Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that general relativity theory may be reduced to the Newton's gravity theory in the limit of a weak gravitational field and slow motion of the material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations to Newton's equation of motion and Poisson's gravitational potential equation, respectively, is scrutinized and proven to be (...) mathematically, physically and dimensionally wrong and also the geometrization of gravity is not really necessary. (shrink)

The arguments are exhibited in favour of the necessity to modify the history of the genesis and advancement of general relativity (GR). I demonstrate that the dynamic creation of GR had been continually governed by internal tensions between two research traditions, that of special relativity and Newton’s gravity. The encounter of the traditions and their interpenetration entailed construction of the hybrid domain at first with an irregular set of theoretical models. Step by step, on eliminating the (...) contradictions between the models contrived, the hybrid set was put into order. It is contended that the main reason of the GR victory over the rival programmes of Abraham and Nordström was a synthetic character of Einstein’s programme. Einstein had put forward as a basic synthetic principle the principle of equivalence that radically differed from that of rival approaches by its open, flexible and contra-ontological character. (shrink)

The current technoscientific progress has led to a sectorization in the philosophy of science. Today the philosophy of science isn't is informal interested in studying old problems about the general characteristics of scientific practice. The interest of the philosopher of science is the study of concepts, problems and riddles of particular disciplines. Then, within this progress of philosophy of science, neuroscientific research stands out, because it invades issues traditionally addressed by the humanities, such as the nature of consciousness, action, (...) knowledge, normativity, etc. As a result, the new area of interdisciplinary study of neuroscience and philosophy arises: neurophilosophy. This emerging area applies neuroscientific concepts to traditional philosophical questions, limiting their responses to neuroscientific revelations about nervous systems. Neurophilosophy research focuses on problems related to the indirect nature of mind and brain, computational or representative analysis of brain process, relationships between psychological and neuroscientific research, adequate adaptations of physical and philosophical concepts in neuroscience and the place of cognitive functions. Now, the temporal representation of conscious experience and the types of the neural architecture to represent objects in time have aroused scientific interest. Under these interests, we focus on the studies on the temporary triadic structure of phenomenological consciousness in Dan Lloyd and Rick Grush. From Grush’s studies, the importance of Kantian ideas for cognitive neuroscience emerges, due to the active way in which Kant conceived space and time as forms of intuition, within which the mind interprets its experience. Under this perspective, the theoretical arguments of Dennett-Kinsbourne and Eagleman-Sejnowski represent winks in the direction of Kant-Husserl within the neuroscientific goal while considering that the contents provided by the mind included space, objects and perception of causal relationships. Then, theories of cognitive neuroscience are beginning to suggest that these elements are also, as Kant argued, interpretative elaborations provided by mind / brain, and not only content received from outside. In other words, current cognitive neuroscientific theories try to pass from its Humean phase to a Kantian phase. So, the challenge has been to explain that these elements are provided by the mind and the world itself, and how they have the content they have come from. These are lacking in current studies. Filling this gap helps to involve the analysis of the scientist’s experience in his theoretical attitude. In this sense, an investigation under the Kantian-Husserlian approach that involves pure intuitions a priori with the experience of the scientific and neuroscientific concepts represents a ground-breaking. At present, a neurophilosophical study about this does not exist. In this sense, one feasible proposal for research would be based on the application of neuroscientific results of Moser-Britt to philosophical problems of foundational notions in relativistic physics: space, time, space-time, field, etc., under the Kantian-Husserlian approach, which allows to demonstrate the multidisciplinary link between neurophilosophy and physics. This represents a ground-breaking area in current interests in scientific research, with a positive impact in the field of neuroscience, and contributing to the study of abstraction emphasizing the importance of Kant’s Copernican turn and Husserl’s phenomenological ideas in the construction of physical theories. -/- . (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational (...) in a generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Furthermore the approach clears up philosophically how quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. The key link between them is the notion of the Bekenstein bound as well as that of quantum temperature. General relativity can be interpreted as a special particular case of quantum gravity. All principles underlain by Einstein (1918) reduce the latter to the former. Consequently their generalization and therefore violation addresses directly a theory of quantum gravity. Quantum measure reinterprets newly the “Bing Bang” theories about the beginning of the universe. It measures jointly any quantum leap and smooth motion complementary to each other and thus, the jump-like initiation of anything and the corresponding continuous process of its appearance. Quantum measure unifies the “Big Bang” and the whole visible expansion of the universe as two complementary “halves” of one and the same, the set of all states of the universe as a whole. It is a scientific viewpoint to the “creation from nothing”. (shrink)

This paper centers on the implicit metaphysics beyond the Theory of Relativity and the Principle of Indeterminacy – two revolutionary theories that have changed 20th Century Physics – using the perspective of Husserlian Transcedental Phenomenology. Albert Einstein (1879-1955) and Werner Heisenberg (1901-1976) abolished the theoretical framework of Classical (Galilean- Newtonian) physics that has been complemented, strengthened by Cartesian metaphysics. Rene Descartes (1596- 1850) introduced a separation between subject and object (as two different and self- enclosed substances) while Galileo and (...) Newton did the “mathematization” of the world. Newtonian physics, however, had an inexplicable postulate of absolute space and absolute time – a kind of geometrical framework, independent of all matter, for the explication of locality and acceleration. Thus, Cartesian modern metaphysics and Galilean- Newtonian physics go hand in hand, resulting to socio- ethical problems, materialism and environmental destruction. Einstein got rid of the Newtonian absolutes and was able to provide a new foundation for our notions of space and time: the four (4) dimensional space- time; simultaneity and the constancy of velocity of light, and the relativity of all systems of reference. Heisenberg, following the theory of quanta of Max Planck, told us of our inability to know sub- atomic phenomena and thus, blurring the line between the Cartesian separation of object and subject, hence, initiating the crisis of the foundations of Classical Physics. But the real crisis, according to Edmund Husserl (1859-1930) is that Modern (Classical) Science had “idealized” the world, severing nature from what he calls the Lebenswelt (life- world), the world that is simply there even before it has been reduced to mere mathematical- logical equations. Husserl thus, aims to establish a new science that returns to the “pre- scientific” and “non- mathematized” world of rich and complex phenomena: phenomena as they “appear to human consciousness”. To overcome the Cartesian equation of subject vs. object (man versus environment), Husserl brackets the external reality of Newtonian Science (epoché = to put in brackets, to suspend judgment) and emphasizes (1) the meaning of “world” different from the “world” of Classical Physics, (2) the intentionality of consciousness (L. in + tendere = to tend towards, to be essentially related to or connected to) which means that even before any scientific- logical description of the external reality, there is always a relation already between consciousness and an external reality. The world is the equiprimordial existence of consciousness and of external reality. My paper aims to look at this new science of the pre- idealized phenomena started by Husserl (a science of phenomena as they appear to conscious, human, lived experience, hence he calls it phenomenology), centering on the life- world and the intentionality of consciousness, as providing a new way of looking at ourselves and the world, in short, as providing a new metaphysics (as an antidote to Cartesian metaphysics) that grounds the revolutionary findings of Einstein and Heisenberg. The environmental destruction, technocracy, socio- ethical problems in the modern world are all rooted in this Galilean- Newtonian- Cartesian interpretation of the relationship between humans and the world after the crumbling of European Medieval Ages. Friedrich Nietzsche (1844-1900) comments that the modern world is going toward a nihilism (L. nihil = nothingness) at the turn of the century. Now, after two World Wars and the dropping of Atomic bomb, the capitalism and imperialism on the one hand, and on the other hand the poverty, hunger of the non- industrialized countries alongside destruction of nature (i.e., global warming), Nietzsche might be correct: unless humanity changes the way it looks at humanity and the kosmos. The works of Einstein, Heisenberg and Husserl seem to be pointing the way for us humans to escape nihilism by a “great existential transformation.” What these thinkers of post- modernity (after Cartesian/ Newtonian/ Galilean modernity) point to are: a) a new therapeutic way of looking at ourselves and our world (metaphysics) and b) a new and corrective notion of “rationality” (different from the objectivist, mathematico- logical way of thinking). This paper is divided into four parts: 1) A summary of Classical Physics and a short history of Quantum Theory 2) Einstein’s Special and General Relativity and Heisenberg’s Indeterminacy Principle 3) Husserl’s discussion of the Crisis of Europe, the life- world and intentionality of consciousness 4) A Metaphysics of Relativity and Indeterminacy and a Corrective notion of Rationality in Husserl’s Phenomenology . (shrink)

A methodological model of origin and settlement of theory-choice situations (previously tried on the theories of Einstein and Lorentz in electrodynamics) is applied to modern Theory of Gravity. The process of origin and growth of empirically-equivalent relativistic theories of gravitation is theoretically reproduced. It is argued that all of them are proposed within the two rival research programmes – (1) metric (A. Einstein et al.) and (2) nonmetric (H. Poincare et al.). Each programme aims at elimination of the cross-contradiction (...) between the special theory of relativity and Newton’s theory of gravitation. New arguments in favor of Einstein’s programme are given. Nevertheless, this does not imply the necessity to rule out all the nonmetric theories, since Einstein’s and Poincare’s programmes are alternative only as different tools of the cross-contradiction elimination. In the other respects these programmes are complementary: description, explanation and prediction of gravitational experimental data entails the usage of the languages of nonmetric theories as well as of metric ones. The part of the present investigation elucidating the necessity of nonmetric theories is an implementation of the ideas of A.Z. Petrov, the founder of Kazan University Relativity Department. Late Alexei Zinovievich had frequently punctuated that the notion of Riemann space-time continuum common for all metric theories obfuscates all the gravitational notions considerably and hampers the analogies with other physical theories at hand. Since the ambiguity is a hallmark of all the general relativism notions, approach to their definitions “should be determined not by analogies and contingent facts, but by general considerations linked the physical measurements theory… No matter how far the events lie out of the frames of classical physical explanations, all the experimental data should be described by classical notions” (Petrov, 1965,pp. 59,66). Key words: Kip S. Thorne, A.P. Lightman, Stepin, theory of gravity . (shrink)

In this paper I shall argue in Section II that two of the standard arguments that have been put forth in support of Einstein’s Special Theory of Relativity do not support that theory and are quite compatible with what might be called an updated and perhaps even an enlightened Newtonian view of the Universe. This view will be presented in Section I. I shall call it the neo-Newtonian Theory, though I hasten to add there are a number of things (...) in it that Newton would not accept, though perhaps Galileo might have. Now there may be other arguments and/or pieces of empirical evidence which support the Special Theory of Relativity and cast doubt upon the neo-Newtonian view. Nevertheless, the two that I am going to examine are usually considered important. It might also be claimed that the two arguments that I am going to examine have only heuristic value. Perhaps this is so but they are usually put forward as supporting the Special Theory and refuting the neo-Newtonian Theory. Again I must stress that it is not my aim to cast any doubt on the Special Theory of Relativity nor on Einstein. His Special Theory and his General Theory stand at the zenith of human achievement. My only aim is to cast doubt on the assumption that the two arguments I examine support the Special Theory. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation (...) can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

The topic of this Handbook entry is the relationship between similarity and dimensional analysis, and some of the philosophical issues involved in understanding and making use of that relationship. Discusses basics of the relationship between units, dimensions, and quantities. It explains the significance of dimensionless parameters, and explains that similarity of a physical systems is established by showing equality of a certain set of dimensionless parameters that characterizes the system behavior. Similarity is always relative -- to some system (...) behavior. Other topics discussed: generalization of the notion of similarity, the difference between relative similarity and partial similarity; how the notion of similarity in science differs from similarity as it has been discussed in recent philosophy. Philosophers' views discussed: R. Giere, N. Goodman, P. Bridgman, and B. Ellis. (shrink)

In his project of going beyond the “modern worldview,” Hiromatsu Wataru attached great importance to Ernst Mach’s philosophical thought and Einstein’s theory of relativity as challenging the premises of modern philosophy, which he characterized as substantialist and bound by the subject / object schema. This paper surveys Hiromatsu’s analysis of Mach’s phenomenalist element-monism, specifically his critique of Mach’s insufficient break with modern philosophy; his inquiry into Einstein’s relativity theory with a focus on its intersubjective cognitive structure; and (...) the way he extends his views on these themes to a general ontological-epistemological theory of the “fourfold structure.” Finally, it examines questions about Hiromatsu’s arguments regarding the tension between the dimensions of synchronic structure and structuring movement. An earlier version of this paper can be found as “Philosophers” in John T. Blackmore, Itagaki Ryōichi, and Tanaka Setsuko, eds., Ernst Mach’s Influence Spreads, 425–76. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

This article had its beginning with Einstein's 1919 paper "Do gravitational fields play an essential role in the structure of elementary particles?" Together with General Relativity's statement that gravity is not a pull but is a push caused by the curvature of space-time, a hypothesis for Earth's ocean tides was developed that does not solely depend on the Sun and Moon as Kepler and Newton believed. It also borrows from Galileo. The breakup of planets and asteroids by (...) white dwarfs, neutron stars or black holes is popularly ascribed by today's science to tidal forces (gravitation emanating from the stellar body and having a greater effect on the near side of a planet/asteroid than the farthest side). Remembering Einstein's 1919 paper, it was apparent that my revised idea of tidal forces improves on current accounts because it views matter and mass as unified with space-time whose curvature is gravitation. Unification is a necessity for modern science's developing view of one united and entangled universe – expressed in the Unified Field Theory, the Theory of Everything, String theory and Loop Quantum Gravity. The writing of this article was also assisted by visualizing the gravitational fields forming space-time being themselves formed by a multitude of weak and presently undetectable gravitational waves. The final part of this article concludes that the section BITS AND TOPOLOGY will lead to the conclusions in ETERNAL LIFE, WORLD PEACE AND PHYSICS' UNIFICATION. The final part also compares cosmology to biological enzymes and biology's substrate of reacting "chemicals" - using virtual particles, hidden variables, gravitation, electromagnetism, electronics’ binary digits, plus topology’s Mobius strip and figure-8 Klein bottle. The product is mass - enzyme, substrate and product are all considered mathematical in nature. Also, gravitation and electromagnetism are united using logic and topology – showing there’s no need in this article for things like mathematical formalism, field equations or tensor calculus. (shrink)

Euler’s interpretation of Newton’s gravity (NG) as Archimedes’ thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler’s, is recalled and compared with the latter. None of these two ‘‘gravitational ethers’’ can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, (...) a compressible ether leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newton’s second law. The observational status for the theory with the older version of the correspondence is summarized. (shrink)

Based on the various documents, 1989-2002, through the original texts, in addition to the author's contributions, this paper presents the refutation of the mathematicians and physicists A. Logunov and M. Mestvirishvil of A. Einstein's "general relativity", from the relativistic theory of gravitation of these authors, who applying the fundamental principle of the science of physics of the conservation of the energy-momentum and using absolute differential calculus they rigorously perform their mathematical tests. It is conclusively shown that, from the (...) Einstein-Grossman-Hilbert equations, gravity is absurdly a metric field devoid of physical reality unlike all other fields in nature that are material fields, interrupting the chain of transformations between the different existing fields. Also, in Einstein's theory the proved "inertial mass" equal to gravitational mass has no physical meaning. Therefore, "general relativity" does not obey the correspondence principle with Newton's gravity. (shrink)

Abstract: The article presents and critically discusses Walton's (and Reed's and Macagno's) argument scheme approach to a theory of good argumentation. In particular, four characteristics of Walton's approach are presented: 1. It presents normative requirements for argumentation in the form of argument schemes, i.e. relatively concrete type descriptions. 2. These schemata are enthymematic, i.e. they omit some of the premises required by other approaches. 3. The actual argument schemes are usually supplemented by critical questions. 4. The method is inductive, bottom-up, (...) gaining the normative schemata by abstraction from empirically collected groups of similar arguments. These characteristics, among others, are then discussed on the basis of four adequacy conditions: AC1: effectiveness in achieving the epistemic goal of obtaining and communicating justified acceptable opinions; AC2: completeness in capturing the good argument types; AC3: efficiency in achieving the goals; AC4: justification of the argument schemes. The discussion then reveals a number of weaknesses in Walton's argument schemes; among other things, they are neither effective (in the defined sense) nor truly justified. Contributing factors to these problems include the schema approach, i.e. not looking at the form of arguments, and the lack of epistemological foundations in the development of good types of arguments. However, the critical analyses reveal a better alternative: an epistemological approach based on epistemological principles. The article concludes with a detailed analysis of the scheme Practical Inference, which confirms the general criticism in detail. (shrink)

The goal of this note is to bring into wider attention the often neglected important work by Bertrand Russell on the foundations of physics published in the late 1920s. In particular, we emphasize how the book The Analysis of Matter can be considered the earliest systematic attempt to unify the modern quantum theory, just emerging by that time, with general relativity. More importantly, it is argued that the idea of what I call Russell space, introduced in Part (...) III of that book, is more fundamental than quantum theory, general relativity, and quantum gravity since the topological ordinal space proposed by Russell would naturally incorporate into its very fabric the emergent nature of spacetime by deploying event assemblages, and not spacetime or particles, as the fundamental building blocks of the world. (shrink)

Recently, a number of philosophers have argued that we can and should “consequentialize” non-consequentialist moral theories, putting them into a consequentialist framework. I argue that these philosophers, usually treated as a group, in fact offer three separate arguments, two of which are incompatible. I show that none represent significant threats to a committed non-consequentialist, and that the literature has suffered due to a failure to distinguish these arguments. I conclude by showing that the failure of the consequentializers’ arguments has implications (...) for disciplines, such as economics, logic, decision theory, and linguistics, which sometimes use a consequentialist structure to represent non-consequentialist ethical theories. (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)

Einstein structured the theoretical frame of his work on gravity under the Special Relativity and Minkowski´s spacetime using three guide principles: The strong principle of equivalence establishes that acceleration and gravity are equivalents. Mach´s principle explains the inertia of the bodies and particles as completely determined by the total mass existent in the universe. And, general covariance searches to extend the principle of relativity from inertial motion to accelerated motion. Mach´s principle was abandoned quickly, (...) class='Hi'>general covariance resulted mathematical property of the tensors and principle of equivalence inconsistent and it can only apply to punctual gravity, no to extended gravity. Also, the basic principle of Special Relativity, i.e., the constancy of the speed of the electromagnetic wave in the vacuum was abandoned, static Minkowski´s spacetime was replaced to dynamic Lorentz´s manifold and the main conceptual fundament of the theory, i.e. spacetime is not known what is. Of other hand, gravity never was conceptually defined; neither answers what is the law of gravity in general. However, the predictions arise of Einstein equations are rigorously exacts. Thus, the conclusion is that on gravity, it has only the equations. In this work it shows that principle of equivalence applies really to punctual and extended gravity, gravity is defined as effect of change of coordinates although in the case of the extended gravity with change of geometry from Minkowski´s spacetime to Lorentz´s manifold; and the gravitational motion is the geodesic motion that well it can declare as the general law of gravity. (shrink)

This discussion treats a set of familiar social derelictions as consequences of the perversion of a universalistic moral theory in the service of an ill-considered or insufficiently examined personal agenda.The set includes racism, sexism, anti-Semitism, homophobia, and class elitism, among other similar pathologies, under the general heading of discrimination. The perversion of moral theory from which these derelictions arise, I argue, involves restricting its scope of application to some preferred subgroup of the moral community of human beings. -/- The (...) following analysis of higher-order discrimination suggests that we often select the individuals who constitute such subgroups for reasons that we ourselves would reject on moral grounds were we to examine them carefully, but that we choose instead to put our rational resources in the service of avoiding any such examination at all costs. The implication is that arguments that truncate the scope of moral theory in fact justify bestowing the gift of moral treatment on a select few who deserve it no more than the many from whom we withhold it. Therefore, it would be precipitous to conclude that universalistic moral theory can be legitimately restricted in its practical scope of application in any way at all. (shrink)

This dissertation examines the dynamical dark matter problem in twentieth century astrophysics from the point of view of History and Philosophy of Science. The dynamical dark matter problem describes the situation astronomers find themselves in with regard to the dynamics of large scale astrophysical systems such as galaxies and galaxy clusters: The observed motions are incompatible with the visible distribution matter given the accepted law of gravitation. This discrepancy has two classes of possible solutions: either there exists copious amounts of (...) some kind of matter that neither emits nor absorbs radiation , or the law of gravitation must be revised. ;Chapter 2 describes the physical and philosophical foundations of dynamical inferences---inferences from discrepancies between well-founded theoretical expectations and reliable observations to the characteristics of candidate solutions. Chapter 3 discusses the history of dark matter . Chapter 4 reviews the present evidence bearing on the dark matter problem. Chapter 5 evaluates the important candidate matter solutions in light of the available evidence. Chapter 6 evaluates two candidate gravitational solutions on evidential and methodological grounds, and addresses the problem of theory choice. I do not try to solve the dark matter problem, but to uncover and evaluate patterns of inference involved in evidential arguments for and against candidate solutions. ;I show that Newton's "Reasoning from Phenomena" is a good framework from which to understand what is going on in this field. I argue that "higher order" and especially non-dynamical evidence is the best hope for solving this problem in dynamics. This is so in part because of "the dark matter double bind": the very existence of the dark matter problem means that we cannot be sure of the overall matter distribution in astrophysical systems, and this in turn means that the observed motions by themselves cannot provide relative confirmation of any theory of gravitational interactions taking place at these scales. I use Newton's Rules of Reasoning to argue that we should retain General Relativity as our theory of gravity at galactic and greater scales, despite the lack of positive evidence to confirm it over its rivals at these scales. (shrink)

In this paper I sketch some arguments that underlie Hegel's chapter on judgment, and I attempt to place them within a broad tradition in the history of logic. Focusing on his analysis of simple predicative assertions or ‘positive judgments’, I first argue that Hegel supplies an instructive alternative to the classical technique of existential quantification. The main advantage of his theory lies in his treatment of the ontological implications of judgments, implications that are inadequately captured by quantification. The second (...) concern of this paper is the manner in which Hegel makes logic not only dependent on ontology generally, but also variant in regard to domains of objects. In other words, he offers a domain-specific logical theory, according to which the form of judgment or inference is specific to the subject of judgment. My third concern lies with the metaphilosophical consequences of this theory, and this includes some more familiar Hegelian themes. It is well known that Hegel frequently questioned the adequacy of the sentential form for expressing higher order truths. My reading of his theory of predication explains and contextualizes this tendency by demystifying notions like the so-called speculative proposition. (shrink)

General Relativity says gravity is a push caused by space-time's curvature. Combining General Relativity with E=mc2 results in distances being totally deleted from space-time/gravity by future technology, and in expansion or contraction of the universe as a whole being eliminated. The road to these conclusions has branches shining light on supersymmetry and superconductivity. This push of gravitational waves may be directed from intergalactic space towards galaxy centres, helping to hold galaxies together and also creating (...) supermassive black holes. Together with the waves' possible production of "dark" matter in higher dimensions, there's ample reason to believe knowledge of gravitational waves has barely begun. Advanced waves are usually discarded by scientists because they're thought to violate the causality principle. Just as advanced waves are usually discarded, very few physicists or mathematicians will venture to ascribe a physical meaning to Wick rotation and "imaginary" time. Here, that maths (when joined with Mobius-strip and Klein-bottle topology) unifies space and time into one space-time, and allows construction of what may be called "imaginary computers". This research idea you're reading is not intended to be a formal theory presenting scientific jargon and mathematical formalism. (shrink)

It presents the basics of the “Relativistic theory of gravitation”, with the inclusion of original texts, from various papers, published between 1987 and 2009, by theirs authors: S. S Gershtein, A. A. Logunov, Yu. M. Loskutov and M. A. Mestvirishvili, additionally, together with the introductions, summaries and conclusions of the author of this paper. The “Relativistic theory of gravitation” is a gauge theory, compatible with the theories of quantum physics of the electromagnetic, weak and strong forces, which defines gravity (...) as the fourth force existing in nature, as a static field equipped with the transmitter particles of the virtual gravitons of spins 2 and 0, within the spirit of Galilei's principle of relativity, in his generalization of Poincaré's Special Relativity that allowed the authors to universalize that the physical laws of nature are complied with regardless of the frames of reference where they apply, integrated into the Grossmann-Einstein Entwurf theory, in its further development, by those authors, therefore, this theory preserves the conservation laws of energy-impulse and angular impulse of the gravitational field jointly to the other material fields existing in nature, in the Riemann's effective spacetime, through its identity with Minkowski's pseudo Euclidean spacetime. (shrink)

This paper is about two requirements on wish reports whose interaction motivates a novel semantics for these ascriptions. The first requirement concerns the ambiguities that arise when determiner phrases, such as definite descriptions, interact with ‘wish’. More specifically, several theorists have recently argued that attitude ascriptions featuring counterfactual attitude verbs license interpretations on which the determiner phrase is interpreted relative to the subject’s beliefs. The second requirement involves the fact that desire reports in general require decision-theoretic notions for their (...) analysis. The current study is motivated by the fact that no existing account captures both of these aspects of wishing. I develop a semantics for wish reports that makes available belief-relative readings but also allows decision-theoretic notions to play a role in shaping the truth conditions of these ascriptions. The general idea is that we can analyze wishing in terms of a two-dimensional notion of expected utility. (shrink)

This paper is an enquiry into the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects. We argue that none of the purported paradoxes rule out time travel either on grounds of logic or metaphysics. More relevantly, modern spacetime theories such as general relativity seem to permit models that feature closed worldlines. We discuss, in the context of Gödel's infamous argument (...) for the ideality of time based on his eponymous spacetime, what this apparent physical possibility of time travel means. Furthermore, we review the recent literature on so-called time machines, i.e., of devices that produce closed worldlines where none would have existed otherwise. Finally, we investigate what the implications of the quantum behaviour of matter for the possibility of time travel might be and explicate in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity. (shrink)

Space-time intervals are the fundamental components of conscious experience, gravity, and a Theory of Everything. Space-time intervals are relationships that arise naturally between events. They have a general covariance (independence of coordinate systems, scale invariance), a physical constancy, that encompasses all frames of reference. There are three basic types of space-time intervals (light-like, time-like, space-like) which interact to create space-time and its properties. Human conscious experience is a four-dimensional space-time continuum created through the processing of space-time intervals (...) by the brain; space-time intervals are the source of conscious experience (observed physical reality). Human conscious experience is modeled by Einstein’s special theory of relativity, a theory designed specifically from the general covariance of space-time intervals (for inertial frames of reference). General relativity is our most accurate description of gravity. In general relativity, the general covariance of space-time intervals is extended to all frames of reference (inertial and non-inertial), including gravitational reference frames; space-time intervals are the source of gravity in general relativity. The general covariance of space-time intervals is further extended to quantum mechanics; space-time intervals are the source of quantum gravity. The general covariance of space-time intervals seamlessly merges general relativity with quantum field theory (the two grand theories of the universe). Space-time intervals consequently are the basis of a Theory of Everything (a single all-encompassing coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe). This theoretical framework encompasses our observed physical reality (conscious experience) as well; space-time intervals link observed physical reality to actual physical reality. This provides an accurate and reliable match between observed physical reality and the physical universe by which we can carry on our activity. The Minkowski metric, which defines generally covariant space-time intervals, may be considered an axiom (premise, postulate) for the Theory of Everything. (shrink)

PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...) all booksellers, including Barnes & Noble, Amazon, and brick-and-mortar bookstores under ISBN 978-0-578-88646-6. ●●●●● In light of the length of this book, readers who would like to have a more detailed description of the book's objectives and method may find it helpful to read the detailed and clearly written Wikipedia entry about this work: From the Wikipedia search page, use the search phrase "Critique of Impure Reason". At least at the time of this writing (11/29/2021), the Wikipedia entry is well-researched and accurate. ●●●●● In addition, a "Primer on Bartlett's CRITIQUE OF IMPURE REASON" has been made available by the author. It is available under its title through PhilPapers and other philosophy online archives. ●●●●● COMMENDATIONS OF THIS WORK, from the back cover of the published edition: ●●●●● “I admire its range of philosophical vision.” – Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh, author of more than 100 books. ●●●●● “Bartlett’s _Critique of Impure Reason_ is an impressive, bold, and ambitious work. Careful scholarship is balanced by original analyses that lead the reader to recognize the limits of meaning, knowledge, and conceptual possibility. The work addresses a host of traditional philosophical problems, among them the nature of space, time, causality, consciousness, the self, other minds, ontology, free will and determinism, and others. The book culminates in a fascinating and profound new understanding of relativity physics and quantum theory.” – Gerhard Preyer, Professor of Philosophy, Goethe-University, Frankfurt am Main, Germany, author of many books including _Concepts of Meaning_, _Beyond Semantics and Pragmatics_, _Intention and Practical Thought_, and _Contextualism in Philosophy_. ●●●●● “[This work’s] goal is of a unique and difficult species: Dr. Bartlett seeks to develop a formal logical calculus on the basis of transcendental philosophical arguments; in fact, he hopes that this calculus will be the formal expression of the transcendental foundation of knowledge.... I consider Dr. Bartlett’s work soundly conceived and executed with great skill.” – C. F. von Weizsäcker, philosopher and physicist, former Director, Max-Planck-Institute, Starnberg, Germany. ●●●●● “Bartlett has written an American “Prolegomena to All Future Metaphysics.” He aims rigorously to eliminate meaningless assertions, reach bedrock, and place philosophy on a firm foundation that will enable it, like science and mathematics, to produce lasting results that generations to come can build on. This is a great book, the fruit of a lifetime of research and reflection, and it deserves serious attention.” — Martin X. Moleski, former Professor, Canisius College, Buffalo, NY, studies of scientific method, the presuppositions of thought, and the self-referential nature of epistemology. ●●●●● “Bartlett has written a book on what might be called the underpinnings of philosophy. It has fascinating depth and breadth, and is all the more striking due to its unifying perspective based on the concepts of reference and self-reference.” – Don Perlis, Professor of Computer Science, University of Maryland, author of numerous publications on self-adjusting autonomous systems and philosophical issues concerning self-reference, mind, and consciousness. ●●●●● ●●●●● The _Critique of Impure Reason: Horizons of Possibility and Meaning_ comprises a major and important contribution to philosophy. Thanks to the generosity of its publisher, this massive 885-page volume has been published as a free open access eBook (3.75MB) as well as an open access printed edition. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. ●●●●● In Kant’s _Critique of Pure Reason_ we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new _Critique_ focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ _conflict_ with the very preconditions of meaning and of knowledge. ●●●●● This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. ●●●●● The _Critique of Impure Reason_ proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. ●●●●● The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of _possible meaning_ are determined. ●●●●● Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, _metalogical projection_. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. ●●●●● Based on original research and rigorous analysis combined with extensive scholarship, the _Critique of Impure Reason_ develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. ●●●●● CONTENTS AT A GLANCE ▪▪▪▪▪ Preface ▪▪▪▪▪ Foreword by Carl Friedrich von Weizsäcker ▪▪▪▪▪ Acknowledgments ▪▪▪▪▪ Avant-propos: A philosopher’s rallying call ▪▪▪▪▪ Introduction ▪▪▪▪▪ A note to the reader ▪▪▪▪▪ A note on conventions ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART I ▪▪▪▪▪ ▪▪▪▪▪ WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN ▪▪▪▪▪ 1 Philosophical-psychological prelude ▪▪▪▪▪ 2 Putting belief in its place: Its psychology and a needed polemic ▪▪▪▪▪ 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference ▪▪▪▪▪ 4 The stepladder to maximum theoretical generality ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART II ▪▪▪▪▪ THE METALOGIC OF REFERENCE ▪▪▪▪▪ A New Approach to Deductive, Transcendental Philosophy ▪▪▪▪▪ 5 Reference, identity, and identification ▪▪▪▪▪ 6 Self-referential argument and the metalogic of reference ▪▪▪▪▪ 7 Possibility theory ▪▪▪▪▪ 8 Presupposition logic, reference, and identification ▪▪▪▪▪ 9 Transcendental argumentation and the metalogic of reference ▪▪▪▪▪ 10 Framework relativity ▪▪▪▪▪ 11 The metalogic of meaning ▪▪▪▪▪ 12 The problem of putative meaning and the logic of meaninglessness ▪▪▪▪▪ 13 Projection ▪▪▪▪▪ 14 Horizons ▪▪▪▪▪ 15 De-projection ▪▪▪▪▪ 16 Self-validation ▪▪▪▪▪ 17 Rationality: Rules of admissibility ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART III ▪▪▪▪▪ PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE ▪▪▪▪▪ Major Problems and Questions of Philosophy and the Philosophy of Science ▪▪▪▪▪ 18 Ontology and the metalogic of reference ▪▪▪▪▪ 19 Discovery or invention in general problem-solving, mathematics, and physics ▪▪▪▪▪ 20 The conceptually unreachable: “The far side” ▪▪▪▪▪ 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism ▪▪▪▪▪ 22 The projections of time, space, and space-time ▪▪▪▪▪ 23 The projections of causality, determinism, and free will ▪▪▪▪▪ 24 Projections of the self and of solipsism ▪▪▪▪▪ 25 Non-relational, agentless reference and referential fields ▪▪▪▪▪ 26 Relativity physics as seen through the lens of the metalogic of reference ▪▪▪▪▪ 27 Quantum theory as seen through the lens of the metalogic of reference ▪▪▪▪▪ 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory ▪▪▪▪▪ ▪▪▪▪▪ PART IV ▪▪▪▪▪ HORIZONS ▪▪▪▪▪ 29 Beyond belief ▪▪▪▪▪ 30 _Critique of Impure Reason_: Its results in retrospect ▪▪▪▪▪ ▪▪▪▪▪ SUPPLEMENT ▪▪▪▪▪ The Formal Structure of the Metalogic of Reference ▪▪▪▪▪ APPENDIX I ▪▪▪▪▪ The Concept of Horizon in the Work of Other Philosophers ▪▪▪▪▪ APPENDIX II ▪▪▪▪▪ Epistemological Intelligence ▪▪▪▪▪ References ▪▪▪▪▪ Index ▪▪▪▪▪ About the author. 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It presents the basics of the “Relativistic theory of gravitation”, with the inclusion of original texts, from various papers, published between 1987 and 2009, by theirs authors: S. S Gershtein, A. A. Logunov, Yu. M. Loskutov and M. A. Mestvirishvili, additionally, together with the introductions, summaries and conclusions of the author of this paper. The “Relativistic theory of gravitation” is a gauge theory, compatible with the theories of quantum physics of the electromagnetic, weak and strong forces, which defines gravity (...) as the fourth force existing in nature, as a static field equipped with the transmitter particles of the virtual gravitons of spins 2 and 0, within the spirit of Galilei's principle of relativity, in his generalization of Poincaré's Special Relativity that allowed the authors to universalize that the physical laws of nature are complied with regardless of the frames of reference where they apply, integrated into the Grossmann-Einstein Entwurf theory, in its further development, by those authors, therefore, this theory preserves the conservation laws of energy-impulse and angular impulse of the gravitational field jointly to the other material fields existing in nature, in the Riemann's effective spacetime, through its identity with Minkowski's pseudo Euclidean spacetime. (shrink)

In this historical article, Newton da Costa discusses Francisco Miró Quesada’s philosophical ideas about logic. He discusses the topics of reason, logic, and action in Miró Quesada’s work, and in the final section he offers his critical view. In particular, he disagrees with Miró Quesada’s stance on the historicity of reason, for whom “reason is essentially absolute”, whereas for da Costa it “is being constructed in the course of history”. Da Costa concludes by emphasizing the importance of Miró Quesada’s theory (...) of logic and reason, despite it still being incomplete. -/- Historical article by Newton da Costa, annotated and translated by J. C. Cifuentes and L. F. Bartolo Alegre. (shrink)

This essay explores Kaila's interpretation of the special theory of relativity. Although the relevance of his work to logical empiricism is well-known, not much has been written on what Kaila calls the ‘Einstein-Minkowski invariance theory’. Kaila's interpretation focuses on two salient features. First, he emphasizes the importance of the invariance of the spacetime interval. The general point about spacetime invariance has been known at least since Minkowski, yet Kaila applies his overall tripartite theory of invariances to space, (...) time and spacetime in an original way. Second, Kaila provides a non-conventionalist argument for the isotropic speed of electromagnetic signals. The standard Einstein synchrony is not a mere convention but a part of a larger empirical theory. According to Kaila's holistic principle of testability, which stands in contrast to the theses of translatability and verification, different items in the theory cannot be sharply divided into conventional and empirical. Kaila's invariantism/non-conventionalism about relativity reflects an interesting case in the gradual transition from positivism to realism within the philosophy of science. (shrink)

Abstract. The theory-change epistemological model, tried on maxwellian revolution and special relativity genesis, is unfolded to apprehend general relativity genesis. It is exhibited that the dynamics of general relativity (GR) construction was largely governed by internal tensions of special relativity and Newton’s theory of gravitation. The research traditions’ encounter engendered construction of the hybrid domain at first with an irregular set of theoretical models. However, step by step, on revealing and gradual eliminating the contradictions (...) between the models involved, the hybrid set was put into order with a help of equivalence principle. A hierarchy of theoretical models starting from the crossbreeds and up to usual hybrids was moulded. The claim to put forward is that Einstein’s unification design could be successfully implemented since his programme embraced the ideas of the Nordström research programme, as well as the presuppositions of the programme of Max Abraham. By and large Einstein’s victory over his rivals became possible because the core of his research strategy was formed by the equivalence principle comprehended in the light of Kantian epistemology. It is stated that the theories of Nordström and Abraham contrived before November 25, 1915, were not merely the scaffolds to construct the GR basic model. They are still the necessary part of the whole GR theory necessary for its common use. Key words: Einstein, Nordstrom, Abraham, general relativity. -/- . (shrink)

In light of the Special Theory of Relativity and the Minkowski creation of ‘spacetime’, the universe is taken to be a four-dimensional entity which postulates bodies as existing within a temporally extended reality. The Special Theory of Relativity’s implications liken the nature of the universe to a ‘block’ within which all events coexist equally in spacetime. Such a view strikes against the very essence of presentism, which holds that all that exists is the instantaneous state of objects (...) in the present moment. With respect to the present moment, events have a clear division into the past or future, however such regions do not exist in reality and the universe is a three-dimensional entity. The consequences of a four-dimensional universe are disturbing to say the least for our everyday human experience, with once objective facts about reality becoming dependent upon an observer’s relative motion and the debate over the extent of true free will in a Block Universe. This paper will look at arguments which seek to rescue the presentist view in light of Special Relativity so such four-dimensionalist implications do not have to be accepted. Two approaches will be considered. The first accepts that presentism is incompatible with Special Relativity, and seeks to show that the theory is ultimately false. The second holds that it is the Block Universe interpretation of Special Relativity that is wrong, and a version of presentism can be reconciled with Special Relativity. The paper will expound and critically examine both of these approaches to review whether the case for the three-dimensionalist and a fundamental passage of time can be made. (shrink)

The present study defines the function of the foundation of science in early modern Dutch philosophy, from the first introduction of Cartesian philosophy in Utrecht University by Henricus Regius to the acceptance of Newtonian physics by Willem Jacob ‘s Gravesande. My main claim is that a foundation of science was required because the conceptual premises of new ways in thinking had to be justified not only as alternatives to the established philosophical paradigms or as an answer to the “sceptical crisis” (...) signalled by Richard Popkin, but also in order to be introduced in the academia. This being my general thesis, different kinds of foundation of scientific knowledge are analysed in the light of the specific problems philosophers had to face. To this end, foundational theories are analysed in the light of 1) the overall aim of their philosophy, 2) the relations of disciplines they thought out, 3) what they regarded as scientific knowledge. Through this analysis, I assess that the foundation of science was carried out by metaphysical, logical and theological arguments, which fitted the needs of answering the didactical and introductory requirements of new paradigms, assessed the reliability of new methodology in leading us to grasp the truth, and provided philosophy with its conceptual apparatus. Finally, I demonstrate that a philosophy of science as a reflection on the principles, methods, concepts and application of modern science emerged in the Dutch Republic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as (...) did Hans Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

En las actividades ordinarias de nuestra vida cotidiana encontramos nuestros actos de percepción confrontados por las cosas materiales. A ellos ─actos de percepción─ les atribuimos una existencia "real" asumiéndolos de tal manera que los sumergimos y transfundimos, de forma múltiple e indefinida, dentro del entorno de realidades análogas que se unen para formar un único mundo al que yo, con mi propio cuerpo, pertenezco. Ahora bien sí frente a la cotidianidad descrita anteriormente asumimos una actitud escéptica acerca de lo que (...) es “real” en el mundo,nos descubriremos haciendo una reflexión filosófica. Bajo esta deliberación encontramos que, por ejemplo, la cualidad "verde", tiene existencia por medio de la sensación "verde"asociada a un objeto dado por la percepción, lo que nos lleva a pensar que no tiene sentido vincularla sensación como cosa en sí misma a cosas materiales existentes en sí mismos , esto nos lleva a pensar que las cualidades de los sentidostienen carácter subjetivo.A pesar de esta reflexión es conveniente acotar que esta subjetividad no interesaa las ciencias exactas ya que éstas procuran lo objetivo. -/- Desde este punto de vista,encontramos dentro de los estudios de Galileo Galilei el principio que subyace al método matemáticoconstructivo de nuestra física moderna ; de esta manera, y bajo este principio,los colores ─ por ejemplo “verde”─ son solo vibraciones en un medio repudiando de esta forma el carácter subjetivo a la vez que se mantiene la objetividad. Sin embargo, dentro del campo de la filosofía el idealismo transcendental de Kant marca un cambio de paradigma en relación a lo anterior. Kant sostiene que no solamente las cualidades de los sentidos tienen carácter subjetivo, sino que espacio y tiempo, conceptos fundacionales dentro de la física, no tienen significación absoluta; en otras palabras, espacio y tiempo son formas de nuestra percepción . Para Kant aquello que sustenta nuestra percepción y aquello que sustenta el conocimiento matemático aplicado a la experiencia son lo mismo: intuiciones puras a priori del espacio y el tiempo. De esta manera, y bajo esta perspectiva, sólo la teoría de la relatividad deja muyen claro que las dos esencias: espacio y tiempo, como formas de la intuición en términos kantianos, no tienen lugar en el mundo construido por la física matemática concebida por Galileo . -/- Según esto, los colores no son siquiera vibraciones en un medio sino simplemente una serie de valores de funciones matemáticas en las que se producen cuatro parámetros independientes que corresponden a las tres dimensiones del espacio y la del tiempo, expresado como principio general esto significa que el mundo real y cada uno de sus constituyentes con sus características sólo pueden ser, en términos husserlianos, objetos intencionales de actos de conciencia . En otras palabras: los datos inmediatos que recibo son las experiencias de la conciencia. Esto nos permite afirmar que la sensación de un objeto está presente de una forma físicamente real para mí con quien esa sensación se relaciona. Esto es lo que Brentano llama objeto intencional ;es así como al percibir un objeto, por ejemplo: veo este “libro” mi atención está totalmente dirigida hacia él. Yo "tengo" la percepción, pero sólo cuando hago de esta percepción ─ acto libre de reflexión ─algo que "conozco" con respecto a ella ─y no sólo el “libro”─ llego precisamente a un segundo acto: objetos intencionales de actos de conciencia, que son a los que referíamos antes . -/- El objeto intencional es inmanente y lo que es inmanente es absoluto ; es exactamente lo que es en la forma en que lo tengo, y puedo reducir esto, su esencia, por los actos de reflexión . En otras palabras, es un componente real de mis experiencias; contrario a lo que sucede con el acto primario de percepción, donde el objeto es trascendental , esto es, se da en una experiencia de conciencia pero no es un componente real de la misma. Por otra parte, los objetos trascendentales tienen sólo una existencia fenoménica; son apariencias que se presentan de múltiples maneras. Ninguno de estos modos de aparición puede pretender presentar aquello que percibimos – por ejemplo el libro- tal como es en sí, además en toda percepción está involucrada la tesis de la realidad del objeto que aparece en ella; este último es, de hecho, un elemento fijo y duradero de la tesis general de la realidad del mundo . En resumen, lo que interesa ver claramente es la importancia enel dato de la conciencia como punto de partida en el que debemos situarnos si queremos comprender el significado absoluto . (shrink)

There is a philosophical tradition of arguing against presentism, the thesis that only presently existing things exist, on the basis of its incompatibility with fundamental physics. I grant that presentism is incompatible with special and general relativity, but argue that presentism is not incompatible with quantum gravity, because there are some theories of quantum gravity that utilize a fixed foliation of spacetime. I reply to various objections to this defense of presentism, and point out a flaw (...) in Gödel's modal argument for the ideality of time. This paper provides an interesting case study of the interplay between physics and philosophy. (shrink)

This paper explores the possibility of constructing a Cartesian space-time that can resolve the dilemma posed by a famous argument from Newton's early essay, De gravitatione. In particular, Huygens' concept of a center-of-mass reference frame is utilized in an attempt to reconcile Descartes' relationalist theory of space and motion with both the Cartesian analysis of bodily impact and conservation law for quantity of motion. After presenting a modern formulation of a Cartesian space-time employing Huygens' frames, a series of (...) Newtonian counter-replies are developed in order to estimate the viability of this relationalist project. (shrink)

The fields of application of general relativity (GR) and quantum field theory (QFT) are different, so most situations require the use of only one of the two theories. The overlaps occur in regions of extremely small size and high mass, such as the black hole or the early universe (immediately after the Big Bang). This conflict is supposed to be solved only by unifying gravity with the other three interactions, to integrate GR and QFT into one theory. (...) At the cosmological level, the standard cosmological model contains Einstein's theory of gravity as part of the "hard core". Dark matter, dark energy, and inflation were added to the theory in response to observations. None of these ancillary hypotheses have yet been confirmed. DOI: 10.13140/RG.2.2.34318.72008. (shrink)

According to Einstein, a universal time does not exist. But what if time is different than what we think of it? Cosmic Microvawe Background Radiation was accepted as a reference for a universal clock and a new time concept has been constructed. According to this new concept, time was tackled as two-dimensional having both a wavelength and a frequency. What our clocks measure is actually a derivation of the frequency of time. A relativistic time dilation actually corresponds to an (...) increase in the wavelength of time. At the point where time wavelength and time frequency is equal, where light is positioned, quantum-world and macro- world are seperated. Gravity was redefined with respect to time and the new two dimensional time fabric of the universe was speculated to be the source of dark energy causing the universe to expand. According to this new point of view quantum realm and macro-world can be better understood. This new time concept provide a basis for our understanding of quantum gravity and provide the long-sought answers to well known problems of it. A prediction of the presented theory is that the universe will expand at various rates at different regions due to the fact that particular surroundings will create different gravities and cause a different gravity- time wavelength effect yielding various time delays for calculating this rate of expansion. (shrink)

This letter was rejected by International Knowledge Press because "we are unable to conclude that these findings would warrant publication in this journal." The letter is suggesting that dark energy, dark matter and universal expansion are intimately related. However, they aren't viewed as revolutions in cosmology which are essential to a complete understanding of the modern universe. They are instead viewed as properties which need to be added to the cosmos when Einstein's theory of gravity (General Relativity) (...) is apparently still not thoroughly comprehended a little over a century since it was published. (shrink)

The paper presents the notion of “Spirit of Nature” in Henry More and describes its position within More’s philosophical system. Through a thorough analysis, it tries to show in what respects it can be considered a scientific object and in what respects it cannot. In the second part of this paper, More’s “Spirit of Nature” is compared to Newton’s various attempts at presenting a metaphysical cause of the force of gravity, using the similarities between the two to see (...) this notorious problem of Newton scholarship in a new light. One thus sees that if Newton drew from Stoic and Neo-Platonic theories of aether or soul of the world, we need to fully acknowledge the fact that these substances were traditionally of a non-dualistic, half-corporeal, half-spiritual nature. Both More’s “Spirit of Nature” and Newton’s aether can thus be understood as different attempts at incorporating such a pneumatic theory into the framework of modern physics, as it was then being formed. (shrink)

I discuss the ontological assumptions and implications of General Relativity. I maintain that General Relativity is a theory about gravitational fields, not about space-time. The latter is a more basic ontological category, that emerges from physical relations among all existents. I also argue that there are no physical singularities in space-time. Singular space-time models do not belong to the ontology of the world: they are not things but concepts, i.e. defective solutions of Einstein’s field equations. I (...) briefly discuss the actual implication of the so-called singularity theorems in General Relativity and some problems related to ontological assumptions of Quantum Gravity. (shrink)

One of the most disputed controversy over the priority of scientific discoveries is that of the law of universal gravitation, between Isaac Newton and Robert Hooke. Hooke accused Newton of plagiarism, of taking over his ideas expressed in previous works. In this paper I try to show, on the basis of previous analysis, that both scientists were wrong: Robert Hooke because his theory was basically only ideas that would never have materialized without Isaac Newton's mathematical support; and the (...) latter was wrong by not recognizing Hooke's ideas in drawing up the theory of gravity. Moreover, after Hooke's death and taking over the Royal Society presidency, Newton removed from the institution any trace of the former president Robert Hooke. For this, I detail the accusations and arguments of each of the parts, and how this dispute was perceived by the contemporaries of the two scientists. I finish the paper with the conclusions drawn from the contents. -/- Keywords: Isaac Newton, Robert Hooke, law of gravity, priority, plagiarism -/- CONTENTS -/- Abstract Introduction Robert Hooke's contribution to the law of universal gravitation Isaac Newton's contribution to the law of universal gravitation Robert Hooke's claim of his priority on the law of universal gravitation Newton's defense The controversy in the opinion of other contemporary scientists What the supporters of Isaac Newton say What the supporters of Robert Hooke say Conclusions Bibliography -/- DOI: 10.13140/RG.2.2.19370.26567 . (shrink)

Physical dimensions like “mass”, “length”, “charge”, represented by the symbols [M], [L], [Q], are not numbers, but used as numbers to perform dimensional analysis in particular, and to write the equations of physics in general, by the physicist. The law of excluded middle falls short of explaining the contradictory meanings of the same symbols. The statements like “m tends to 0”, “r tends to 0”, “q tends to 0”, used by the physicist, are inconsistent on dimensional (...) grounds because “m”, “r”, “q” represent quantities with physical dimensions of [M], [L], [Q] respectively and “0” represents just a number—devoid of physical dimension. Consequently, due to the involvement of the statement “q tends to 0'', where q is the test charge” in the definition of electric field leads to either circular reasoning or a contradiction regarding the experimental verification of the smallest charge in the Millikan–Fletcher oil drop experiment. Considering such issues as problematic, by choice, I make an inquiry regarding the basic language in terms of which physics is written, with an aim of exploring how truthfully the verbal statements can be converted to the corresponding physico-mathematical expressions, where “physico-mathematical” signifies the involvement of physical dimensions. Such investigation necessitates an explanation by demonstration of “self inquiry”, “middle way”, “dependent origination”, “emptiness/relational existence”, which are certain terms that signify the basic tenets of Buddhism. In light of such demonstration I explain my view of “definition”; the relations among quantity, physical dimension and number; meaninglessness of “zero quantity” and the associated logico-linguistic fallacy; difference between unit and unity. Considering the importance of the notion of electric field in physics, I present a critical analysis of the definitions of electric field due to Maxwell and Jackson, along with the physico-mathematical conversions of the verbal statements. The analysis of Jackson’s definition points towards an expression of the electric field as an infinite series due to the associated “limiting process” of the test charge. However, it brings out the necessity of a postulate regarding the existence of charges, which nevertheless follows from the definition of quantity. Consequently, I explain the notion of undecidable charges that act as the middle way to resolve the contradiction regarding the Millikan–Fletcher oil drop experiment. In passing, I provide a logico-linguistic analysis, in physico-mathematical terms, of two verbal statements of Maxwell in relation to his definition of electric field, which suggests Maxwell’s conception of dependent origination of distance and charge ) and that of emptiness in the context of relative vacuum. This work is an appeal for the dissociation of the categorical disciplines of logic and physics and on the large, a fruitful merger of Eastern philosophy and Western science. Nevertheless, it remains open to how the reader relates to this work, which is the essence of emptiness. (shrink)

The evolution of gravitational tests from an epistemological perspective framed in the concept of rational reconstruction of Imre Lakatos, based on his methodology of research programmes. Unlike other works on the same subject, the evaluated period is very extensive, starting with Newton's natural philosophy and up to the quantum gravity theories of today. In order to explain in a more rational way the complex evolution of the gravity concept of the last century, I propose a natural extension (...) of the methodology of the research programmes of Lakatos that I then use during the paper. I believe that this approach offers a new perspective on how evolved over time the concept of gravity and the methods of testing each theory of gravity, through observations and experiments. I argue, based on the methodology of the research programmes and the studies of scientists and philosophers, that the current theories of quantum gravity are degenerative, due to the lack of experimental evidence over a long period of time and of self-immunization against the possibility of falsification. Moreover, a methodological current is being developed that assigns a secondary, unimportant role to verification through observations and/or experiments. For this reason, it will not be possible to have a complete theory of quantum gravity in its current form, which to include to the limit the general relativity, since physical theories have always been adjusted, during their evolution, based on observational or experimental tests, and verified by the predictions made. Also, contrary to a widespread opinion and current active programs regarding the unification of all the fundamental forces of physics in a single final theory, based on string theory, I argue that this unification is generally unlikely, and it is not possible anyway for a unification to be developed based on current theories of quantum gravity, including string theory. In addition, I support the views of some scientists and philosophers that currently too much resources are being consumed on the idea of developing quantum gravity theories, and in particular string theory, to include general relativity and to unify gravity with other forces, as long as science does not impose such research programs. -/- DOI: 10.13140/RG.2.2.35350.70724 . (shrink)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the Bible, (...) and analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)

General Relativity generated various early philosophical interpretations. His adherents have highlighted the "relativization of inertia" and the concept of simultaneity, Kantians and Neo-Kantians have underlined the approach of certain synthetic "intellectual forms" (especially the principle of general covariance, and logical empirics have emphasized the philosophical methodological significance of the theory. Reichenbach approached the GR through the "relativity of geometry" thesis, trying to build a "constructive axiomatization" of relativity based on "elementary matters of fact" (Elementartatbestande) (...) for the observable behavior of light rays, rods and clocks. The mathematician Hermann Weyl attempted a reconstruction of Einstein's theory based on the epistemology of a "pure infinitesimal geometry", an extended geometry with additional terms that formally identified with the potential of the electromagnetic field. DOI: 10.13140/RG.2.2.11641.93281. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...) and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

Since the onset of logical positivism, the general wisdom of the philosophy of science has it that the kantian philosophy of (space and) time has been superseded by the theory of relativity, in the same sense in which the latter has replaced Newton’s theory of absolute space and time. On the wake of Cassirer and Gödel, in this paper I raise doubts on this commonplace by suggesting some conditions that are necessary to defend the ideality of time (...) in the sense of Kant. In the last part of the paper I bring to bear some contemporary physical theories on such conditions. (shrink)