Following the practice of human beings everywhere historians distinguish the real or most significant cause of an occurrence or state of affairs from ‘less important considerations’, ‘precipitating circumstances’, or ‘mere conditions’. I shall term claims that some phenomenon is most basically to be attributed to some one of the factors causally necessary for its occurrence attributive causal explanations or causal attributions and discuss here the extent to which moral convictions are constitutive of them.

This paper presents a qualitative comparison of opposing views of elementary matter—the Copenhagen approach in quantum mechanics and the theory of general relativity. It discusses in detail some of their main conceptual differences, when each theory is fully exploited as a theory of matter, and it indicates why each of these theories, at its presently accepted state, is incomplete without the other. But it is then argued on logical grounds that they cannot be fused, thus indicating the need for a (...) third revolution in contemporary physics. Toward this goal, the approach discussed is one of further generalizing the theory of general relativity in a way that incorporates the inertial manifestations of matter in covariant fashion, with quantum mechanics serving as a low-energy, linear approximation. Such a theoretical extension of general relativity will be discussed, with applications in elementary particle physics, such as the appearance of mass spectra in the microdomain, as an asymptotic feature of matter, mass doublets (electron-muon and proton-heavy proton), the explanation of pair annihilation and creation from a deterministic field theory, charge quantization, and features of pions. (shrink)

The discussion of mathematical knowledge and its relation to the construction of an appropriate diagram in Aristotle's Metaphysics Θ 9. 1051 a21—33 is an important, if compressed, account of Aristotle's most mature thoughts on mathematical knowledge. The discussion of what sort of previous knowledge one must have for understanding a theorem recalls the discussion at An. Post. A 1. 71 a 17–21, where the epistemological point is similar and the examples the same. The first example, that the interior angles of (...) a triangle equal two right angles, appears no less than thirty times in the corpus . The example of the angle inscribed in a semicircle being a right angle also occurs at An. Post. B 11. 94a 27–34, but in a very different context from its two companions. Illustrations of both theorems provided clear stock examples for Aristotle. (shrink)

In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

It is shown that Einstein abandoned his earlier view that there are material consequences, such as asymmetric aging, implied by the space-time transformations of transformations of relativity theory.

The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables must be expressible as nonsingular fields, implies a particular generalization of the standard forms of the conservation equations and leads to (...) a removal of the problem of the infinite self-energy of point sources. A further generalization of the mathematical expression of electromagnetism occurs when it is asserted that the form of the laws must be compatible with the symmetry requirements of the irreducible representations of the Poincaré group. This yields a factorization of the vector field equations, giving a set of two uncoupled two-component spinor equations. It is shown that the latter lead to twice as many conservation equations for electromagnetism, compared with the vector formalism, thus making extra predictions that are not made in the latter formalism. It is shown that the extra conservation equations reveal themselves only when incorporating the requirements of Faraday's interpretation of the field solutions. (shrink)

The first part of this paper examines conditions in accord with Einstein's criterion of regularity on the field solutions everywhere that would correspond to the existence of a black hole star, following from solutions of his (nonvacuum) field equations. ‘Black hole’ is defined here as a star whose matter is so condensed as to correspond to a complete family of spatially closed geodesics. The condition imposed is that the angular momentum of a test body in each of the closed geodesics (...) is a constant of the motion. The second part of the paper examines the implications in the problem of the condensed star of a generalized (factorized) version of the metrical field equations, discovered earlier by the author. It is found that in general relativity stars should naturally pulsate, and in its succeeding cycles the gravitational radius of the star is attenuated by a factor exp(−0.349T), where T is the pulsation period. Conditions are discussed for the possibility that the (relatively) regular emissions of radiation from a pulsar may be dynamically rooted in a (smaller) part of the pulsation cycle when the star is out of the black hole state (less dense → open geodesics)—when radiation would be emitted to the outside world—and the (greater) part of the cycle when it is in the black hole state (more dense → closed geodesics)—when radiation would not be emitted. (shrink)

This paper responds briefly to the criticism of Rodrigues and Rosa on my earlier analysis of the twin paradox. The main point that I have emphasized (and that the authors have not refuted, either logically or mathematically) is the error in directly identifying anabstract measure relative to a reference frame [and its transformations to all other possible reference frames in which the laws of nature are to be compared (such as temporal and spatial measures)], with aphysical extension and duration of (...) a material body. (shrink)

The author argues, Contra hume, That "the motives of human action are not related to the action in the way in which the causes of the sort of physical behaviour to which hume refers are related to that behaviour." the author contends this because he is opposed to the consequence of hume's theory that "moral appraisal presupposes 'necessity' or determinism." he concludes that we do have to explain morality in terms of human motives, But that a different sort of causality (...) is involved here than in the physical world. (staff). (shrink)

It is commonly held that moral judgements are implicitly general — or universalizable — in that if anyone is morally obligated to perform or refrain from some action, everyone in relevantly similar circumstances is similarly obligated. I undertake here to show that David Hume fully subscribed to this thesis and that because of the way it is related to his conceptions of obligation and what he terms the practicality of morals he is pushed to insist that the moral sentiments of (...) human beings across space and time are much more uniform than he knew them to be. My discussion places Hume in the historical context of the controversy about 'the general foundation of morals' referred to near the beginning of the second Enquiry, and it is part of my thesis that Hume's moral philosophy can be understood only in terms of arguments and counter-arguments developed by other contributors to the controversy. (shrink)

The precessional frequency of a gyroscope in a reference frame that orbits about a gravitational body is compared between Einstein's tensor formulation of general relativity and the author's quaternion generalization—obtained from a factorization of the tensor form. The difference in predictions then suggests an experiment that could choose which of these formulations of general relativity is more valid in the analysis of gyroscopic motion.

he following is an essay by Emmanuel Levinas, newly translated by Mendel Kranz, concerning Jewish culture and education, Hebrew studies, and Zionism. The essay was first published in 1954 in the United States by The Alliance Review, a small journal affiliated with the Alliance israélite universelle, and has since been almost entirely forgotten. In 2011–2012, it was republished in French by Denis Poizat based on the original draft found in the Alliance archives. Preceding Levinas’s essay is a preface by (...) Kranz that situates it at the intersection of Levinas’s postwar project for Judaism, his relation to Zionism, and the colonial backdrop of the ENIO—three issues that are rarely considered together in Levinas scholarship. Poizat also provides some commentary on the question of education and the similarities between this and other essays by Levinas. (shrink)