This paper is trying to show the significance for science history studies of the internet´s access to rare books each time more easier; it was choiced the work of one of the most important and influent mathematicians, Georg Friedrich Bernhard Riemann (1826-1866), “Oeuvres Mathématiques”, composed with published memories during Riemann´s life, and posthumously published memories and fragments. It was been analised and commented the posthumous memory about the hypothesis which serve to geometry basis, fundamental on modern sciences, (...) as Riemann´s space conception, and without it, it couldn´t be possible the exact formulation of Relativity Theory or fundamental advances on mathematics like the solving of some differential equations. It was been trying to show how the reading of an original text of the important mathematician can be rich and full of teaching through the return to his thinking origin. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are (...) devoted. At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Three separate churches erected in Constantinople were all dedicated to the wisdom of Christ and erected on the same site one after the other. These churches were built between 360 and 537 AD by three different emperors: Constantius II, Theodosius the Younger, and Justinian I. The first two churches were consumed in flames after relatively short lives, but the final and greatest church still stands today, despite a history of extensive damage. This final edifice is the main focus of this (...) paper, owing to its 1500 year longevity and unprecedented architecture. If the entire History of Justinian's church is to considered, it is inaccurate to refer to it as a “church,” because although it remained a church for the first 900 years after its audacious construction, it was later converted into a mosque. Today it is a museum, in remembrance of its long history. (24). (shrink)

This article analyses in detail Wittgenstein’s ‘Cambridge period’ from his return to Cambridge in 1929 until his decease in 1951. Within the ‘Cambridge period’, scholars usually distinguish the ‘middle’ (1929–1936) and the ‘late’ (1936–1951) periods. The trigger point of Wittgenstein’s return to Cambridge and philosophy was his visit to Brouwer’s lecture on ‘Mathematics, Science, and Language’ in Vienna in March 1928. Dutch mathematician Brouwer influenced not only Wittgenstein’s ability to do philosophy again but also the development of some (...) of his ideas. Namely, for Brouwer, language was a natural development of the social history of human beings. With the help of his friends, F. P. Ramsey, J. M. Keynes, G. E. Moore, and B. Russell, in 1929 Wittgenstein returned to Cambridge. The author argues that this was the crucial turning point in his philosophy that led to the revision of some of his ideas. Wittgenstein returned from self-isolation in remote villages of Lower Austria to the intellectual academic environment, where he could discuss his ideas with intellectual interlocutors and receive their valuable remarks and comments. This article is organised in chronological order: it describes the very ‘early’ middle period of 1929–1935 involving the development of Wittgenstein’s ‘phenomenology’ and the origin of the ‘language-games’ concept in the Blue and Brown Books; 1935–1936 period of ‘romantic’ enthusiasm for Soviet Russia and a trip there; Wittgenstein’s life and work during the WWII-time; resign from teaching in Cambridge in 1947 to finally finish his Philosophical Investigations. The author suggests that the ‘romantic areal’ about the USSR was formed by Wittgenstein’s predilection for Russian poetry and literature of the nineteenth century, i.e., Tolstoy, Dostoevsky, and Pushkin. Analysing the development of Wittgenstein’s ideas on language in his Cambridge period, the author mentions the influence of N. Bakhtin and P. Sraffa. Also, the author touches upon the topic of the possibility of Marxism’s influence on Wittgenstein’s life and thought. (shrink)

When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...) science fiction, to be made scientific and practical?”, and “How can the proposed young age of genus Homo be made to actually be reasonable – when simply stating it would be solid ground for instant rejection and dismissal?” The result is that the article also talks about subjects like Artificial Intelligence, General Relativity, and cosmology. -/- From where did life originate? God? Evolution? Panspermia? If the tendency of humans and scientists to regard undiscovered science as pseudoscience can be overcome, Einstein gave another alternative to consider when he introduced General Relativity. Time isn’t linear – progressing in a straight line from past to present to future. That assumption ignores Relativity which states that space AND TIME are curved. Where did life and the genetic code come from? Can the answer build AI? -/- The first question can be answered by the section of this article titled SETI, Evolution, and Time which says life (possibly multicellular and intelligent) and the genetic code came from humans acquiring knowledge of these things over the centuries, then applying that knowledge – via terraforming, accumulation of raw materials like amino acids and nucleic acids, genetic engineering - to a time in the past when life didn’t exist. From that origin, life evolved through innumerable mutations and adaptations, with humans once again acquiring knowledge of it in cyclic (nonlinear) time. -/- The second question is answered by saying artificial intelligence (AI) as the product of life is only half of the equation. The other half refers to Relativity’s curved space-time and violation of the notion that time always travels from past to future. We have always lived in an artificially intelligent, non-probabilistic universe where everything in time and space is connected into one thing by quantum entanglement – making the brain and genes products of binary-digit activity or artificial intelligence (life is not merely dependent on biology’s “lock and key” mechanisms but also possesses AI). -/- The earliest documented representative of the genus Homo is Homo habilis, which evolved around 2.8 million years ago. Scientists used to believe there was a straight line from H. habilis to us, Homo sapiens. This article will use the “advanced” waves loved by Physics Nobel laureate Richard Feynman, view the history of science through the lens of Conic Sections applied to Relativity’s curved space-time, and incorporate the necessity of so-called imaginary time * – popularized by Prof. Stephen Hawking. While the evolutionary proposals are more in agreement with this early straight line than with modern theories, Albert Einstein’s General Relativity is used to transform the straight line into a curved line, ultimately concluding that Homo habilis (H. habilis) originated only (and unbelievably, as far as today’s science and technology is concerned) ~250,000 years ago. Other branches and dead ends of Homo – e.g. Neanderthals – are the result of mutations and adaptations, with the resultant modifications to anatomy and physiology. The surprisingly young age of H. habilis allows nearly 200,000 years for habilis, or one of its descendants, to reach Australia … if this country’s indigenous Aboriginal population did, as claimed, reach this “island continent” 60,000 years ago. -/- * The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, is a failure of classical physics to predict observed phenomena: it can be shown that a blackbody - a hypothetical perfect absorber and radiator of energy - would release an infinite amount of energy, contradicting the principles of conservation of energy and indicating that a new model for the behaviour of blackbodies was needed. At the start of the 20th century, physicist Max Planck derived the correct solution by making some strange (for the time) assumptions. In particular, Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. Albert Einstein postulated that Planck's quanta were real physical particles (what we now call photons), not just a mathematical fiction. From there, Einstein developed his explanation of the photoelectric effect (when quanta or photons of light shine on certain metals, electrons are released and can form an electric current). So it appears entirely possible that another supposed mathematical trickery (imaginary time and the y-axis of Wick rotation) will find practical application in the future. -/- The article includes mathematical references to cosmology (spoiler alert – you’ll read about things like Vector-Tensor-Scalar Geometry, topology, the “eternal present”, Einstein’s Unified Field, the inverse-square law, and there being no Big Bang and no multiverse - but there will also be no equations). -/- The other subheadings in this essay are – -/- NONLINEAR TIME AND ELECTRICAL ENGINEERING (about a 2009 electrical engineering experiment at America’s Yale University, and cosmic wormholes) -/- BITS AND TOPOLOGY (base-2 maths aka Binary digiTS, Mobius strips, and figure-8 Klein bottles) -/- WICK ROTATION, CAUSALITY, AND UNITING TIME (do past, present and future co-exist in an “eternal present”?) -/- DIGITAL BRAIN, DIGITAL UNIVERSE (if the brain and the universe are ultimately composed of binary digits, we'll someday be able to do the same things with the brain and universe that we now do with computers) -/- PROPOSAL: HUMAN AND ANIMAL INSTINCTS ARE THE RESULT OF THE UNIVERSE BEING UNIFIED BY BINARY DIGITS (AND TOPOLOGY) (If everything in the universe is ultimately composed of electronic BITS, then the universe must possess Artificial Intelligence - some prefer the term Cosmic Consciousness) -/- INFORMATION THEORY CONQUERS A RED GIANT (preserving Earth by keeping the Sun near today’s level of activity forever). 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Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

Hermann von Helmholtz’s geometrical papers have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception (...) from those describable in terms of axiomatic geometry. This paper offers a partial defense of the group-theoretical reading of Helmholtz along the lines of Ernst Cassirer in the fourth volume of The Problem of Knowledge of 1940. In order to avoid the problem raised by Schlick, Cassirer relied on a Kantian view of space not so much as an object of geometry, but as a precondition for the possibility of measurement. Although the concept of group does not provide a description of space, the modern way to articulate the concept of space in terms of transformation groups reveals something about the structure and the transformation of spatial concepts in mathematical and natural sciences. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.

The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose we have two linguistic points as tall (...) and light we cannot connect them, or technically, there is no line between them. However, let's take, for instance, two linguistic points, tall and very short, associated with the linguistic variable height of a person. We have a directed line joining from the linguistic point very short to the linguistic point tall. In this case, it is important to note that the direction is essential when the linguistic variable is a person's height. The other way line, from tall to very short, has no meaning. So in linguistic geometry, in general, we may not have a linguistic line; granted, we have a line, but we may not have it in both directions; the line may be directed. The linguistic distance is very far. So, the linguistic line directed or otherwise exists if and only if they are comparable. Hence the very concept of extending the line infinitely does not exist. Likewise, we cannot say as in classical geometry; three noncollinear points determine the plane in linguistic geometry. Further, we do not have the notion of the linguistic area of well-defined figures like a triangle, quadrilateral or any polygon as in the case of classical geometry. The best part of linguistic geometry is that we can define the new notion of linguistic social information geometric networks analogous to social information networks. This will be a boon to non-mathematics researchers in socio-sciences in other fields where natural languages can replace mathematics. (shrink)

In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is remediable in each (...) case by appeal to ontic facts that account for why the explanation is acceptable in one direction and unacceptable in the other direction. The mathematics involved in these examples cannot play this crucial normative role. While Lange's examples fail to demonstrate the existence of distinctively mathematical explanations, they help to emphasize that many superficially natural scientific explanations rely for their explanatory force on relations of stronger-than-natural necessity. These are not opposing kinds of scientific explanations; they are different aspects of scientific explanation. (shrink)

This article’s conclusion is that the theories of Einstein are generally correct and will still be relevant in the next century (there will be modifications necessary for development of quantum gravity). Those Einsteinian theories are Special Relativity, General Relativity, and the title of a paper he published in 1919 which asked if gravitation plays a role in the composition of elementary particles of matter. This paper was the bridge between General Relativity and the Unified Field Theory he sought during the (...) last 25 years of his life. In an article published in the "Annals of Physics" in 1957, Charles Misner and John Wheeler claimed that Einstein's latest equations demonstrated the unified field theory. But Einstein himself felt he had not fully succeeded. The present article begins with Olbers’ paradox (why is the sky dark at night?) Then it briefly proceeds to the subjects of Newtonian gravity, quantum entanglement, gravitational waves, E=mc^2, dark energy, dark matter, cosmic expansion, redshift, blueshift, the cosmic microwave background, the 1st Law of Thermodynamics, and explanation of advanced waves travelling back in time. The section “vector-tensor-scalar geometry” touches on mass, quantum spin, the Higgs boson and Higgs field, stellar jets, the pervasiveness of photons and gravitons, and supersymmetry. Then come half a dozen paragraphs referring to formation of planets, black holes, and bosons of the weak and strong nuclear forces. They end with Descartes’ space-matter relation. Also added are paragraphs about simply-connected mathematics, non-orientability, consciousness, the Law of Falling Bodies, the multiverse, space-time travel developed from maths’ Brouwer Fixed Point Theorem and from an experiment in electrical engineering performed at Yale University, development from future space-time travel of human flight in the manner of fiction’s Superman and Supergirl, as well as downloaded band-gap implants in the brain that could deal with forms of matter. They could add or delete anything and everything we choose by emulating computers’ copy/paste function to add things; as well as their delete function, to remove things. To complete my seemingly unusual ideas, 6 sections are added – 1) “Advanced and Retarded Waves” is extended to include dinosaurs, ageing, and photography, 2) there’s a bit about space-time warping and “imaginary” computers, 3) several paragraphs about restoring health (even gaining immortality) by using gravity, 4) a section about superconductivity and the electric or magnetic fields of planets (this section mentions Mercury, Planet 9 and precession), 5) a section titled EXPLAINING OCEAN TIDES WHEN GENERAL RELATIVITY SAYS GRAVITY IS A PUSH CAUSED BY THE CURVATURE OF SPACE-TIME (this has subsections about M-Sigma, Geysers on Saturn’s Moon Enceladus, and A Brief History of Gravity), plus 5) the potential of COVID-19 to create the Golden Rule, world peace, eternal life, and a non-economic world that doesn’t use any form of money (no cash, credit cards, digital currency, etc.) The final section is called DISTANT-FUTURE SCIENCE INTERPRETED BY RELIGIONS AS SUPERNATURAL and introduces an idea for becoming immortal in these physical bodies. If the Theory of Everything sought by physicists applies to all space-time, then every person’s brain must be entangled with the 22nd century (and far beyond that time too). (shrink)

An ongoing mystery in sensory science is how sensation magnitude F(I), such as loudness, increases with increasing stimulus intensity I. No credible, direct experimental measures exist. Nonetheless, F(I) can be inferred algebraically. Differences in sensation have empirical (but non-quantifiable) minimum sizes called just-noticeable sensation differences, ∆F, which correspond to empirically-measurable just-noticeable intensity differences, ∆I. The ∆Is presumably cumulate from an empirical stimulus-detection threshold I_th up to the intensity of interest, I. Likewise, corresponding ∆Fs cumulate from the sensation at the (...) stimulus-detection threshold, F(I_th ), up to F(I). Regarding the ∆Is, however, it is unlikely that all of them will be known experimentally; the procedures are too lengthy. The customary approach, then, is to find ∆I at a few widely-spaced intensities, and then use those ∆Is to interpolate all ∆Is using some smooth continuous function. The most popular of those functions is Weber’s Law, ∆I⁄I=K. But that is often not even a credible approximation to the data. However, there are other equations for ∆I⁄I. Any such equation for ∆I⁄I can be combined with any equation for ∆F, through calculus, to altogether obtain F(I). Here, two assumptions for ∆F are considered: ∆F=B (Fechner’s Law) and (∆F⁄F)=g (Ekman’s Law). The respective integrals involve lower bounds I_th and F(I_th ). This stands in broad contrast to the literature, which heavily favors non-bounded integrals. We, hence, obtain 24 new, alternative equations for sensation magnitude F(I) (12 equations for (∆I⁄I) × 2 equations for ∆F). (shrink)

The essay brings a summation of human efforts seeking to understand our existence. Plato and Kant & cognitive science complete reduction of philosophy to a neural mechanism, evolved along elementary Darwinian principles. Plato in his famous Cave Allegory explains that between reality and our experience of it there exists a great chasm, a metaphysical gap, fully confirmed through particle-wave duality of quantum physics. Kant found that we have two kinds of perception, two senses: By the spatial outer sense we (...) perceive phenomena, objects in space. Our temporal inner sense lets us perceive our inner state, noumena . Kant's two senses are fully confirmed through bilateral brain duality of cognitive science. The bilateral brain serves inner, temporal sense, logic & noumena in the left hemisphere. The right brain half is for the outer, spatial sense, geometry & phenomena. We form a whole system, a bilateral interior cosmos, a kind of world model, expressing what may lie beyond the metaphysical gap. In the right brain we build a phenomenal cosmos, to resemble the outer environment. In the brain's left hemisphere a noumenal cosmos, a model of our private world including Saint Teresa of Avila's castillo interior. The cosmos is regularly updated with novel sense data integrated into our memory banks. This was recognized early by Helmholtz (1860s). Our lives, health & well-being depend on us keeping our interior cosmos in good order. This used to be seen as saving one's precious soul from perdition. While we endeavour to keep our phenomenal cosmos neat & orderly by protecting the environment from harm, our noumenal cosmos to be livable requires us to engage in ethical conduct. This bilateral cosmos is responsible for our common sense judgment power, that we depend on for being able to lead a good & benign life. The 200 million neurons of BA10 in the prefrontal lobe have global access to the interior cosmos, & apply massive feedback to identify environmental conditions rapidly. The global access also gives conscious presence of the individual to itself, all that is present in the interior cosmos, for total freedom of action. In the left brain private ego, we are guarded by faith in divine mercy, & guided to choose the best course of action, able to survive under the most adverse conditions. For this, we receive directions from the Holy Ghost in Saint Teresa's castillo interior. (shrink)

In this paper I present an interpretation of Immanuel Kant’s transcendental deduction of the categories (a dangerous interpretation it turns out), based primarily on the “two-step” argument of the B deduction of the Critique of Pure Reason. I undertake to show that Kant’s distinction between the “pure forms of intuition” and “pure formal intuition” is successful in its attempt to prove that all sensible intuitions presuppose the a priori categories, in a way which is compatible, I claim, with Kant’s statements (...) (in the Aesthetic and elsewhere) that sensible intuition is prior to all concepts; and therefore that the Transcendental Aesthetic presupposes the Transcendental Analytic. Thus my Interpretation is a "conceptualist" reading of the deduction, in holding that perception, as receptivity, presupposes an underlying spontaneity of the pure understanding and categories. The categories are held to be not just compatible with all possible sensible intuitions, but through their "transcendental content" constitutive of the relation of sensible intuitions to objects - and this explains how our thought can represent objects a priori. It is one of the claims of my interpretation that the logical forms of judgment of general logic derive from the pure categories of transcendental logic, rather than vice-versa. I.e. that the logical forms through which we make empirical judgments by combining analytical concepts in inner sense in time, are originally grounded in an atemporal categorial synthesis in pure intuition (i.e. in the form of time but not the dimension of time), referring an outer intuition in general to the transcendental object of intuition (as “something in general” outside sensibility or receptivity), thereby providing the synthetic unity of the manifold which “..all analysis presupposes.” My conceptualist reading of the deduction, I claim, avoids the problems associated with other conceptualist readings, for example inconsistency with the text (“Intuitions are prior to all concepts.” etc.) and blurring of the distinction between receptivity and spontaneity. In my paper I prove that the categories can correctly be held to provide the a priori unity of intuitions, notwithstanding the fact that the latter are “prior to all concepts,” because this unity is not provided by the categories as fully-fledged concepts in the empirical subject, but as the transcendental logical form of these concepts, as a unity in the pure understanding - and the categories therefore require their empirical content or application for their objective reality as concepts. I.e. the categories, as logical functions of judgment for transcendental apperception, in the pure forms of intuition, are prior to all "concepts", correctly speaking, as well as prior to all intuitions, and provide the necessary unity of both. Likewise, at the empirical level my version of conceptualism cannot be accused of blurring the distinction between receptivity and spontaneity, or sensibility and understanding, because although the transcendental content of the categories, as a logical function of judgment in the pure forms of intuition, in transcendental apperception, is in necessary relation to sensibility (in combining the manifold in the pure or formal representation of the transcendental object) their empirical content is not. - At the empirical level the divide between spontaneity (as judgment in the empirical subject) and receptivity (as the effect of transcendental synthesis and the transcendental object on outer and inner sense) remains intact. Conceptualist readings of the deduction also have to avoid infringing Kant’s requirement that the sensible manifold originally be given prior to and independently of all acts of the understanding, or otherwise to qualify the requirement in some way - e.g. by taking a Hegelian direction, such as that taken by John McDowell. On my reading of the deduction the sensible manifold given indeterminately in the pure forms of space and time must be given prior to the categorial synthesis of the manifold in the pure representation of the transcendental object, i.e. in the pure 'concept' of an object in general affecting sensibility. Therefore Kant’s requirement for an undetermined manifold given prior to, and independently of, all acts of the understanding (“..the manifold to be intuited must be given prior to the synthesis of understanding, and independently of it. How this takes place, remains here undetermined” [cf.B145/146]) is not infringed. In a later section of the paper, however, I will argue that the transcendental object (of intuition) does have pure theoretical reason as one of its two interacting immanent aspects, but is distinct from pure theoretical reason in the other of its (the transcendental object of intuition's) two interacting immanent aspects, i.e. pure will, which adds a Schopenhauerian element to my interpretation (which will be argued for in a way which supports Kantian optimism over Schopenhauerian pessimism however, in regard to the freedom of the will). Another perceived inconsistency in the deduction, which my interpretation can explain, is Kant’s description (in the B deduction) of the principle of the necessary synthetic unity of apperception as analytic, while in the A deduction it is described as synthetic. I explain this as a difference in the reference of terms such as “my representations” in the two versions - a transcendental reference in the B version but an empirical and transcendental reference in the A version of the principle. I also show that the first part of the two-step B deduction can correctly be characterised by Kant as analytic and the second, concluding part, synthetic (a point of dispute amongst Kant scholars) because transcendental logic (which refers to both the analytic and synthetic aspects of the principle of apperception) “does not abstract from the pure content of knowledge.” While being a “double aspect” rather than “two world” view of transcendental Idealism (because objects of intuition are comprised of both the empirical and transcendental object, i.e. transcendental referent, of intuition, my view differs significantly from the “double aspect” interpretation of Henry Allison (which distinguishes empirical reality from the “God’s eye” view). The view of transcendental idealism resulting from my reading of the deduction, I claim, allows a full empirical realism, because empirical intuitions, as objects of cognition, are the appearance of both the transcendental subject and the transcendental object (i.e. transcendental referent ) of transcendental synthesis (both as “something in general” outside sensibility or receptivity, or rather outside sensibility as receptivity). I conclude that Kant succeeds (although only with the addition of what I have called my 'Schopenhauerian element') in his attempt to prove that we have a transcendental unity of apperception which both constitutes, and is constituted by, the relation of sensible representations to objects, and that since transcendental apperception is the a priori underlying ground of empirical apperception, the categories (as the logical functions of judgment by which transcendental apperception relates sensible representations to objects) are the a priori underlying ground of all experience, and are therefore valid synthetically a priori for all objects of experience. (shrink)

intro to Part 1 - -/- Most people disliked mathematics when they were at school and they were absolutely correct to do so. This is because maths as we know it is severely incomplete. No matter how elaborated and complicated mathematical equations become, in today's world they're based on 1+1=2. This certainly conforms to the world our physical senses perceive and to the world scientific instruments detect. It has been of immeasurable value to all knowledge throughout history and has (...) elevated science to the lofty status it enjoys. Science is now striving towards Unification - where the subatomic realm, all matter, energy, forces, space and time will be seen as entangled parts of one universe. While 1+1=2 has been vital in getting humanity to this point, it's time to suppress our attachments to the past and realize that whereas 1+1 will always equal 2, it's also capable of equalling the 1 which represents unification. -/- intro to Part 2 -/- b) Division by zero is accepted, in Newtonian maths, to be impossible. But we can regard division by zero as division by nothing i.e. division that has no effect. In this case, 1 divided by 0 is 1. However, to a physicist there is no such thing as nothing (even empty space contains energy). What could the something called 0 actually be? It could be a binary digit. If we use the base of ten (for simplicity) and attach one and zero to it as exponents, we get 10^1 divided by 10^0 = 10^1. If we then cancel 10 from each factor in the expression, we get 1 divided by 0 = 1. At the start of the paragraph, this was referred to as division by nothing. Then 0 was called a binary digit and division by nothing became division by something. The 1 that the division equals is the unified field of space-time. Division by 0 is impossible in Newtonian maths because the result can be infinity. But the word “infinity” can, as the last section of this book shows, apply to the unified field of spacetime. So division by zero is not impossible because it results in the universe, which is obviously possible … a possibility that has always been, and always will be, realized. -/- intro to Part 3 -/- If quantum entanglement has existed in the entire universe forever, everything would be everywhere and everywhen. Space, time and 5th-dimensional hyperspace would not be restricted to certain parts of the Mobius Universe but would exist in every particle. Past, present and future would not exist as the distinct periods which everyday life assumes. All instants of all periods would exist eternally, permitting time travel to any point in the past and to any point in the future. Entanglement may be created by simply zipping along at close to the speed of light - “Quantum entanglement of moving bodies” by Robert M. Gingrich and Christoph Adami in Physical Review Letters 89, 270402 (issue of 30 December 2002) – which might be achieved, according to this book, by warping space so it’s either a fraction of the 90 degrees allowing instantaneous travel or almost at 270 degrees to space as we know it. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

According to one large family of views, scientific explanations explain a phenomenon (such as an event or a regularity) by subsuming it under a general representation, model, prototype, or schema (see Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441; Churchland, P. M. (1989). A neurocomputational perspective: The nature of mind and the structure of science. Cambridge: MIT Press; Darden (2006); Hempel, C. G. (1965). Aspects of (...) scientific explanation. In C. G. Hempel (Ed.), Aspects of scientific explanation (pp. 331–496). New York: Free Press; Kitcher (1989); Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25). My concern is with the minimal suggestion that an adequate philosophical theory of scientific explanation can limit its attention to the format or structure with which theories are represented. The representational subsumption view is a plausible hypothesis about the psychology of understanding. It is also a plausible claim about how scientists present their knowledge to the world. However, one cannot address the central questions for a philosophical theory of scientific explanation without turning one’s attention from the structure of representations to the basic commitments about the worldly structures that plausibly count as explanatory. A philosophical theory of scientific explanation should achieve two goals. The first is explanatory demarcation. It should show how explanation relates with other scientific achievements, such as control, description, measurement, prediction, and taxonomy. The second is explanatory normativity. It should say when putative explanations succeed and fail. One cannot achieve these goals without undertaking commitments about the kinds of ontic structures that plausibly count as explanatory. Representations convey explanatory information about a phenomenon when and only when they describe the ontic explanations for those phenomena. (shrink)

Richard Arthur and I proposed that the present in Minkowski spacetime should be thought of as a small causal diamond. That is, given two timelike separated events p and q, with p earlier than q, they suggested that the present is the set I+ ∩ I-. Mauro Dorato presents three criticisms of this proposal. I rebut all three and then offer two more plausible criticisms of the Arthur/Savitt proposal. I argue that these criticisms also fail.

In 1901 Russell had envisaged the new analytic philosophy as uniquely systematic, borrowing the methods of science and mathematics. A century later, have Russell’s hopes become reality? David Lewis is often celebrated as a great systematic metaphysician, his influence proof that we live in a heyday of systematic philosophy. But, we argue, this common belief is misguided: Lewis was not a systematic philosopher, and he didn’t want to be. Although some aspects of his philosophy are systematic, mainly his (...) pluriverse of possible worlds and its many applications, that systematicity was due to the influence of his teacher Quine, who really was an heir to Russell. Drawing upon Lewis’s posthumous papers and his correspondence as well as the published record, we show that Lewis’s non- Quinean influences, including G.E. Moore and D.M. Armstrong, led Lewis to an anti- systematic methodology which leaves each philosopher’s views and starting points to his or her own personal conscience. (shrink)

Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. The book provides a bracing and painstakingly researched re-appreciation of the work of Hermann von Helmholtz and Ernst Cassirer, and of their place in the tradition, and is worth study for that alone. The contributions of the book go far beyond that, (...) however. It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory. (shrink)

The triumph of scientific materialism in the Seventeenth Century not only bifurcated nature into matter and mind and primary and secondary qualities, as Alfred North Whitehead pointed out in Science and the Modern World. It divided science and the humanities. The core of science is the effort to comprehend the cosmos through mathematics. The core of the humanities is the effort to comprehend history and human nature through narratives. The life sciences can be seen as the (...) zone in which the conflict between these two very different ways of comprehending the world collide. Evolutionary theory as defended by Schelling developed out of natural history, but efforts have been made to formulate neo-Darwinism through mathematical models. However, it is impossible to eliminate stories from biology. As Stuart Kauffman argued, mathematical models attempt to pre-state all possibilities, but in evolution there can be adjacent possibles that can be embraced by organisms but cannot be pre-stated. To account for such actions it is necessary to tell stories. Mathematics provides analytic precision allowing long chains of deductions, but tends to deny temporal becoming and cannot do justice to the openness of the future, while narratives focus on processes and events, but lack exactitude that would provide precise deductions and predictions. In advancing mathematics adequate to life, Robert Rosen argued that living beings as anticipatory systems must have models of themselves, and strove to develop a form of mathematics able to model life itself. It has been convincingly argued that narratives are central to human self-creation and they are lived out before being explicitly told. Their models of themselves are first and foremost, stories or narratives. If this is the case, might not living beings as biological entities be characterized by proto-stories or narratives in their models of themselves? Biosemiotics, largely inspired by C.S. Peirce, provides a bridge between mathematical and narrative comprehension, conceiving them as different forms of semiosis. The study of life through biosemiotics could reveal how mathematics and narratives can be understood in relation to each other. This could have implications for how we understand science and the humanities and their relationship to each other. In this paper I will examine work in theoretical biology that might advance these efforts. (shrink)

The aim of this article is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this article (...) aims to reopen the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written. (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)

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)

This book contextualizes David Hume's philosophy of physical science, exploring both Hume's background in the history of early modern natural philosophy and its subsequent impact on the scientific tradition.

Os minerais possuem uma influência direta em diversos processos fisiológicos no organismo animal e, mesmo com tamanha importância, por vezes são negligenciados pelos produtores para seu fornecimento para os animais. Este estudo teve como objetivo avaliar o desempenho reprodutivo de rebanhos de bovinos, caprinos e ovinos em 8 propriedades rurais nas cidades de Sanharó, Pesqueira, Arcoverde, Belo Jardim e São Bento do Una através da adição de suplemento mineral e mistura múltipla aos animais de forma a atender suas necessidades básicas (...) para mantença e reprodução. Foram avaliados os desempenhos de 4 touros e 25 vacas, 3 bodes e 50 cabras e 4 carneiros e 48 ovelhas em diferentes propriedades, avaliando como a adição de um suplemento mineral específico da espécie impacta de forma positiva nos índices reprodutivos avaliados que foram taxa de cio, taxa de serviço, taxa de concepção, taxa de fertilidade, taxa de prenhez, taxa de perdas gestacionais, taxa de natalidade e taxa de mortalidade. O experimento teve duração de 2 anos e pôde-se avaliar cerca de 2 partos nas vacas e, mais ou menos, 3 partos em cabras e ovelhas. Os dados foram computados e avaliados estatisticamente no Excel para conferir se os índices reprodutivos melhoraram em função da adição de minerais na ração dos animais. Conferiu-se que houve diferença significativa entre todos os índices avaliados, ou seja, a adição de minerais na ração dos animais melhora a eficiência reprodutiva de machos e fêmeas de animais ruminantes, sendo de suma importância sua disponibilização de forma correta para alcançar bons índices reprodutivos na fazenda na busca pela obtenção de neonatos que poderão ser comercializados. -/- REFERÊNCIAS BIBLIOGRÁFICAS ASTRO, G. B. A importância da adição de minerais na dieta de caprinos e ovinos no Agreste de Pernambuco. Trabalho de Conclusão de Curso (Técnico Subsequente em Agropecuária) - IFPE Campus Belo Jardim. Belo Jardim, 2023. 44 p. BALAMURUGAN, B. et al. Mineral an important nutrient for efficient reproductive health in dairy cattle. Int. J. Environ. Sci. Technol, v. 6, n. 1, p. 694-701, 2017. Barros NN, Bomfim MAD. Mistura múltipla para caprinos e ovinos. In: Anais VIII PECNORDESTE – Seminário Nordestino de Pecuária, 8; 2004; Fortaleza, Brasil. Fortaleza: FAEC, 2004. p. 50-57. BERCHIELLI, T. T.; PIRES, A. V.; OLIVEIRA, S. G. (Eds.). Nutrição de ruminantes. Jaboticabal: Funep, 2011. COTTA, T. Minerais e vitaminas para bovinos, ovinos e caprinos. Viçosa: Aprenda Fácil, 2001. DANTAS, C. C. O.; DE MATTOS NEGRÃO, F. Funções e sintomas de deficiência dos minerais essenciais utilizados para suplementação dos bovinos de corte. UNICiências, v. 14, n. 2, 2010. DA SILVA EIC. A água na nutrição animal. 1ª ed. Recife, PE: Instituto Agronômico de Pernambuco, 2023. DA SILVA, Emanuel Isaque Cordeiro. Cálculos de consumo e digestibilidade de alimentos e nutrientes para ruminantes. Revista Universitária Brasileira, v. 1, n. 3, 2023. DA SILVA, Emanuel Isaque Cordeiro. Concentrados e Rações Para Cabras em Lactação. 2022. DA SILVA, Emanuel Isaque Cordeiro. Efeitos da raça e do manejo nutricional sobre as características de qualidade da carcaça e da carne em ovinos. Revista Universitária Brasileira, v. 2, n. 1, 2024. DA SILVA, Emanuel Isaque Cordeiro. Fisiologia da Reprodução de Bovinos Leiteiros: Aspectos Básicos e Clínicos. Emanuel Isaque Cordeiro da Silva, 2022. DA SILVA, Emanuel Isaque Cordeiro. Formulação de ração para caprinos. Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Formulação de ração para ovinos. 2021. DA SILVA, Emanuel Isaque Cordeiro. Formulação e Avaliação de Suplemento Mineral Para Caprinos. Instrução Técnica Para o Produtor Rural de Pernambuco, v. 3, n. 1, p. 1-4, 2023. DA SILVA, Emanuel Isaque Cordeiro. Formulação e fabricação de rações para ruminantes. 1ª ed. Belo Jardim: Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Formulação e Fabricação de Rações Para Ruminantes: Bovinos, Caprinos e Ovinos. 2021. DA SILVA, Emanuel Isaque Cordeiro. Manejo Reprodutivo e Índices Zootécnicos em Gado de Leite. 2023. DA SILVA, Emanuel Isaque Cordeiro. Métodos de Formulação e Balanceamento de Rações para Bovinos. Belo Jardim: Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Nutrição e Suplementação Mineral de Bovinos de Corte. Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Nutrição Sobre a Reprodução e Fertilidade dos Bovinos. Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Opções de concentrados para vacas em lactação no Semiárido. 2022. DA SILVA, Emanuel Isaque Cordeiro. Relação e Efeitos Bioquímico-nutricionais Sobre os Cistos Ovarianos em Vacas. DA SILVA, Emanuel Isaque Cordeiro. Relação e Efeitos Bioquímico-nutricionais Sobre os Transtornos do Ciclo Estral em Vacas. DA SILVA, E. I. C. Suplementação e formulação de sal mineral e mistura múltipla para bovinos. Revista Universitária Brasileira, v. 2, n. 1, 2024. DE MENDONÇA JÚNIOR, A. F. et al. Minerais: importância de uso na dieta de ruminantes. Agropecuária Científica no Semiárido, v. 7, n. 1, p. 01-13, 2011. DE PAULA SILVEIRA, L. Suplementação mineral para bovinos. Medicina Veterinária e Zootecnia, v. 11, n. 5, p. 489-500, 2017. FADLALLA, I. M. T. The Interactions of Some Minerals Elements in Health and Reproductive Performance of Dairy Cows. New Advances in the Dairy Industry, 2022. FERGUSON, J. D. Nutrition and reproduction in dairy cows. Veterinary clinics of North America: Food animal practice, v. 7, n. 2, p. 483-507, 1991. GALVANI, D. B.; BOMFIM, MAD. Mistura múltipla para caprinos e ovinos: nova fórmula dispensa adaptação. 2015. HAENLEIN, G. F. W.; ANKE, M. Mineral and trace element research in goats: A review. Small Ruminant Research, v. 95, n. 1, p. 2-19, 2011. KAWAS, J. R.; ANDRADE-MONTEMAYOR, H.; LU, C. D. Strategic nutrient supplementation of free-ranging goats. Small Ruminant Research, v. 89, n. 2-3, p. 234-243, 2010. KESSLER, J. Mineral nutrition of goats. In: Goat nutrition, v. 46, p. 104-119, 1991. LOPES, H. O. S. Suplementação de baixo custo para bovinos: mineral e alimentar. 1998. MANERA, D. B. et al. Mineral mixtures from solid salt residues for lambs. Revista Brasileira de Zootecnia, v. 43, p. 485-491, 2014. MASTERS, D. G. Practical implications of mineral and vitamin imbalance in grazing sheep. Animal Production Science, v. 58, n. 8, p. 1438-1450, 2018. MORAES, S. da S. Importância da suplementação mineral para bovinos de corte. Campo Grande, MS: Embrapa Gado de Corte, 2001., 2001. NICODEMO, M. L. F. et al. Minerais na eficiência reprodutiva de bovinos. 1ª ed. São Carlos: Embrapa Pecuária Sudeste, 2008. 50 p. NIX, J.. Trace minerals important for goat reproduction. Sweetlix Livestock Supplement System, 2002. NOGUEIRA, É. et al. Nutrição aplicada à reprodução de bovinos de corte. In: MEDEIROS, S. R. et al. (Eds.). Nutrição de bovinos de corte: fundamentos e aplicações. 1ª ed. Brasília: Embrapa, 2015. p. 143-156. PASA, C.. Relação reprodução animal e os minerais. Biodiversidade, v. 9, n. 1, 2010. PEIXOTO, P. V. et al. Eficiência reprodutiva de matrizes bovinas de corte submetidas a três diferentes tipos de suplementação mineral. Pesquisa Veterinária Brasileira, v. 23, p. 125-130, 2003. PRADA, F. Influência da nutrição animal na reprodução de touros: revisão. Revista de Educação Continuada do CRMV-SP, v. 8, n. 1, p. 68-76, 2005. ROGÉRIO, M. C. P. et al. Manejo alimentar de caprinos e ovinos nos trópicos. Veterinária e Zootecnia, v. 23, n. 3, p. 326-346, 2016. SARTORI, R.; GUARDIEIRO, M. M. Fatores nutricionais associados à reprodução da fêmea bovina. Revista Brasileira de Zootecnia, v. 39, p. 422-432, 2010. SHARMA, M. C. et al. Mineral nutrition and reproductive performance of the dairy animals: a review. The Indian Journal of Animal Sciences, v. 77, n. 7, 2007. SILVA, D. C. et al. Importância do uso de minerais na dieta de bovinos reprodutores. Vet. zootec, p. 38-52, 2018. SOUZA, G. V. Suplementação de minerais na reprodução de bovinos. Trabalho de Conclusão de Curso (Graduação em Zootecnia) - UFG. Jataí, 2014. 32 p. TEIXEIRA, J. C. Nutrição de ruminantes. Lavras: FAEPE, 1992. UNDERWOOD, E. J.; SUTTLE, N. F. Los minerales en la nutrición del ganado. 3ª ed. Zaragoza: Acribia, 2003. VALADARES FILHO, S. C. et al. (Eds.). Tabelas brasileiras de composição de alimentos para ruminantes. 1ª ed. Viçosa: UFV, 2015. VALENTIM, J. K. et al. Fatores nutricionais aplicados à reprodução de ruminantes. UNICIÊNCIAS, v. 23, n. 2, p. 77-82, 2019. VASCONCELOS, F. F. Suplementação mineral no manejo reprodutivo ovino. Dissertação (Mestrado em Medicina Veterinária) - Centro de Ciências Rurais, UFSM. Santa Maria, 2012. 50 p. VÁZQUEZ-ARMIJO, J. F. et al. Trace elements in sheep and goats reproduction: a review. Tropical and Subtropical Agroecosystems, v. 14, n. 1, p. 1-13, 2011. VELLADURAI, C.; SELVARAJU, M.; NAPOLEAN, R. E. Effects of macro and micro minerals on reproduction in dairy cattle a review. International Journal of Scientific Research in Science and Technology, v. 2, n. 1, p. 68-70, 2016. YASOTHAI, R. Importance of minerals on reproduction in dairy cattle. International Journal of Science, Environment and Technology, v. 3, n. 6, p. 2051-2057, 2014. (shrink)

O Brasil possui um efeito significativo de caprinos, sendo o Nordeste a região com maior expressão deste rebanho. Por mais que a caprinocultura nordestina enfrente inúmeros desafios como a alta mortalidade dos cabritos, escassez de recursos alimentares, abates clandestinos etc., a atividade vem ganhando notoriedade, oferecendo aos consumidores produtos de qualidade para consumo. Diante deste cenário, separou-se 20 caprinos das raças Boer e SPRD, distribuídos em dois grupos, 10 animais recebendo dieta à base de feno padrão de capim Tifton-85 e (...) suplementação concentrada de 25 g/cabeça/dia e o suplemento de palma forrageira cv. Miúda juntamente com farelo da vagem da algaroba e grãos de feijão guandu, misturados e fornecidos em duas refeições diárias (8h e 16h) e um grupo de 10 animais, o grupo controle, recebendo apenas feno padrão e o concentrado na mesma proporção que o grupo experimental. Os animais foram separados preconizando-se a homogeneização do peso corporal e a idade. Foram avaliados os padrões de ganho de peso diário, o consumo de matéria seca e de nutrientes e a idade de abate destes animais conforme o desempenho. Os animais iniciaram o experimento com 25,6±1,6 kg e foram abatidos com 35±2,5 kg. O grupo experimental apresentou maior ganho de peso diário em comparação com o grupo controle (128±6 g vs. 106±9 g), consequentemente o grupo experimental apresentou uma idade de abate menor do que o grupo controle (73±4 vs. 89±8 dias). O rendimento de carcaça do grupo experimental foi maior que o do grupo controle (54,2±0,8 vs. 52,7±0,7%). Diante desses resultados, pôde-se afirmar que uma dieta com palma miúda, farelo da vagem de algaroba e grãos de feijão guandu favorece um maior ganho de peso e um encurtamento na idade de abate de caprinos de corte e SPRD. REFERÊNCIAS BIBLIOGRÁFICAS ABEBE, H.; TAMIR, B.. Effects of supplementation with pigeon pea (Cajanus cajun), cowpea (Vigna unguiculata) and lablab (Lablab purpureus) on feed intake, body weight gain and carcass characteristics in Wollo sheep fed grass hay. International Journal of Advanced Research in Biological Sciences, v. 3, n. 2, p. 280-295, 2016. ALMEIDA, M. A. D. et al. (Orgs.). Criando caprinos e ovinos no Semiárido: manejo e doenças 1ª ed. Salvador: EDUFBA, 2023. ARAÚJO, G. G. L. Alternativas alimentares para caprinos e ovinos no Semiárido. In: VII Seminário Nordestino Pecuário - PECNORDESTE 2003. Anais. Fortaleza - CE, 2003. p. 61-80. BARROS, J. R. L; CRUZ, G. R. B.; MELO, D. A. Caracterização do manejo alimentar de caprinos e ovinos na microrregião do cariri ocidental do estado da Paraíba. Revista Brasileira de Agroecologia, v. 13, n. 4, 2018. BELMONT, A. R. B. et al. Algaroba na alimentação animal. 1ª ed. Natal: SEBRAE/RN, 2016. CONTRERAS-VILLARREAL, V. et al. Complementación alimenticia con mezquite y naranja en cabras: efecto sobre el calostro, leche y cabritos. Abanico veterinario, v. 12, 2022. DA SILVA EIC. A água na nutrição animal. 1ª ed. Recife, PE: Instituto Agronômico de Pernambuco, 2023. DA SILVA, Emanuel Isaque Cordeiro. Cálculos de consumo e digestibilidade de alimentos e nutrientes para ruminantes. Revista Universitária Brasileira, v. 1, n. 3, p. 71-88, 2023. DA SILVA, Emanuel Isaque Cordeiro. Concentrados e Rações Para Cabras em Lactação. 2022. DA SILVA, Emanuel Isaque Cordeiro. Efeitos da raça e do manejo nutricional sobre as características de qualidade da carcaça e da carne em ovinos. Revista Universitária Brasileira, v. 2, n. 1, p. 61-81, 2024. DA SILVA, Emanuel Isaque Cordeiro. Fisiologia da Reprodução de Bovinos Leiteiros: Aspectos Básicos e Clínicos. Emanuel Isaque Cordeiro da Silva, 2022. DA SILVA, Emanuel Isaque Cordeiro. Formulação de ração para caprinos. Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Formulação e Avaliação de Suplemento Mineral Para Caprinos. Instrução Técnica Para o Produtor Rural de Pernambuco, v. 3, n. 1, p. 1-4, 2023. DA SILVA, Emanuel Isaque Cordeiro. Formulação e fabricação de rações para ruminantes. 1ª ed. Belo Jardim: Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Formulação e Fabricação de Rações Para Ruminantes: Bovinos, Caprinos e Ovinos. 2021. DA SILVA, Emanuel Isaque Cordeiro. Manejo Reprodutivo e Índices Zootécnicos em Gado de Leite. 2023. DA SILVA, Emanuel Isaque Cordeiro. Métodos de Formulação e Balanceamento de Rações para Bovinos. Belo Jardim: Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Nutrição Sobre a Reprodução e Fertilidade dos Bovinos. Emanuel Isaque Cordeiro da Silva, 2021. DA SILVA, Emanuel Isaque Cordeiro. Opções de concentrados para vacas em lactação no Semiárido. 2022. DA SILVA, E. I. C. Suplementação e formulação de sal mineral e mistura múltipla para bovinos. Revista Universitária Brasileira, v. 2, n. 1, 2024. 27-52. DA SILVA, K. B. Utilização de palma forrageira (Nopalea cochenillifera) como fonte exclusiva de forragem na dieta de ovinos. Tese (Doutorado Integrado em Zootecnia) - Centro de Ciências Agrárias, Campus II - UFPB. Areia, 2021. 83 p. GARCÍA-LÓPEZ, J. C. et al. Producción y contenido nutrimental de vainas de tres variantes de mezquite (Prosopis laevigata) en el altiplano potosino, México. Agrociencia, v. 53, n. 6, p. 821-831, 2019. LUCENA, R. B. Utilização da palma forrageira (nopalea cochenillifera) nas formas in natura e desidratada sobre: consumo, digestibilidade, balanço hídrico e absorção de minerais em ovinos. Dissertação (Mestrado em Nutrição de Ruminantes) - Departamento de Zootecnia, UFRPE. Recife, 2011. 77 p. MEDEIROS, L. P.; SAMPAIO, C. F. Desempenho de caprinos SRD em regime de confinamento. In: V Seminário de Pesquisa Agropecuária do Piauí. Anais. Teresina: Embrapa, 1988. p. 183-185. OLIVEIRA, A. P. D. Mandioca e farelo da vagem de algaroba na alimentação de caprinos mestiços. Dissertação (Mestrado em Ciência Animal) - Centro de Ciências Agrárias, Ambientais e Biológicas, UFRB. Cruz das Almas, 2012. 57 p. OLIVEIRA, L. L. et al. Native legumes and spineless cactus in supplementation of goats grazing in Caatinga rangeland: intake, performance, carcass characteristics, and meat quality. Acta Scientiarum. Animal Sciences, v. 44, p. e56445, 2022. OLIVEIRA, L. L. Suplementação com leguminosas sobre o desempenho e característica da carcaça de caprinos em crescimento no Semiárido. Dissertação (Mestrado em Ciência Animal e Pastagens) - UFRPE. Garanhuns, 2014. 90 p. OLIVEIRA, R. L. et al. Alimentos alternativos na dieta de ruminantes. Revista Científica de Produção Animal, v. 15, n. 2, p. 141-160, 2013. ROGÉRIO, M. C. P. et al. Manejo alimentar de caprinos e ovinos nos trópicos. Veterinária e Zootecnia, v. 23, n. 3, p. 326-346, 2016. SILVA, J. G. M. et al. Cactáceas nativas na alimentação de ruminantes. Revista Científica de Produção Animal. v. 15, n. 1. p. 53-62. 2013. SOUSA, F. A. Desempenho de cabritos alimentados com variedades de palma forrageira resistente a cochonilha do carmim. Dissertação (Mestrado em Zootecnia) - Centro de Ciências Agrárias, UFPB. Areia, 2015. 71 p. VALADARES FILHO, S. C. et al. (Eds.). Tabelas brasileiras de composição de alimentos para ruminantes. 1ª ed. Viçosa: UFV, 2015. (shrink)

I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.

Contemporary discussions about operational definition often hark back to Stanley Smith Stevens’ classic papers on psychological operationism (1935ab). Still, he was far from the only psychologist to call for conceptual hygiene. Some of Stevens’ direct colleagues at Harvard---most notably B. F. Skinner and E. G. Boring---were also actively applying Bridgman’s conceptual strictures to the study of mind and behavior. In this paper, I shed new light on the history of operationism by reconstructing the Harvard debates about operational definition in the (...) years before Stevens published his seminal articles. Building on a large set of archival evidence from the Harvard University Archives, I argue that we can get a more complete understanding of Stevens’ contributions if we better grasp the operationisms of his former teachers and direct colleagues at Harvard’s Department of Philosophy and Psychology. (shrink)

Look! Up in the bookshelf! Is it science? Is it science-fiction? No, it's Super Science: strange visitor from the future who can be everywhere in the universe and everywhen in time, can change the world in a single bound and who - disguised as a mild mannered author - fights for truth, justice and the super-scientific way. -/- Though I put a lot of hard work into this book, I can't take all the credit. I believe that (...) the whole universe - everything on Earth and in space plus everything in the past, present, and future - is entangled and unified. Everybody is part of this unity, so anybody could have written the ideas in this book. It turned out to be me simply because I've got intense curiosity about the book's contents, enough persistence and imagination to combine science with topics like religion and philosophy, and enough spare time to assemble all the pre-existing pieces in space and time (my contribution to the book is like putting together the pieces of a big jigsaw puzzle). -/- This book, with its vast collection of scientific fact and study results, presents some fascinating theories and is an expansive journey through my research. The topic will appeal to the science-minded reader who is open to speculating on how conditions may evolve in the future, perhaps questioning the very foundations of our place in the universe. This book is not written as a single story but is a collection of 9 articles written in the first half of 2022. Each chapter of this book is presented as a research paper. There's the abstract, the introduction, the keywords, the body of the work divided into sections, and a reference section. Though this might turn some readers off, I'm a member of ResearchGate, a community of researchers. So it isn't surprising that I've presented this book this way. Each article is meant to be self-contained and well explained in plain English. As a result, some explanations appear in several of the articles. -/- Please be patient when you encounter jargon and mathematics - I've tried to keep these to a minimum but they're bound to put in an appearance in a book that's largely about science (and I have compiled an enormous amount of intricate research for this project, hopefully impressing with the organization). Quotes from a range of scientists and icons in the industry should add further fascination to the descriptions, inspiring the reader into more of an openness to speculating on the distant future. There's a lot to absorb here but understanding the future . . . It Don't Come Easy (just ask Ringo Starr who once dreamed he was an alien living on another planet in the future. -/- Contents -/- Special Relativity's Consequences For General Relativity, Quantum Mechanics And Quantum Gravity (Can Science And The Paranormal Coexist?) -/- Intergalactic Travel and Riemann Hypothesis - featuring Dark Matter, Dark Energy, Higgs Boson, Higgs Field, Electroweak Interaction, No Big Bang, Other Dimensions, Plus Other Physics and Mathematics -/- New Perspectives On Life, Death, Cancer and Covid-19 Arising From An Artificially Intelligent, Non-probabilistic Universe -/- Unipositional Interpretation Of Quantum Mechanics Means Entanglement Occurring Simultaneously With Gravitational Slingshots Reduces Problems Associated With Spaceflight -/- Unipositional Interpretation Of Quantum Mechanics Explains Time Dilation, Updates Cosmology -/- WHERE DID EVERYTHING COME FROM – Combining Science, Mathematics, Computers, Religion, Philosophy, Relativity, Quantum Physics, Darwinism, and a Podcast to Reach One Person’s Plausible Ideas -/- Thoughts on Artificial Intelligence and the Origin of Life Resulting from General Relativity, with Neo-Darwinist Reference to Human Evolution and Mathematical Reference to Cosmology -/- Planet 9 and Black Hole Versus Relativity’s Precession and Dark Matter -/- THE WORLD’S REAL-LIFE EXPERIMENTS WITH COVID-19 AND PHYSICS ALTER SOCIETY AND GLOBAL ECONOMICS . (shrink)

This chapter describes the potential far‐reaching consequences of contemplative higher education for the fields of science and medicine.

In this article, we propose the Fair Priority Model for COVID-19 vaccine distribution, and emphasize three fundamental values we believe should be considered when distributing a COVID-19 vaccine among countries: Benefiting people and limiting harm, prioritizing the disadvantaged, and equal moral concern for all individuals. The Priority Model addresses these values by focusing on mitigating three types of harms caused by COVID-19: death and permanent organ damage, indirect health consequences, such as health care system strain and stress, as well as (...) economic destruction. It proposes proceeding in three phases: the first addresses premature death, the second long-term health issues and economic harms, and the third aims to contain viral transmission fully and restore pre-pandemic activity. -/- To those who may deem an ethical framework irrelevant because of the belief that many countries will pursue "vaccine nationalism," we argue such a framework still has broad relevance. Reasonable national partiality would permit countries to focus on vaccine distribution within their borders up until the rate of transmission is below 1, at which point there would not be sufficient vaccine-preventable harm to justify retaining a vaccine. When a government reaches the limit of national partiality, it should release vaccines for other countries. -/- We also argue against two other recent proposals. Distributing a vaccine proportional to a country's population mistakenly assumes that equality requires treating differently situated countries identically. Prioritizing countries according to the number of front-line health care workers, the proportion of the population over 65, and the number of people with comorbidities within each country may exacerbate disadvantage and end up giving the vaccine in large part to wealthy nations. (shrink)

The role of mathematics in the development of Gilles Deleuze's (1925-95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze's interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770-1831) presents in the Science of Logic . Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal calculus (...) in his treatment of the problem of the infinitesimal. Against the role that Hegel assigns to integration as the inverse transformation of differentiation in the development of his dialectical logic, Deleuze strategically redeploys Leibniz's account of integration as a method of summation in the form of a series in the development of his philosophy of difference. By demonstrating the relation between the differential point of view of the Leibnizian infinitesimal calculus and the differential calculus of contemporary mathematics, I argue that Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic, and by doing so, sets up the critical perspective from which to construct an alternative logic of relations characteristic of a philosophy of difference. The mode of operation of this logic is then demonstrated by drawing upon the mathematical philosophy of Albert Lautman (1908-44), which plays a significant role in Deleuze's project of constructing a philosophy of difference. Indeed, the logic of relations that Deleuze constructs is dialectical in the Lautmanian sense. (shrink)

Hermann Weyl was one of the most important figures involved in the early elaboration of the general theory of relativity and its fundamentally geometrical spacetime picture of the world. Weyl’s development of “pure infinitesimal geometry” out of relativity theory was the basis of his remarkable attempt at unifying gravitation and electromagnetism. Many interpreters have focused primarily on Weyl’s philosophical influences, especially the influence of Husserl’s transcendental phenomenology, as the motivation for these efforts. In this article, I argue both that these (...) efforts are most naturally understood as an outgrowth of the distinctive mathematical-physical tradition in Göttingen and also that phenomenology has little to no constructive role to play in them. (shrink)

This chapter explores how science and technology studies (STS) have evolved over the past generation. It surveys the contrasting perspectives of philosophers, sociologists, scholars of the humanities, wider publics, and scientists themselves. It describes contrasting views about the practice and purpose for studying the history of science. -/- ISBN 978-1-85168-681-0.

Abstract: The analytical, comparative cross-sectional study was conducted to assess the thyroid profiles and modified lipid profiles levels among Sudanese patients with coronary heart disease performed on forty-one patients with coronary heart disease as test group collected from Sudan Heart Center, Al rebat teaching hospital and Al mawada hospital in Khartoum state, during the period between November 2017 and May 2018. Furthermore, the test group compared with forty-one apparently healthy volunteers as control group was selected with the same inclusion criteria. (...) Spectrophotometeric methods were used for measurement of lipid profile. Thyroid hormones (T3 &T4) and thyroid stimulating hormone were measured by using Sandwich Enzyme-Linked Immunosorbent Assay (ELISA). Moreover, statistical package for social science (SPSS version 23) computer software was used for data analysis. The study clearly demonstrated that there was statistically significant decrease in T3, and significant increase in T4 levels in test group compared to control with (P. value 0.047) for T3, and (P. value 0.002) for T4.Nonetheless, the result of this study indicated a significant elevation in mean of total cholesterol, low density lipoprotein-cholesterol levels and significant decrease in high density lipoprotein –cholesterol in test group compared to control (P.value 0.000). In conclusion Coronary heart diseases patients have significantly low Triiodothyronine, elevated Thyroxin, and normal Thyroid Stimulating Hormone levels, with significantly higher Total Cholesterol, Low Density Lipoprotein-Cholesterol concentrations, and lower HighDensity Lipoprotein-Cholesterol concentrations. (shrink)

Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from (...) the central position it used to have in philosophy of science and placed logic at center stage in the 20th century philosophy of science. Only in recent decades logic has begun to loose its monopoly and geometry and topology received a new chance to find a place in philosophy of science. (shrink)

Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and (...) the epistemological question of how we know about them are central to the philosophy of mathematics. These and related philosophical questions are of particular interest because of mathematics’ unusual status. Mathematics is exceptional in that, on the one hand, it appears unhesitatingly true—no one doubts that 2 + 3 = 5—but on the other, as just noted, it is not about the physical world. This ambivalent status is what gives the philosophy of mathematics its special interest. The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science. Science has over the past few centuries become increasingly mathematical, and indeed the fundamental science of nature, physics, is today recognised as a branch of applied mathematics. The second is that mathematics underwent a transformation in the course of nineteenth century: having started the century as a rather traditional-looking science of quantity it emerged a hundred years later a radically transformed abstract theory of structure. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Developed by Frege, Cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. These volumes will collect the major works in this major field, with a focus on the last few decades. The anthology will include technical work, which interprets philosophically significant mathematical results or subfields of mathematics, as well as purely philosophical writing, aimed at those without advanced mathematics. The collection should be of interest to both philosophers and mathematicians, as well as to anyone who is susceptible to wondering what the main intellectual tool used in science, economics and finance, and indeed everyday life is ultimately about. (shrink)

This paper introduces a new, expanded range of relevant cognitive psychological research on collaborative recall and social memory to the philosophical debate on extended and distributed cognition. We start by examining the case for extended cognition based on the complementarity of inner and outer resources, by which neural, bodily, social, and environmental resources with disparate but complementary properties are integrated into hybrid cognitive systems, transforming or augmenting the nature of remembering or decision-making. Adams and Aizawa, noting this distinctive complementarity argument, (...) say that they agree with it completely: but they describe it as “a non-revolutionary approach” which leaves “the cognitive psychology of memory as the study of processes that take place, essentially without exception, within nervous systems.” In response, we carve out, on distinct conceptual and empirical grounds, a rich middle ground between internalist forms of cognitivism and radical anti-cognitivism. Drawing both on extended cognition literature and on Sterelny’s account of the “scaffolded mind” (this issue), we develop a multidimensional framework for understanding varying relations between agents and external resources, both technological and social. On this basis we argue that, independent of any more “revolutionary” metaphysical claims about the partial constitution of cognitive processes by external resources, a thesis of scaffolded or distributed cognition can substantially influence or transform explanatory practice in cognitive science. Critics also cite various empirical results as evidence against the idea that remembering can extend beyond skull and skin. We respond with a more principled, representative survey of the scientific psychology of memory, focussing in particular on robust recent empirical traditions for the study of collaborative recall and transactive social memory. We describe our own empirical research on socially distributed remembering, aimed at identifying conditions for mnemonic emergence in collaborative groups. Philosophical debates about extended, embedded, and distributed cognition can thus make richer, mutually beneficial contact with independently motivated research programs in the cognitive psychology of memory. (shrink)

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of (...) time the ”niches” which constitute the boundary conditions on selec- tion. More generally, by the mathematical unprestatability of the ”phase space”, no laws of mo- tion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound concep- tual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of symmetries as invariant preserving transformations will allow us to under- stand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to differential cases. Mutations or other causal differ- ences will allow us to stress that ”non conservation princi- ples” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as sym- metries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter. (shrink)

I argue that the familiar picture of the rise of analytic philosophy through the early work of G. E. Moore and Bertrand Russell is incomplete and to some degree erroneous. Archival evidence suggests that a considerable influence on Moore, especially evident in his 1899 paper ‘The nature of judgment,’ comes from the literature in nineteenth-century empirical psychology rather than nineteenth-century neo-Hegelianism, as is widely believed. I argue that the conceptual influences of Moore’s paper are more likely to have had their (...) source in the work of two of Moore’s teachers, G. F. Stout and James Ward. What may be called an anti-psychologism about psychology characterizes the work of these and other psychologists of the period. I argue that the anti-psychologism that is the main aim of Moore’s early theory of judgment is an adaptation of this notion, which is significantly dissimilar from the notion defended by Bradley, traditionally thought to have been a key influence on Moore.Keywords: G. E. Moore; Bertrand Russell; Propositions; Anti-psychologism; Early analytic philosophy; G. F. Stout. (shrink)

This paper investigates a well-known case of simultaneous discovery in twentieth-century chemistry, the origins of the concept of hybridisation, in the light of Kuhn's insights. There has been no ambiguity as to who discovered this concept, when it was "rst in print, and how important it was. The full-#edged form of the concept was published in 1931 independently by two American scientists John C. Slater (1900}1976) and Linus Pauling (1901}1994), although both of them had made their ideas public earlier: Slater (...) at the American Physical Society meetings in 1930, and Pauling in the Proceedings of the National Academy of Sciences in 1928. Slater and Pauling both argued for the necessity of using an s orbital as well as three p orbitals in the carbon atom in order to explain carbon's four valences and the tetrahedral structure of methane. The metaphor &hybridisation' for denoting this mix of s and p orbitals was "rst used by Robert S. Mulliken and J. H. Van Vleck before gaining currency with the scienti"c community around 1935.2 The concept of hybridisation was indeed indispensable for extending the quantum-mechanical interpretation of the chemical bond as an electron pairing from diatomic molecules to polyatomic ones. To be sure, the emergence of hybridisation attests to scientists' growing interest in exploring the borderland between physics and chemistry, a trend that led to the creation of physical chemistry in the late nineteenth century and of chemical physics and quantum chemistry in the 1920s and 30s. Slater and Pauling themselves experienced and on many occasions talked about the fruitfulness of interdisciplinary research; and historians have legitimately illuminated their works by examining them in this broad context.3 Yet the careful analysis of their research notes and published papers reveals that Slater and Pauling were working in quite disparate disciplinary traditions, with di!erent approaches, for di!erent audiences, and towards di!erent goals. The aim of this paper is to explore their di!erent routes to a common destination*hybridisation*and thereby to explicate tensions existing between physics and chemistry amidst the institutional and conceptual overlapping of the two disciplines. (shrink)

Our question is: can we embed minimal negation in implicative logics weaker than I→? Previous results show how to define minimal negation in the positive fragment of the logic of relevance R and in contractionless intuitionistic logic. Is it possible to endow weaker positive logics with minimal negation? This paper prooves that minimal negation can be embedded in even such a weak system as Anderson and Belnap’s minimal positive logic.

The chapter begins with an initial survey of ups and downs of contextualist history of philosophy during the twentieth century in Britain and America, which finds that historically serious history of philosophy has been on the rise. It then considers ways in which the study of past philosophy has been used and is used in philosophy, and makes a case for the philosophical value and necessity of a contextually oriented approach. It examines some uses of past texts and of history (...) that reveal limits to noncontextual history, including Strawson's Kant, Rorty's grand diagnosis of the Western tradition, and Friedman on Kant's philosophy of mathematics. It then considers ways in which the history of philosophy may become philosophically deeper by becoming more historical, and instances in which history of philosophy of various stripes has or may deliver a philosophical payoff. Along the way, it urges historians of philosophy to attend not only to individual philosophers and their problems and projects, but also to the larger shape of the history of philosophy and its narrative themes. (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)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, kinds of (...) logic). This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the (...) finite and the infinite. His work continues to inspire and challenge philosophers, mathematicians, and scientists, inviting them to explore the profound and often enigmatic questions at the heart of human understanding. -/- Kurt Gödel's Broader Contributions to Philosophy Kurt Gödel, while primarily known for his monumental incompleteness theorems, made significant contributions that extended beyond the realm of mathematical logic. His philosophical pursuits deeply engaged with the works of eminent philosophers like Immanuel Kant and Edmund Husserl. Gödel's explorations into the nature of time, the structure of the universe, and the relationship between mathematics and reality reveal a profound and multifaceted intellectual legacy. -/- Engagement with Immanuel Kant Gödel held a deep interest in the philosophy of Immanuel Kant. He admired Kant's critical philosophy, particularly the distinction between the noumenal and phenomenal worlds. Kant posited that human experience is shaped by the mind’s inherent structures, leading to the conclusion that certain aspects of reality (the noumenal world) are fundamentally unknowable. Gödel’s incompleteness theorems echoed this Kantian theme, illustrating the limits of formal systems in capturing the totality of mathematical truth. Gödel believed that mathematical truths exis t independently of human thought, akin to Kant's noumenal realm. This philosophical alignment provided a robust foundation for Gödel's Platonism, which asserted the existence of mathematical objects as real, albeit abstract, entities. -/- Influence of Edmund Husserl Gödel was also profoundly influenced by Edmund Husserl, the founder of phenomenology. Husserl's phenomenology emphasizes the direct investigation and description of phenomena as consciously experienced, without preconceived theories about their causal explanation. Gödel saw Husserl's work as a pathway to bridge the gap between the abstract world of mathematics and concrete human experience. Husserl's ideas about the structures of consciousness and the intentionality of thought resonated with Gödel's views on mathematical intuition. Gödel believed that human minds could access mathematical truths through intuition, a concept that draws on Husserlian phenomenological methods. -/- The Nature of Time and the Universe Gödel's philosophical inquiries extended to the nature of time and the structure of the universe. His collaboration with Albert Einstein at the Institute for Advanced Study led to the development of the "Gödel metric" in 1949. This solution to Einstein's field equations of general relativity described a rotating universe where time travel to the past was theoretically possible. Gödel's model challenged conventional notions of time and causality, suggesting that the universe might have a more intricate structure than previously thought. Gödel's exploration of time was not just a mathematical curiosity but a profound philosophical statement about the nature of reality. He questioned whether time was an objective feature of the universe or a construct of human consciousness. His work hinted at a timeless realm of mathematical truths, aligning with his Platonist view. -/- Mathematics and Reality Gödel's philosophical outlook extended to the broader relationship between mathematics and reality. He believed that mathematics provided a more profound insight into the nature of reality than empirical science. For Gödel, mathematical truths were timeless and unchangeable, existing independently of human cognition. This perspective led Gödel to critique the materialist and mechanistic views that dominated 20th-century science and philosophy. He argued that a purely physicalist interpretation of the universe failed to account for the existence of abstract mathematical objects and the human capacity to understand them. Gödel's philosophy suggested a more integrated view of reality, where both physical and abstract realms coexist and inform each other. -/- Gödel's Exploration of Time Kurt Gödel, one of the most profound logicians of the 20th century, ventured beyond the confines of mathematical logic to explore the nature of time. His inquiries into the concept of time were not merely theoretical musings but were grounded in rigorous mathematical formulations. Gödel's exploration of time challenged conventional views and opened new avenues of thought in both physics and philosophy. -/- Gödel and Einstein Gödel’s interest in the nature of time was significantly influenced by his friendship with Albert Einstein. Both were faculty members at the Institute for Advanced Study in Princeton, where they engaged in deep discussions about the nature of reality, time, and space. Gödel's exploration of time culminated in his solution to Einstein's field equations of general relativity, known as the Gödel metric. -/- The Gödel Metric In 1949, Gödel presented a model of a rotating universe, which became known as the Gödel metric. This solution to the equations of general relativity depicted a universe where time travel to the past was theoretically possible. Gödel’s rotating universe contained closed timelike curves (CTCs), paths in spacetime that loop back on themselves, allowing for the possibility of traveling back in time. The Gödel metric posed a significant philosophical challenge to the conventional understanding of time. If time travel were possible, it would imply that time is not linear and absolute, as commonly perceived, but rather malleable and subject to the geometry of spacetime. This raised profound questions about causality, the nature of temporal succession, and the very structure of reality. -/- Philosophical Implications Gödel’s exploration of time extended beyond the mathematical implications to broader philosophical inquiries: Nature of Time: Gödel questioned whether time was an objective feature of the universe or a construct of human consciousness. His work suggested that our understanding of time as a linear progression from past to present to future might be an illusion, shaped by the limitations of human perception. -/- Causality and Free Will: The existence of closed timelike curves in Gödel’s model raised questions about causality and free will. If one could travel back in time, it would imply that future events could influence the past, potentially leading to paradoxes and challenging the notion of a deterministic universe. -/- Temporal Ontology: Gödel's work contributed to debates in temporal ontology, particularly the debate between presentism (the view that only the present exists) and eternalism (the view that past, present, and future all equally exist). Gödel’s rotating universe model seemed to support eternalism, suggesting a block universe where all points in time are equally real. Philosophy of Science: Gödel’s exploration of time had implications for the philosophy of science, particularly in the context of understanding the limits of scientific theories. His work underscored the importance of considering philosophical questions when developing scientific theories, as they shape our fundamental understanding of concepts like time and space. -/- Legacy Gödel’s exploration of time remains a significant and controversial contribution to both physics and philosophy. His work challenged established notions and encouraged deeper inquiries into the nature of reality. Gödel’s rotating universe model continues to be a topic of interest in theoretical physics and cosmology, inspiring new research into the nature of time and the possibility of time travel. In philosophy, Gödel’s inquiries into time have prompted ongoing debates about the nature of temporal reality, the relationship between mathematics and physical phenomena, and the limits of human understanding. His work exemplifies the intersection of mathematical rigor and philosophical inquiry, demonstrating the profound insights that can emerge from such an interdisciplinary approach. The Temporal Ontology of Kurt Gödel Kurt Gödel's profound contributions to mathematics and logic extend into the realm of temporal ontology—the philosophical study of the nature of time and its properties. Gödel's insights challenge conventional perceptions of time and suggest a more intricate, layered understanding of temporal reality. This essay explores Gödel's contributions to temporal ontology, particularly through his engagement with relativity and his philosophical reflections. -/- Gödel's Rotating Universe One of Gödel’s most notable contributions to temporal ontology comes from his work in cosmology, specifically his solution to Einstein’s field equations of general relativity, known as the Gödel metric. Introduced in 1949, the Gödel metric describes a rotating universe with closed timelike curves (CTCs). These curves imply that, in such a universe, time travel to the past is theoretically possible, presenting a significant challenge to conventional views of linear, unidirectional time. -/- Implica tions for Temporal Ontology Gödel's rotating universe model has profound implications for our understanding of time: Eternalism vs. Presentism: Gödel’s model supports the philosophical stance known as eternalism, which posits that past, present, and future events are equally real. In contrast to presentism, which holds that only the present moment exists, eternalism suggests a "block universe" where time is another dimension like space. Gödel’s rotating universe, with its CTCs, reinforces this view by demonstrating that all points in time could, in principle, be interconnected in a consistent manner. Non-linearity of Time: The possibility of closed timelike curves challenges the idea of time as a linear sequence of events. In Gödel’s universe, time is not merely a straight path from past to future but can loop back on itself, allowing for complex interactions between different temporal moments. This non-linearity has implications for our understanding of causality and the nature of temporal succession. Objective vs. Subjective Time: Gödel’s work invites reflection on the distinction between objective time (the time that exists independently of human perception) and subjective time (the time as experienced by individuals). His model suggests that our subjective experience of a linear flow of time may not correspond to the objective structure of the universe. This raises questions about the relationship between human consciousness and the underlying temporal reality. -/- Gödel and Philosophical Reflections on Time Gödel’s engagement with temporal ontology was not limited to his cosmological work. He also reflected deeply on philosophical questions about the nature of time and reality, drawing on the ideas of other philosophers and integrating them into his own thinking. Kantian Influences: Gödel was influenced by Immanuel Kant’s distinction between the noumenal world (things as they are in themselves) and the phenomenal world (things as they appear to human observers). Gödel’s views on time echoed this distinction, suggesting that our perception of time might be a phenomenon shaped by the limitations of human cognition, while the true nature of time (the noumenal aspect) might be far more complex and non-linear. Husserlian Phenomenology: Gödel’s interest in Edmund Husserl’s phenomenology also informed his views on time. Husserl’s emphasis on the structures of consciousness and the intentionality of thought resonated with Gödel’s belief in the importance of intuition in accessing mathematical truths. Gödel’s reflections on time incorporated a phenomenological perspective, considering how temporal experience is structured by human consciousness. Mathematical Platonism: Gödel’s Platonist views extended to his understanding of time. Just as he believed in the independent existence of mathematical objects, Gödel saw time as an objective entity with a structure that transcends human perception. His work on the Gödel metric can be seen as an attempt to uncover this objective structure, revealing the deeper realities that underlie our experience of time. (shrink)

The objective of the paper is the methodological presentation of the basic principles towards a critical interdisciplinary approach for studying the history of monuments restoration, valid for different cultures. The proposed integrated framework offers the possibility to study and document monuments restoration in various spatial levels e.g. global, continental, international, national, regional, and local. The conceptual and methodological aspects are based on the following fundamental pillars a) the development of science and technology, including relevant history of education, b) the (...) evolution of the restoration philosophy, c) the incorporation of the above in restoration projects at a lower level, d) the infiltration of the above in restoration interventions at the lowest level. The author expects that the above successive and/or parallel levels of scientific branches can contribute effectively to the analysis, synthesis and comparative assessment of the aspects and criteria that influenced monuments restoration timeline. The challenge for the researcher of the monuments restoration history is the adjustment of the whole process to his own –under research- level in such a way as to take advantage of all theinterdisciplinary inputs creating, thus, inventive links and stimulating new information and knowledge. The above are briefly tested in the case study of Thessaloniki, Macedonia, Greece. Such an inductive approach will enable all disciplines to devote their finest efforts towards understanding, documenting and studying monuments restoration history and, thus, support effectively a sustainable future for the world’s cultural heritagel audience. (shrink)

Fruitful dialogue between faith and science occurs when Christians and scientists meaningfully answer the questions that they pose to each other in a disciplined conversation that refines their perspectives iteratively, each respecting the diligent conscientious work of the other. When questions are answered in this way the answers then form the basis for the continuation of the discussion and agreed solutions will chart principles and procedures for feedback and modification.