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 my dissertation (Rutgers, 2007) I developed the proposal that one can establish that material quantum objects behave classically just in case there is a “local plane wave” regime, which naturally corresponds to the suppression of all quantum interference.

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)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, (...) Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (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)

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)

In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) the abstract with the concrete, the physical with the non-physical, and the possible with the impossible, just to name a few. -/- Proposed by David Lewis (1991) alongside his defence of classical mereology (the major theory of parthood which permits such transcategorial composites through its principle of unrestricted composition) it is my contention that mixed fusions are an under-examined consequence of indiscriminate mereological fusion which harbour a multitude of complications. In my attempt to discern their substantive character, throughout this thesis I make a case study of mixed fusions and uncover several problematic consequences which I think follow from their most plausible assessment. -/- These include: (1) that mixed fusions’ probable membership relations may lead to dubious foundational loops in the mereological Universe, or (2) otherwise that mixed fusions oblige an implausible ontological priority of the mereological Universe as a whole; (3) that mixed fusions contradict the reductive account of set theory they are proposed within, by plausibly being seen to have the same members as their class parts, and (4) that mixed fusions therefore confound a mereological thesis of Composition as Identity, which some (including Lewis) use to support classical mereology – a consequence which is potentially self-defeating; (5) that mixed fusions as sums of abstract and concrete entities both subvert Lewis’s (1986) system of modal realism, while (6) also undermining less expansive theories of possible worlds; and finally, (7) that even where some of the foregoing is resisted, it remains implausible that mixed fusions are ontologically innocent, because their supposed distinction from their parts in this case ensures that they need to be counted as additional entities in one’s ontology. -/- To be clear, I do not advance a theory of mereological hybrid nihilism in the sense of denying all cases of transcategorial composition. (I only cover a few select instances of mereological hybridism via mixed fusions after all.) Rather, I deny that mereological hybridism is plausible in full generality, by demonstrating that any cases of it are at least limited by the constraints that I identify. This in turn vindicates a call for a restriction on parthood theories and composition principles which allow certain types of categorially mixed entities – including restricting classical mereology with its principle of unrestricted composition. -/- Although theories of parthood like the standard classical mereology are not ordinarily developed for the sake of mereological hybrids like mixed fusions, these and other transcategorial composites are still among the logical consequences of such parthood systems operating with sufficient generality. The significance of my thesis, then, comes from showcasing how some of these kinds of entities do not conform to the systems in which they are included as required, and hence I argue for the rejection of unrestricted mereological hybridism as well as any mereological principles which support it. (shrink)

In this paper I present the common structure of quantum theories with a primitive ontology, and discuss in what sense the classical world emerges from quantum theories as understood in this framework. In addition, I argue that the primitive ontology approach is better at answering this question than the rival wave function ontology approach or any other approach in which the classical world is nonreductively ‘emergent:’ even if the classical limit within this framework needs to be (...) fully developed, the difficulties are technical rather than conceptual, while this is not true for the alternatives. (shrink)

The concept of hierarchical organization is commonplace in science. Subatomic particles compose atoms, which compose molecules; cells compose tissues, which compose organs, which compose organisms; etc. Hierarchical organization is particularly prominent in ecology, a field of research explicitly arranged around levels of ecological organization. The concept of levels of organization is also central to a variety of debates in philosophy of science. Yet many difficulties plague the concept of discrete hierarchical levels. In this paper, we show how these difficulties undermine (...) various implications ascribed to hierarchical organization, and we suggest the concept of scale as a promising alternative to levels. Investigating causal processes at different scales offers a way to retain a notion of quasi-levels that avoids the difficulties inherent in the classic concept of hierarchical levels of organization. Throughout, our focus is on ecology, but the results generalize to other invocations of hierarchy in science and philosophy of science. (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 Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory (...) validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

For decades, much literature on causality has focused on causal processes and causal reasoning in the natural sciences. According to a relatively new trend however, such research on causality remains insufficient because of its refusal to accept a certain degree of pluralism within the concept, a pluralism that is evident in how we use ideas of cause and effect in everyday life. I will build on work in this latter trend, following philosophers like G. E. M. Anscombe and N. Cartwright. (...) I explore the limits of the concept of causality by determining the extent to which our ideas can remain consistent as we stretch this concept along two dimensions, one concerning the maximizing of the effect and the other the maximizing of explanatory depth. Dealing with the cause of the universe, such an investigation touches upon some issues in current empirical cosmology and revisits some classic arguments regarding philosophy of religion and the Platonic notion of participation. The results indicate that the use of current conceptual, logical and analytic tools can deliver new insights that are useful especially for those interested in how causality in the natural sciences links with causality in everyday life. (shrink)

The debate between instrumentalist and technological determinist positions on the nature of technology characterised the early history of the philosophy of technology. In recent years however technological determinism has ceased to be viewed as a credible philosophical position within the field. This paper uses Merleau-Ponty’s phenomenology to reconsider the technological determinist outlook in phenomenological terms as an experiential response to the encounter with the phenomenon of modern technology. Recasting the instrumentalist-determinist debate in a phenomenological manner enables one to reconcile the (...) apparent dualism of the instrumentalist and determinist positions through Merleau-Ponty’s ontology of the flesh. This ontology has recently been used to ground accounts of virtual embodiment. We argue that in addition to explaining away the classical form of technological determinism, it can also phenomenologically ground a novel understanding of technological determinism. Namely, a technological determinism of virtual embodiment. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for (...) Cut—elimination, but the other does not.). (shrink)

Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we (...) also derive a classical-particle version of the Higgs mechanism. (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 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? In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not (...) valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete. After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views. -/- DOI: 10.58679/TW62329. (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)

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?

The present paper proposes a route to modal claims that allows us to infer to certain possibilities even if they are sensorily unimaginable and beyond the evidential capacity of stipulative imagining. After a brief introduction, Sect. 2 discusses imaginative resistance to help carve a niche for the kinds of inferences about which this essay is chiefly concerned. Section 3 provides three classic examples, along with a discussion of their similarities and differences. Section 4 recasts the notion of potential explanation in (...) Lipton’s (Inference to the best explanation, Routledge, Abingdon, 2004) in order to accommodate inferences to possibility claims; Sect. 5 then attempts to characterise a principle underlying such inferences. Section 6 concludes by discussing how the proposal relates to other modal epistemologies, with emphasis on the potential of such inferences to produce genuinely new ideas. (shrink)

In this essay I highlight the importance of the phenomenon of living speech and the communicative dimension of experience in phenomenological research. Specifically, I critically consider the charge of phonocentrism raised by Derrida to phenomenology which appears to have discredited any attempt to approach the phenomenon of vocality for fear of falling back into a metaphysics of presence and adopting the stance of atomistic subjectivity. It may be true that classical phenomenology of consciousness privileges the first person point of (...) view and is guilty of a subjectivist bias but one finds rich resources within the dialogical tradition, notably Buber, as well as in the works of Humboldt and Plato's Dialogues, which highlight a fundamental duality of self and the other, which plays out between You and I within living speech, and to thus correct the invidualist position of classical phenomenology. (shrink)

Self-knowledge, at first glance, seems to be naturally and easily accessible to each of us. We commonly believe that we need much less effort to understand ourselves than to understand the world. The authoress of the paper uncovers the fallacy of this popular view referring to the fundamental conceptions and philosophical ideas of the classical Yoga. She tries to demystify our deceptive self-understanding explaining the definitions of ignorance (avidya), I-am-ness (asmita), desire (raga), aversion (dvesha) and fear of death (abhinivesha) (...) given by the author of the oldest Yoga treatise. Besides, the paper discusses briefly how we can make use of our limited, incorrect self-knowledge as far as we are aware that it needs to be transcended. In the final part of the paper, the issue of self-discipline consisting basically in cultivation of detachment and the practice of meditation is addressed. (shrink)

As Richard Bernstein has suggested, there is a very rich and interesting story to be told about how the classical pragmatists (Dewey, Peirce, and James) understood G. W. R Hegel, made use of Hegel, and ultimately distanced themselves from Hegel. That story cannot be told here. Indeed, the story is so rich and complicated that even its beginnings cannot be told here. But what can be provided, perhaps, is a limited, though hopefully illuminating, perspective on a few salient aspects (...) of the relationship between the classical pragmatists and Hegel. While the following reflections offer no definitive answers about this relationship, they might at least suggest some fruitful lines of enquiry for future discussion. (shrink)

Science is now studying biodiversity on a massive scale. These studies are occurring not just at the scale of larger plants and animals, but also at the scale of minute entities such as bacteria and viruses. This expansion has led to the development of a specific sub-field of “microbial diversity”. In this paper, I investigate how microbial diversity faces two of the classical issues encountered by the concept of “ biodiversity ”: the issues of defining the units of biodiversity (...) and of choosing a mathematical measure of diversity. I also show that the extension of the scope of biodiversity to microbial entities such as viruses and many other not-clearly-alive entities raises yet another foundational issue: that of defining a “lower-limit” of biodiversity. (shrink)

In this essay, I look at more or less sympathetic portrayals of egoists in film. I start by explaining some basic concepts: psychological egoism; ethical egoism; default egoism; rational egoism; egotism; cynicism; narcissism; and psychopathy. I then review in-depth two excellent WWII films, Stalag 17 and The Bridge on the River Kwai. I note that the key protagonist in both pictures is the same type of character—both played by the same fine actor, William Holden. The main protagonist in both is (...) a soldier in a POW camp, who appears completely egoistic; however, in both cases, the movie shows that he is just a man acting for self-preservation, but within moral limits. The character in both cases is certainly not an egotist, nor a narcissist, much less a psychopath. (shrink)

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.

A major question in sensory science is how a sensation of magnitude F (such as loudness) depends upon a sensory stimulus of physical intensity I (such as a sound-pressure-wave of root-mean-square sound-pressure-level). An empirical just-noticeable sensation difference (∆F)_j at F_j specifies a just-noticeable intensity difference (∆I)_j at I_j. Classically, intensity differences accumulate from a stimulus-detection threshold I_th up to a desired intensity I. The corresponding sensation differences likewise accumulate up to F(I) from F(I_th ), the non-zero sensation (as suggested by (...) hearing studies) at I_th. Consequently, sensation growth F(I) can be obtained through classic Fechnerian integration, in which some empirically-based relation for the Weber Fraction, ∆I⁄I, is combined with either Fechner’s Law ∆F=B or Ekman’s Law (∆F⁄F)=g. The number of steps in I is equated to the number of steps in F; an infinite series ensues, whose higher-order terms are traditionally ignored (Fechnerian integration). But also, remarkably, so are the integration bounds I_th and F(I_th ). Here, we depart from orthodoxy by including those bounds. Bounded Fechnerian integration is first used to derive hypothetical sensation-growth equations for which the differential ∆F(I)=F(I+∆I)-F(I) does indeed return either Fechner’s Law or Ekman’s Law respectively. One relation emerges: linear growth of sensation F with intensity I. Subsequently, 24 sensation-growth equations F(I) that the author had derived using bounded Fechnerian integration (12 equations for the Weber Fraction (∆I⁄I), each combined with either Fechner’s Law or with Ekman’s Law) are scrutinized for whether their differentials F(I+∆I)-F(I) return the respective Fechner’s Law or Ekman’s Law, particularly in the previously-unexamined limits (∆I⁄I)≪1 and (∆I⁄I)→0. Classic claims made by Luce and Edwards (1958) are then examined, viz., that three popular forms of the Weber Fraction, when combined with Fechner’s Law, produce sensation-magnitude equations that subsequently return the selfsame Fechner’s Law. When sensation-growth equations are derived here using bounded Fechnerian integration, Luce and Edwards (1958) prove to be wrong. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise (...) algorithmic computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

Over the last two decades there has been a growing interest in the transcendental dialectic of Critique of Pure Reason in Germany. Authors, however, often do not pay enough attention to the fact that Kant’s theory of reason (in the narrow sense) and the concept of ideas derived from it is not limited to this text. The purpose of this article is to compare and analyze the functionality of mind as a subjective ability developed by Kant and Fichte with the (...) Hegelian expansion of the mind to the idea of universal rationality. The relevance of such a comparison is connected with the need to demonstrate how the Hegelian paradigm of absolute rationality causes either the subsequent rejection of reason as a philosophical principle in the 19th and´20th centuries counter-discourse, or reduction of reason to the concept of pragmatic rationality. In the first part of this paper, the author intends to differentiate between at least 7 different types of ideas and their functions in Kant’s works. In the second part, he demonstrates how Fichte tries to systematize them beginning with reason, which at first creates an idea of itself. Special attention is paid to the way that Fichte categorizes them with the help of 5 spheres of action or 5 worldviews. The third and final part of the article discusses how Hegel goes beyond the frame of the transcendental philosophy of consciousness using different demands linked to the concepts of “reason” and “ideas”. Although these requirements are not found in Kant and Fichte, they entail a set of difficulties, which the author considers in conclusion. The author’s interpretation of the theory of ideas and their functions in Kant, Fichte and Hegel demonstrates the dynamic character of the theories of reason in classical German philosophy, as well as the relevance of the 7 types of ideas that retain their significance for philosophy of the 21st century. Keywords: Kant and German idealism, types of ideas, functions of reason, worldviews, the problem of different demands. В Германии на протяжении последних двух десятилетий возрос интерес к трансцендентальной диалектике «Критики чистого разума». Однако авторы часто не обращают внимания на то, что кантовская теория разума (в узком смысле), в которой разворачивается работа с идеями, не ограничивается этим текстом. Целью данной статьи является сравнительный анализ разработанной Кантом и Фихте функциональности разума как субъективной способности с гегелевским расширением разума до идеи всеобщей разумности. Актуальность такого сравнения связана с необходимостью продемонстрировать то, каким образом гегелевская парадигма абсолютной разумности вызывает либо последующий отказ от разума как философского принципа в контрдискурсе XIX–XX вв., либо редукцию разума к понятию прагматической рациональности. В первой части данной статьи вводится различение по меньшей мере семи различных видов идей и связанных с ними функций в философии Канта. Во второй части демонстрируется попытка Фихте их систематизировать исходя из утверждения том, что разум должен сначала создать идею о самом себе. Проанализировано также предложенное Фихте распределение идей на пять сфер действенности или типов мировоззрения. В третьей, итоговой части статьи рассмотрен выход гегелевской мысли за рамки трансцендентальной философии сознания. Автор статьи связывает этот процесс с выдвижением не осуществимых в контексте философии Канта и Фихте требований к понятиям «разум» и «идея» и анализирует ряд сложностей, вызванных этими требованиями. Таким образом, интерпретация учения об идеях и их функциях у Канта, Фихте и Гегеля демонстрирует динамический характер теорий разума в классической немецкой философии и актуальность семи видов идей, которые сохраняют свое значение для философии XXI в. Ключевые слова: Кант и немецкий идеализм, виды идей, функции разума, мировоззрение, проблема различных требований. (shrink)

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and even (...) independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility, incompleteness, the limits of computation,and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things,a non- quantum mechanical uncertainty principle and a proof of monotheism. There are obvious connections to the classic work of Chaitin, Solomonoff, Komolgarov and Wittgenstein and to the notion that no program (and thus no device) can generate a sequence (or device) with greater complexity than it possesses. One might say this body of work implies atheism since there cannot be any entity more complex than the physical universe and from the Wittgensteinian viewpoint, ‘more complex’ is meaningless (has no conditions of satisfaction, i.e., truth-maker or test). Even a ‘God’ (i.e., a ‘device’ with limitless time/space and energy) cannot determine whether a given ‘number’ is ‘random’ nor can find a certain way to show that a given ‘formula’, ‘theorem’ or ‘sentence’ or ‘device’ (all these being complex language games) is part of a particular ‘system’. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my article The Logical Structure of Philosophy, Psychology, Mind and Language as Revealed in Wittgenstein and Searle 59p(2016). For all my articles on Wittgenstein and Searle see my e-book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Wittgenstein and Searle 367p (2016). Those interested in all my writings in their most recent versions may consult my e-book Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2016’ 662p (2016). -/- All of my papers and books have now been published in revised versions both in ebooks and in printed books. -/- Talking Monkeys: Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B071HVC7YP. -/- The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle--Articles and Reviews 2006-2016 (2017) https://www.amazon.com/dp/B071P1RP1B. -/- Suicidal Utopian Delusions in the 21st century: Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B0711R5LGX . (shrink)

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

Roberto Frega’s Pragmatism and the Wide View of Democracy reformulates the question of democracy posed by our current historic conjuncture using the resources of a variety of pragmatic thinkers. He brings into the contemporary conversation regarding democracy’s fortunes both classical and somewhat neglected figures in the pragmatic tradition to deal with questions of power, ontology, and politics. In particular, Frega takes a social philosophical starting point and draws out the consequences of this fundamental shift in approach to questions of (...) democratic and political theory. This turn to social philosophy as a theoretically more sufficient conceptual vocabulary, extended in detail by Frega, raises questions regarding the work that a social ontology does in clarifying the role of economic and political approaches to democracy that are worth further exploration. Likewise, the practical proposals for moving beyond methodological nationalism with respect to forming publics for the sake of problem-solving, while providing a clarifying and fresh starting point, are still too beholden to models of agency and expressions of coordinated action that themselves are the very fruit of those systems which undermine democratic power in the first instance. (shrink)

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv dot org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, (...) and even independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility, incompleteness, the limits of computation, and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things, a non- quantum mechanical uncertainty principle and a proof of monotheism. There are obvious connections to the classic work of Chaitin, Solomonoff, Komolgarov and Wittgenstein and to the notion that no program (and thus no device) can generate a sequence (or device) with greater complexity than it possesses. One might say this body of work implies atheism since there cannot be any entity more complex than the physical universe and from the Wittgensteinian viewpoint, ‘more complex’ is meaningless (has no conditions of satisfaction, i.e., truth-maker or test). Even a ‘God’ (i.e., a ‘device’with limitless time/space and energy) cannot determine whether a given ‘number’ is ‘random’, nor find a certain way to show that a given ‘formula’, ‘theorem’ or ‘sentence’ or ‘device’ (all these being complex language games) is part of a particular ‘system’. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 2nd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

The four volume work of which this book is a part has been praised as one of the great monuments of theoretical scholarship in sociology of the century. The praise has come largely from the older generation of students of Parsons and Merton. A great deal of dispraise has come from Alexander's own generation. Alan Sica's (1983) brilliant, biting review of Volume I speaks for many of Alexander's peers. Volume II is likely to be even more controversial. This volume begins (...) the substantive task of the text, the reinterpretation of the 'theoretical logic' of the classical sociologists, a reinterpretation governed by the intention of transcending the errors and limitations of the 'presuppositional' reasoning of the classical thinkers. For Alexander's sociological audience the second volume is the beginning of what really counts, and Volume II is indeed quite a different affair from the first, 'philosophical' volume: the prose tightens, and the air of getting down to work is palpable. (shrink)

The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not (...) exist at the same time. However, contrary to these claims, there is no inadequacy in the two-valued system of classical logic in explanation the intermediate situations in existence. The law of exclusion and the intermediate situations in the external world are separate things. The law of excluded middle has been inevitably accepted by other logic systems which are considered to reject this principle. The many-valued and the fuzzy logic systems do not transcend the classical logic. Misconceptions from incomplete information and incomplete research are effective in these criticisms. In addition, it is also effective to move the discussion about the intellectual conception (tasawwur) into the field of judgmental assent (tasdiq) and confusion of the mawhum (imaginable) with the ma‘kûl (intellegible). (shrink)

New methods for reading and understanding the religious sources have been applied along with the modern period. Some issues, that have already gained a certain shape in the classical period, have been discussed again as a result of the application of new methods and thus a number of conclusions which exceed the boundaries framed by Ijma (consensus of the Ummah) were reached. In the course of time, these discussions were not limited to transactions [al-Mu`amalat] but also expanded to worship (...) (al-'Ibadah) and faith (al-aqāʾid) issues. One of these debate topics is the issue whether it is mandatory for the Jews and Christians (Ahl al-Kitāb) to believe in and follow prophet Muhammad (pbuh) and the last holy book al-Quran to be on the straight path and to reach salvation. The detection and analysis of these historical breaking points in the modern period is of importance. To analyse these breaking points in the interpretation of the verses, two tafseers which reflect the traditional method and understanding (at-Tibyan and Bilmen’s Tafseer) are compared with two other tafseers (Çağdaş Tefsir and Kuran Yolu) which are written in the last 40 years period. (shrink)

ABSTRACT. Two arguments have recently been advanced that Maxwell-Boltzmann particles are indistinguishable just like Bose-Einstein and Fermi-Dirac particles. Bringing modal metaphysics to bear on these arguments shows that ontological indistinguishability for classical (MB) particles does not follow. The first argument, resting on symmetry in the occupation representation for all three cases, fails since peculiar correlations exist in the quantum (BE and FD) context as harbingers of ontic indistinguishability, while the indistinguishability of classical particles remains purely epistemic. The second (...) argument, deriving from the classical limits of quantum statistical partition functions, embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a third argument is considered that attempts to deflate metaphysical concerns altogether by showing that the phase-space and distribution-space representations of MB-statistics have contrary haecceitistic import. Careful analysis shows this argument to fail as well, leaving de re modality unproblematically grounding particle identity in the classical context while genuine puzzlement about the underlying ontology remains for quantum statistics. (shrink)

It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways (...) out of the paradox, I conclude that the classical theist should accept Marilyn Adams’s view that no norms apply to gods. (shrink)

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal (...) world is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. -/- The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. -/- The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. -/- The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. -/- The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. -/- In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold. (shrink)

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well (...) as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity. (shrink)

The emphasis on the limitations of objectivity, in specific guises and networks, has been a continuing theme of contemporary analytic philosophy for the past few decades. The popular sport of baiting feminist philosophers — into pointing to what's left out of objective knowledge, or into describing what methods, exactly, they would offer to replace the powerful objective methods grounding scientific knowledge — embodies a blatant double standard which has the effect of constantly putting feminist epistemologists on the defensive, on the (...) fringes, on the run.This strategy can only work if objectivity is transparent, simple, stable, and clear in its meaning. It most certainly is not. In fact, taking objectivity as a sort of beautiful primitive, self-evident in its value, and all-powerful in its revelatory power, requires careless philosophy, and the best workers in metaphysics, epistemology, and philosophy of science have made reworked definitions of objectivity absolutely central to their own projects. In fact, classic feminist concerns with exploring the impact of sex and gender on knowledge, understanding, and other relations between human beings and the rest of the world fall squarely within the sort of human and social settings thatare already considered central in most current analytic metaphysics, epistemology, and philosophy of science. I argue that the burden of proof is clearly on those who wish toreject the centrality and relevance of sex and gender to our most fundamental philosophical work on knowledge and reality. (shrink)

The classical theory of computation does not represent an adequate model of reality for simulation in the social sciences. The aim of this paper is to construct a methodological perspective that is able to conciliate the formal and empirical logic of program verification in computer science, with the interpretative and multiparadigmatic logic of the social sciences. We attempt to evaluate whether social simulation implies an additional perspective about the way one can understand the concepts of program and computation. We (...) demonstrate that the logic of social simulation implies at least two distinct types of program verifications that reflect an epistemological distinction in the kind of knowledge one can have about programs. Computer programs seem to possess a causal capability (Fetzer, 1999) and an intentional capability that scientific theories seem not to possess. This distinction is associated with two types of program verification, which we call empirical and intentional verification. We demonstrate, by this means, that computational phenomena are also intentional phenomena, and that such is particularly manifest in agent-based social simulation. Ascertaining the credibility of results in social simulation requires a focus on the identification of a new category of knowledge we can have about computer programs. This knowledge should be considered an outcome of an experimental exercise, albeit not empirical, acquired within a context of limited consensus. The perspective of intentional computation seems to be the only one possible to reflect the multiparadigmatic character of social science in terms of agent-based computational social science. We contribute, additionally, to the clarification of several questions that are found in the methodological perspectives of the discipline, such as the computational nature, the logic of program scalability, and the multiparadigmatic character of agent-based simulation in the social sciences. (shrink)

Through this contribution I aim to explore the horizons and limits of digital medicine in light of an embodied approach to the issue of care. I will sketch the historical background of digital medicine and show the contemporary status of this interdisciplinary field, as well as its applications and outcomes. Then, I will address a critique of the computational theory of mind (CTM) upon which many contemporary mental health apps are designed. This approach to the mind is inscribed into the (...) modern trend of neuromania, which conceives the embodied, living human being as a mere series of data analyses and algorithms, with the brain as the seat of the person. Drawing on continental philosophy and classical phenomenology I will develop a notion of health conceived as a moral enterprise, showing how wellbeing and vitality are not reducible to a product made by technologies or doctors, but rather they are the results of an embodied encounter. As such, empathy and person-centered care cannot be achieved by digital medicine. They are the result of a journey into the regions of recognition, embodied presence and the aliveness constituting the person. Finally, I will show how the issue of care cannot be separated from an embodied encounter between people, especially in case of dementia. (shrink)

In this chapter, we outline the interdisciplinary contributions that philosophy, psychology, and neuroscience have provided in the understanding of the self and identity, focusing on one specific line of burgeoning research: the importance of morality to perceptions of self and identity. Of course, this rather limited focus will exclude much of what psychologists and neuroscientists take to be important to the study of self and identity (that plethora of self-hyphenated terms seen in psychology and neuroscience: self-regulation, self-esteem, self-knowledge, self-concept, self-perception, (...) and more). We will likewise not engage with many canonical philosophical treatments of self and identity. But we will lay out a body of research that brings together classic themes in philosophy, psychology, and neuroscience to raise empirically tractable philosophical questions, and philosophically rigorous empirical questions about self and identity. More specifically, in section 4.2, we will review some recent research that has treated traditional philosophical questions about self and identity as empirical questions. Within this body of work, we will be primarily concerned with the finding that morality (more so than memory) is perceived to be at the core of self and identity. Then, in section 4.3, we raise and respond to a variety of questions and criticisms: first, about the operationalization of identity concepts in the empirical literature; second, about the generalizability of the moral self effect; third, about the direction of change; fourth, about connections with recent work in neuroscience; and fifth, about the target of evaluation. Finally, in section 4.4, we consider a variety of implications and applications of this work on the moral self. Throughout, we aim to highlight connections between classical themes in philosophy, psychology, and neuroscience, while also suggesting new directions for interdisciplinary collaboration. (shrink)

K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent, publicly available, and contains theorems both from formal and constructive mathematics. Any theorem of any mathematician from past or present forever belongs to K. Mathematical statements with known constructive proofs exist in K separately and form the set K_c⊆K. We assume that mathematical sets are atemporal entities. They exist formally in ZFC theory although their (...) properties can be time-dependent (when they depend on K) or informal. The true statement "K is non-empty" is outside K forever because K is not a formal set. Paul Cohen proved in 1963 that the equality 2^{\aleph_0}=\aleph_1 is independent of ZFC. Before 1963, the statement "There is a known constructively defined integer n⩾1 such that 2^{\aleph_0}=\aleph_n" was outside K. Since 1963, this statement is outside K forever. The true statement "There exists a set X⊆{1,...,49} such that card(X)=6 and X never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside K forever. In Martin-Löf's terminology, every currently known theorem is actually true whereas every theorem (known or unknown) is potentially true. Actual truth is knowledge dependent and tensed. Potential truth is knowledge independent and tenseless. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. For every such statement, its truth concerning the current mathematical knowledge is implied by a true statement of the form: (the conjunction of i conditions of the form α∈K)∧(the conjunction of j conditions of the form β∉K)∧(the conjunction of k conditions of the form γ∈K_c)∧(the conjunction of l conditions of the form δ∉K_c), where i,j,k,l∈N and α,β,γ,δ are mathematical statements. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a mathematical statement depends on time, where the statement is formally stated in the classical mathematics without the predicate K. In this article, mathematical statements on decidable sets X⊆N refer to time because they refer to the current mathematical knowledge on X. They cannot be formally stated in the classical mathematics without the predicate K and their logical values may change in time. For a set X⊆N whose infiniteness is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(X)=ω" is outside K. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove the assumption of the above statement. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧(Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. We prove that there exists a naturally defined set C⊆N which satisfies the following conditions (6)-(11). (6) A known and simple algorithm for every k∈N decides whether or not k∈C. (7) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(C)=ω" is outside K. (8) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(N\C)=ω" is outside K. (9) It is conjectured, though so far unproven, that C is infinite. (10) For every known algorithm A with no input, the statement "A returns an integer n satisfying card(C)<ω ⇒ C⊆(-∞,n]" is outside K. (11) For every known algorithm A with no input, the statement "A returns an integer m satisfying card(N\C)<ω ⇒ N\C⊆(-∞,m]" is outside K. The set C={k∈N: 2^{2^k}+1 is composite} is naturally defined and satisfies conditions (6)-(11). (shrink)

In present times, Science has undergone a drastic change due to the critical examination of its methods of acquiring scientific knowledge. It has become more and more contiguous to philosophy. Relativity theory and Quantum Mechanics have revolutionized our concepts of classical physics in their analysis of matter and have created not only a new mathematical symbolism but a revision of a large number of its basic concepts. Relativity has shown that all material objects and processes exist in the integral (...) form of space-time, of which the relations of space and time are different but inseparable aspects. Its modification of our classical concepts of mass, length, force, the law of addition of velocities, the principle of simultaneity along with a new interpretation of laws of conservation of energy, momentum and angular momentum are of a more universal nature. The theory of relativity has demonstrated for the first time the inner necessity of the idea of dialectical contradiction in the theoretical development of the concepts of physics. Quantum mechanics has continued which began in physics with the advent of the theory of relativity. With the development of quantum mechanics, the notion of a strict continuity in the spectrum of values of physical quantities is no longer valid, the classical concept of trajectory is rejected, the principle of classical determinism is questioned. It has shown that the basic laws of nature are not dynamic but statistical and that the probabilistic form of causality is the fundamental form while classical determinism is just its limiting case. In this article, an attempt is made to present a comprehensive picture of the impact of relativity theory and quantum mechanics on a large number of concepts of philosophy. It has been shown that these theories have called for a drastic revision of the seminal kernels of the traditional philosophy of science. (shrink)

In the remainder of this article, we will disarm an important motivation for epistemic contextualism and interest-relative invariantism. We will accomplish this by presenting a stringent test of whether there is a stakes effect on ordinary knowledge ascription. Having shown that, even on a stringent way of testing, stakes fail to impact ordinary knowledge ascription, we will conclude that we should take another look at classical invariantism. Here is how we will proceed. Section 1 lays out some limitations of (...) previous research on stakes. Section 2 presents our study and concludes that there is little evidence for a substantial stakes effect. Section 3 responds to objections. The conclusion clears the way for classical invariantism. (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method ofion”, the philosophical fruitfulness of the new (...) method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)