo, Difesa degli attributi divini, tratta il problema (...) del male proponendo un’etica deista contrapposta alle soluzioni oscure e contraddittorie degli uomini di Chiesa. Il secondo, Il perfetto inganno del clericalismo, colpisce la tradizione in genere, ricostruendo la presunta contraffazione di una clausola dei Trentanove Articoli di religione – le basi dottrinali della confessione anglicana. Si delinea la possibilità di ricostruire sulla base della ragione una teologia laica e una vera religione. (shrink)

Russian Abstract: Данный документ является сборником «заметок на полях», раскрывающих состав и содержание метода структурно-онтологического анализа. Указанный метод разработан для системного описания предметной области изучаемых явлений. Он включает специальную процедуру по построению структурно-онтологических матриц и алгоритм их описания. Междисциплинарная направленность метода продемонстрирована на примере анализа процесса социализации личности. English Abstract: This document is a collection of `marginal notes` revealing the composition and content of the structural ontological analysis method. The specified method is developed for a systemic description of the subject (...) matter area of the studied phenomena. It includes a special procedure for constructing structural-ontological matrices and an algorithm for their description. The interdisciplinary focus of the method is demonstrated by the example of an analysis of the personality socialization process. (shrink)