There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the (...) standard classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?

Conceptual Metaphor Theory makes some strong claims against so-called Classical Theory which spans the accounts of metaphors from Aristotle to Davidson. Most of these theories, because of their traditional literal-metaphorical distinction, fail to take into account the phenomenon of conceptual metaphor. I argue that the underlying mechanism for explaining metaphor bears some striking resemblances among all of these theories. A mapping between two structures is always expressed. Conceptual Metaphor Theory insists, however, that the literal-metaphorical distinction of (...) Classical Theories is empirically wrong. I claim that this criticism is based rather on terminological decisions than on empirical issues. Conceptual Metaphor Theory focusses primarily on conventional metaphors and struggles to extend its mechanism to novel metaphors, whereas Classical Theories focus on novel metaphors and struggle to extend their mechanisms to conventional metaphors. Since all of these theories study metaphors from the synchronic point of view, they are unable to take into account any semantic change. A diachronic perspective is what we need here, one which would allow us to explain the role of metaphor in semantic change and the development of language in general. (shrink)

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that (...) the truth-paradoxes and the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)

The classical theory of probability has long been abandoned and is seen by most philosophers as a non-contender—a mere precursor to newer and better theories. In this paper I argue that this is a mistake. The main reasons for its rejection—all related to the notorious principle of indifference—are that it is circular, of limited applicability, inconsistent, and dependent upon unjustified empirical assumptions. I argue that none of these claims is true and that the classical theory remains (...) to be refuted. (shrink)

We will argue here, that one of the salient messages of standard quantum formalism implies a failure of Classical Theory of Knowledge (hereafter CTK) which is primarily based on the presumption that, our knowledge is predetermined by Nature. This failure provides pointers against the classically held ontological definiteness of future. Quantum formalism admits interpretation , that suggests, that there is no such thing as ‘universal global present’ in the sense of being able to confirm a complete set of (...) facts of matter about it, unless this is coupled with a specific observation recipe. (shrink)

The paper studies in detail a precise formal construction of spacetime from matter suggested by the logician John Burgess. We presuppose a continuous and perdurantistic matter ontology. The result is a systematic method to translate claims about the geometry of a flat relativistic, or classical, spacetime into claims about geometrical relations between matter points. The approach is extended to electric and magnetic fields by treating them as multifields defined on matter, rather than as fields in the vacuum. A few (...) tentative suggestions are made to adapt the method to general relativity and to quantum theories. (shrink)

Ao mesmo tempo que o malogro da assim chamada teoria clássica dos conceitos - de acordo com a qual definições são a maneira apropriada de caracterizar conceitos - é um consenso, a filosofia metafísica da religião parece ainda lidar com o conceito de Deus de forma predominantemente definicional. Podemos então nos perguntar: Seria esse malogro suficiente para inviabilizar uma caracterização definicional do conceito de Deus? Meu propósito central neste artigo é responder essa pergunta. Adoto uma ênfase representacional. Em outras palavras, (...) desejo analisar até que ponto os problemas mais importantes levantados contra a teoria clássica dos conceitos afetam uma abordagem definicional-representacional do conceito de Deus. Como resultado desse esforço, mostro que as críticas à teoria clássica que ameaçam tal abordagem dependem da pluralidade característica ao contexto inter-religioso, que por si só cria outros problemas. (shrink)

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, (...) it is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The point (...) is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

It is exhibited that mature scientific economical theory is a set of propositions that describe the relationship between theoretical objects of two types - basic objects and derivative ones. The set of basic objects makes up the aggregate of initial idealizations (the Fundamental Theoretical Scheme or FTS) with no direct reference to experimental data. The derivative theoretical objects are formed from the basic ones according to certain rules. The sets of derivative objects form partial theoretical schemes or PTS. Any (...) mature economics scientific theory grows due to transitions, in order to describe each new experimental situation, from FTS to PTS. Each PTS construction from the FTS represents a problem that cannot be reduced to a strict algorithm. (shrink)

With his influence on the development of physiology, physics and geometry, Hermann von Helmholtz – like few scientists of the second half of the 19th century – is representative of the research in natural science in Germany. The development of his understanding of science is not less representative. Until the late sixties, he emphatically claimed the truth of science; later on, he began to see the conditions for the validity of scientific knowledge in relative terms, and this can, in summary, (...) be referred to as hypothesizing. Already in the past century, HeImholtz made first approaches to an understanding of science, which were incompatible with his own former position and which pointed to the modern age to an astonishingly large extent. A comparison with Karl R. Popper's logic of research will illustrate how closely he nevertheless approached modern understanding of science. In Popper's logic of research, hypothesizing of scientific knowledge is definitely much more advanced than in Helmholtz's theory of science. What begins vaguely to emerge with Helmholtz has already become an explicitly formulated programme with Popper. Although HeImholtz and Popper are not on a direct line of epistemological development and Popper refers to HeImholtz only rarely and casually, there are in fact surprising points of contact which have not been taken notice of so far and which appear above all if one looks at Helmholtz's understanding of science against the background of Popper's logic of research. (shrink)

It is exhibited that mature scientific economical theory is a set of propositions that describe the relationship between theoretical objects of two types - basic objects and derivative ones. The set of basic objects makes up the aggregate of initial idealizations (the Fundamental Theoretical Scheme or FTS) with no direct reference to experimental data. The derivative theoretical objects are formed from the basic ones according to certain rules. The sets of derivative objects form partial theoretical schemes or PTS. Any (...) mature economics scientific theory grows due to transitions, in order to describe each new experimental situation, from FTS to PTS. Each PTS construction from the FTS represents a problem that cannot be reduced to a strict algorithm. (shrink)

Every countable language which conforms to classical logic is shown to have an extension which has a consistent definitional theory of truth. That extension has a consistent semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when sentences of the object lqanguage are valuated by their meanings.

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose (...) of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

Albert Einstein proposed three tests of general relativity, later named the classic tests of general relativity, in 1916: the precession of the perihelion of Mercury's orbit, sun light deflection, and the gravitational redshift of the light. For gravitational testing, the indirect effects of gravity are always used, usually particles that are influenced by gravity. In the presence of gravity, the particles move along curved geodesic lines. The sources of gravity that cause the curvature of spacetime are material bodies, depending on (...) their mass. But in relativity the mass relates to the energy through the formula E = mc2, and the energy with the momentum, according to the special relativity. DOI: 10.13140/RG.2.2.25608.16648. (shrink)

Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with (...) semantic generalizations – are addressed. Finally, I’ll introduce the case studies that I’ll be dealing with in part II. Chapter 2 is concerned with the origins and development of Jaśkowski’s discussive logic. The main idea of this chapter is to systematize the various stages of the development of discussive logic related researches from two different angles, i.e., its connections to modal logics and its proof theory, by highlighting virtues and vices. Chapter 3 focuses on the Gentzen-style proof theory of discussive logic, by providing a characterization of it in terms of labelled sequent calculi. Chapter 4 deals with the Gentzen-style proof theory of relevant logics, again by employing the methodology of labelled sequent calculi. This time, instead of working with a single logic, I’ll deal with a whole family of them. More precisely, I’ll study in terms of proof systems those relevant logics that can be characterised, at the semantic level, by reduced Routley-Meyer models, i.e., relational structures with a ternary relation between states and a unique base element. Chapter 5 investigates the proof theory of a modal expansion of intuitionistic propositional logic obtained by adding an ‘actuality’ operator to the connectives. This logic was introduced also using Gentzen sequents. Unfortunately, the original proof system is not cut-free. This chapter shows how to solve this problem by moving to hypersequents. Chapter 6 concludes the investigations and discusses the future of the research presented throughout the dissertation. (shrink)

Double negations are easily recognised in both the so-called “negative literature” and the original texts of some important scientific theories. Often they are not equivalent to the corresponding affirmative propositions. In the case the law of double negation fails they belong to non-classical logic, as first, intuitionist logic. Through a comparative analysis of the theories including them the main features of a new kind of theoretical organization governed by intuitionist logic are obtained. Its arguing proceeds through doubly negated propositions (...) and ad absurdum arguments. Then, the final doubly negated predicate is translated in the corresponding affirmative one, from which all the consequences are deduced in order to test them against reality. According to this model the true formalization of intuitionist logic is Kolmogorov’s 1932 paper. The above analysis also shows that modal words play an auxiliary or substitutive role to intuitionist propositions. In addition, it is shown that Vasiliev’s paraconsistent logic is represented through doubly negated propositions. By means of these three kinds of logic one can attribute a specific kind of logic to each of the three distinct steps of the process of building a scientific theory from the experimental data to its final theoretical system. It is also shown that the definition of negation is of a structural kind, rather than of an objective kind or a subjective kind: it has to be referred to the organization of the theory to which it belongs. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to (...) languages containing the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

Currently there are at least four sizeable projects going on to establish the gravitational acceleration of massive antiparticles on earth. While general relativity and modern quantum theories strictly forbid any repulsive gravity, it has not yet been established experimentally that gravity is attraction only. With that in mind, the Elementary Process Theory (EPT) is a rather abstract theory that has been developed from the hypothesis that massive antiparticles are repulsed by the gravitational field of a body of ordinary (...) matter: the EPT essentially describes the elementary processes by which the smallest massive systems have to interact with their environments for repulsive gravity to exist. In this paper we model a nonrelativistic, one-component massive system that evolves in time by the processes as described by the EPT in an environment described by classical fields: the main result is a semi-classical model of a process at Planck scale by which a non-relativistic onecomponent system interacts with its environment, such that the interaction has both gravitational and electromagnetic aspects. Some worked-out examples are provided, among which the repulsion of an antineutron by the gravitational field of the earth. The general conclusion is that the semi-classical model of the EPT corresponds to non-relativistic classical mechanics. Further research is aimed at demonstrating that the EPT has a model that reproduces the successful predictions of general relativity. (shrink)

The paper explains why the de Broglie–Bohm theory reduces to Newtonian mechanics in the macroscopic classical limit. The quantum-to-classical transition is based on three steps: (i) interaction with the environment produces effectively factorized states, leading to the formation of _effective wave functions_ and hence _decoherence_; (ii) the effective wave functions selected by the environment—the pointer states of decoherence theory—will be well-localized wave packets, typically Gaussian states; (iii) the quantum potential of a Gaussian state becomes negligible under (...) standard classicality conditions; therefore, the effective wave function will move according to Newtonian mechanics in the correct classical limit. As a result, a Bohmian system in interaction with the environment will be described by an effective Gaussian state and—when the system is macroscopic—it will move according to Newtonian mechanics. (shrink)

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.

According to a classic but nowadays discarded philosophical theory, perceptual experience is a complex of nonconceptual sensory states and full-blown propositional beliefs. This classical dual-component theory of experience is often taken to be obsolete. In particular, there seem to be cases in which perceptual experience and belief conflict: cases of known illusions, wherein subjects have beliefs contrary to the contents of their experiences. Modern dual-component theories reject the belief requirement and instead hold that perceptual experience is a (...) complex of nonconceptual sensory states and some other sort of conceptual state. The most popular modern dual-component theory appeals to sui generis propositional attitudes called ‘perceptual seemings’. This article argues that the classical dual-component theory has the resources to explain known illusions without giving up the claim that the conceptual components of experience are beliefs. The classical dual-component view, though often viewed as outdated and implausible, should be regarded as a serious contender in contemporary debates about the nature of perceptual experience. (shrink)

Book review of Paul Horwich, Probability and Evidence (Cambridge Philosophy Classics edition), Cambridge: Cambridge University Press, 2016, 147pp, £14.99 (paperback).

This dissertation is an analysis of the development of dialectic and argumentation theory in post-classical Islamic intellectual history. The central concerns of the thesis are; treatises on the theoretical understanding of the concept of dialectic and argumentation theory, and how, in practice, the concept of dialectic, as expressed in the Greek classical tradition, was received and used by five communities in the Islamic intellectual camp. It shows how dialectic as an argumentative discourse diffused into five communities (...) (theologicians, poets, grammarians, philosophers and jurists) and how these local dialectics that the individual communities developed fused into a single system to form a general argumentation theory (adab al-bahth) applicable to all fields. I evaluate a treatise by Shams al-Din Samarqandi (d.702/1302), the founder of this general theory, and the treatises that were written after him as a result of his work. I concentrate specifically on work by Adud al-Din al-Iji (d.756/1355), Sayyid Sharif al-Jurjani (d.816/1413), Taşköprüzâde (d.968/1561), Saçaklızâde (d.1150/1737) and Gelenbevî (d.1205/1791) and analyze how each writer (from Samarqandi to Gelenbevî) altered the shape of argumentative discourse and how later intellectuals in the post-classical Islamic world responded to that discourse bequeathed by their predecessors. What is striking about the period that this dissertation investigates (from 1300-1800) is the persistence of what could be called the linguistic turn in argumentation theory. After a centuries-long run, the jadal-based dialectic of the classical period was displaced by a new argumentation theory, which was dominantly linguistic in character. This linguistic turn in argumentation dates from the final quarter of the fourteenth century in Iji's impressively prescient work on 'ilm al-wad'. This idea, which finally surfaced in the post-classical period, that argumentation is about definition and that, therefore, defining is the business of language—even perhaps, that language is the only available medium for understanding and being understood—affected the way that argumentation theory was processed throughout most of the period in question. The argumentative discourse that started with Ibn al-Rawandi in the third/ninth century left a permanent imprint on Islamic intellectual history, which was then full of concepts, terminology and objectives from this discourse up until the late nineteenth century. From this perspective, Islamic intellectual history can be read as the tension between two languages: the "language of dialectic" (jadal) and the "language of demonstration" (burhan), each of which refer not only to a significant feature of that history, but also to a feature that could dramatically alter the interpretation of that history. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, (...) which is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

This essay critically examines some classic philosophical and legal theories of privacy, organized into four categories: the nonintrusion, seclusion, limitation, and control theories of privacy. Although each theory includes one or more important insights regarding the concept of privacy, I argue that each falls short of providing an adequate account of privacy. I then examine and defend a theory of privacy that incorporates elements of the classic theories into one unified theory: the Restricted Access/Limited Control (RALC) (...) class='Hi'>theory of privacy. Using an example involving data-mining technology on the Internet, I show how RALC can help us to frame an online privacy policy that is sufficiently comprehensive in scope to address a wide range of privacy concerns that arise in connection with computers and information technology. (shrink)

The self-interaction spin-2 approach to GR has been extremely influential in the particle physics community. Leaving no doubt regarding its heuristic value, we argue that any view of the metric field of GR as nothing but a stand-in for a self-coupling field in at spacetime runs into a dilemma: either the view is physically incomplete in so far as it requires recourse to GR after all, or it leads to an absurd multiplication of alternative viewpoints on GR rendering any understanding (...) of the metric field as nothing but a spin-2 field in at spacetime unjustified. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of (...) this paper is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good candidate for recovering the classical limit of quantum theory. Indeed, in a Bohmian framework, the issue of the classical limit reduces to showing how classical trajectories can emerge from Bohmian ones, under specific classicality assumptions. In this paper, we shall (...) focus on a technical problem that arises from the dynamics of a Bohmian system in bounded regions; and we suggest that a possible solution is supplied by the action of environmental decoherence. However, we shall show that, in order to implement decoherence in a Bohmian framework, a stronger condition is required rather than the usual one. (shrink)

In The Mind Doesn’t Work that Way, Jerry Fodor argues that mental representations have context sensitive features relevant to cognition, and that, therefore, the Classical Computational Theory of Mind (CTM) is mistaken. We call this the Globality Argument. This is an in principle argument against CTM. We argue that it is self-defeating. We consider an alternative argument constructed from materials in the discussion, which avoids the pitfalls of the official argument. We argue that it is also unsound and (...) that, while it is an empirical issue whether context sensitive features of mental representations are relevant to cognition, it is empirically implausible. (shrink)

Indigenous people often do not get the full benefits of economic development, regardless of their proximity to production factors. While many academics have recognised and investigated indigenous people’s problems, relatively few have suggested entrepreneurship as a means to addressing them. In this paper, we explore Peredo et al.’s (2004) work, ‘Towards a theory of indigenous entrepreneurship – a theory of entrepreneurship that accounts for indigenous people and sustainability’. Using Scopus and Google Scholar, a bibliometric analysis confirmed the impact (...) of this work, first published some 16 years ago. The analysis reveals that the paper has been referenced over 300 times, with over 70% of these citations originating from online academic journal articles and books and 30% from different types of websites. The paper’s substantial impact on future research in indigenous entrepreneurship indicates that it is and will continue to be a foundational work on indigenous entrepreneurship. (shrink)

The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is proposed which expresses its key inherent property. The definition is operational and powerful. Many other properties of inertial frames follow from the definition, or it makes them plausible. In particular, the definition shows why physical laws obey space and time (...) symmetries and the principle of relativity, it resolves the problem of clock synchronization and the role of light in it, as well as the problem of the geometry of inertial frames. (shrink)

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 (...) limit. We then use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics. (shrink)

The impetus theory of motion states that to be in motion is to have a non-zero velocity. The at-at theory of motion states that to be in motion is to be at different places at different times, which in classical physics is naturally understood as the reduction of velocities to position developments. I first defend the at-at theory against the criticism raised by Arntzenius that it renders determinism impossible. I then develop a novel impetus theory (...) of motion that reduces positions to velocity developments. As this impetus theory of motion is by construction a mirror image of the at-at theory of motion, I claim that the two theories of motion are in fact epistemically on par—despite the unfamiliar metaphysical picture of the world furnished by the impetus version. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory (...) of finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

The relevance of this study is due to the need to analyze foreign scientific literature in the field of philosophy of law, revealing trends in the evolution and development of natural law theories. Despite the significant number of publications on the theory of natural law its key theses and arguments are discussed by post-soviet scientists in isolation from modern discussions by foreign jurists. The subject of the research in the paper is the reconstruction and rational interpretation of the arguments (...) of natural law theories forming the doctrine of the so-called New Classical Natural Law (NCNL) and presented in the works of John Finnis and Germain Grisez. The purpose of this study is an attempt to reveal the logical structure of the natural law argumentation, especially the answers to the Question «Why would it be rational for agents to respect other people’s natural rights?». The paper uses traditional methods typical of philosophical and legal research, including methods of logical and linguistic analysis, historical reconstruction and rational interpretation. The novelty of this paper is due to a new approach to the disclosure of arguments and the logical structure of the reasoning of proponents of the theory of natural law. Clarification of the nature, advantages and disadvantages of such an argument can become the main one for further philosophical and legal research. (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification (...) of classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and (...) relativistic—using relativity and conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice. (shrink)

There is a fault line running through classical liberalism as to whether or not democratic self-governance is a necessary part of a liberal social order. The democratic and non-democratic strains of classical liberalism are both present today—particularly in America. Many contemporary libertarians and neo-Austrian economists represent the non-democratic strain in their promotion of non-democratic sovereign city-states (startup cities or charter cities). We will take the late James M. Buchanan as a representative of the democratic strain of classical (...) liberalism. Since the fundamental norm of classical liberalism is consent, we must start with the intellectual history of the voluntary slavery contract, the coverture marriage contract, and the voluntary non-democratic constitution (or pactum subjectionis). Next we recover the theory of inalienable rights that descends from the Reformation doctrine of the inalienability of conscience through the Enlightenment (e.g., Spinoza and Hutcheson) in the abolitionist and democratic movements. Consent-based governments divide into those based on the subjects' alienation of power to a sovereign and those based on the citizens' delegation of power to representatives. Inalienable rights theory rules out that alienation in favor of delegation, so the citizens remain the ultimate principals and the form of government is democratic. Thus the argument concludes in agreement with Buchanan that the classical liberal endorsement of sovereign individuals acting in the marketplace generalizes to the joint action of individuals as the principals in their own organizations. (shrink)

For a classical theory T, ℋ(T) denotes the intuitionistic theory of T-normal (i.e. locally T) Kripke structures. S. Buss has asked for a characterization of the theories in the range of ℋ and raised the particular question of whether HA is an ℋ-theory. We show that Ti∈ range(ℋ) iff Ti = ℋ(T). As a corollary, no fragment of HA extending iΠ1 belongs to the range of ℋ. A. Visser has already proved that HA is not in (...) the range of H by different methods. We provide more examples of theories not in the range of ℋ. We show PA-normality of once-branching Kripke models of HA + MP, where it is not known whether the same holds if MP is dropped. (shrink)

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas (...) provided it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

Two radically different views about time are possible. According to the first, the universe is three dimensional. It has a past and a future, but that does not mean it is spread out in time as it is spread out in the three dimensions of space. This view requires that there is an unambiguous, absolute, cosmic-wide "now" at each instant. According to the second view about time, the universe is four dimensional. It is spread out in both space and time (...) - in space-time in short. Special and general relativity rule out the first view. There is, according to relativity theory, no such thing as an unambiguous, absolute cosmic-wide "now" at each instant. However, we have every reason to hold that both special and general relativity are false. Not only does the historical record tell us that physics advances from one false theory to another. Furthermore, elsewhere I have shown that we must interpret physics as having established physicalism - in so far as physics can ever establish anything theoretical. Physicalism, here, is to be interpreted as the thesis that the universe is such that some unified "theory of everything" is true. Granted physicalism, it follows immediately that any physical theory that is about a restricted range of phenomena only, cannot be true, whatever its empirical success may be. It follows that both special and general relativity are false. This does not mean of course that the implication of these two theories that there is no unambiguous cosmic-wide "now" at each instant is false. It still may be the case that the first view of time, indicated at the outset, is false. Are there grounds for holding that an unambiguous cosmic-wide "now" does exist, despite special and general relativity, both of which imply that it does not exist? There are such grounds. Elsewhere I have argued that, in order to solve the quantum wave/particle problem and make sense of the quantum domain we need to interpret quantum theory as a fundamentally probabilistic theory, a theory which specifies how quantum entities - electrons, photons, atoms - interact with one another probabilistically. It is conceivable that this is correct, and the ultimate laws of the universe are probabilistic in character. If so, probabilistic transitions could define unambiguous, absolute cosmic-wide "nows" at each instant. It is entirely unsurprising that special and general relativity have nothing to say about the matter. Both theories are pre-quantum mechanical, classical theories, and general relativity in particular is deterministic. The universe may indeed be three dimensional, with a past and a future, but not spread out in four dimensional space-time, despite the fact that relativity theories appear to rule this out. These considerations, finally, have implications for views about the arrow of time and free will. (shrink)

A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume.

David Albert has recently argued that classical electromagnetic theory (EM) is not time reversal invariant (non-TRI), while David Malament rejects this argument and maintains the orthodox result, that EM is TRI. Both Albert's and Malament's arguments are analysed, and both are found wanting in certain respects. It is argued here that the result really depends on the choice of theoretical ontology choosen to interpret EM theory, and there is more than one plausible choice. Albert and Malament have (...) choosen different plausible ontologies; but neither shows that their choice of interpretation is definitive. Deeper principles about this choice are examined. The extension to EM theory with magnetic monopoles is also examined. It is concluded that, despite certain flaws in his account, Albert's analysis does reveal serious problems in the orthodox account, which Malament's response does not adequately address. (shrink)

It has been known for long time that intuition plays significant role in many professions and human life, including in entrepreneurship, government, and also in detective or law enforcement activities. Even women are known to possess better intuitive feelings or “hunch” compared to men. Despite these examples, such a precognitive interdiction is hardly accepted in established science. In this paper, we discuss briefly the advanced solutions of Maxwell equations, and then make connection between syntropy and precognition from classical perspective. (...) It is our hope that the new proposed method can be verified with experimental data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (shrink)