From the perspective of biological cybernetics, “real world” robots have no fundamental advantage over computer simulations when used as models for biological behavior. They can even weaken biological relevance. From an engineering point of view, however, robots can benefit from solutions found in biological systems. We emphasize the importance of this distinction and give examples for artificial systems based on insect biology.

A Study of the sources of a Plutarchan Life may be excused on two grounds: first, a knowledge of the sources is important for a critical evaluation of the Life's historical worth; and second, such a study is instructive for the understanding of Plutarch's methods of composition, which, in its turn, helps considerably in the historical evaluation. For this second object the Titus is particularly well suited, since the problem, owing to the survival in large part of his main (...) source, is infinitely simpler than in many of the other Lives, and it is on these grounds that the present study seeks to justify itself. (shrink)

A lattice L is coordinatizable, if it is isomorphic to the lattice L of principal right ideals of some von Neumann regular ring R. This forces L to be complemented modular. All known sufficient conditions for coordinatizability, due first to von Neumann, then to Jónsson, are first-order. Nevertheless, we prove that coordinatizability of lattices is not first-order, by finding a non-coordinatizable lattice K with a coordinatizable countable elementary extension L. This solves a 1960 problem of Jónsson. We also (...) prove that there is no [Formula: see text] statement equivalent to coordinatizability. Furthermore, the class of coordinatizable lattices is not closed under countable directed unions; this solves another problem of Jónsson from 1962. (shrink)

In regard to the explanation of actions that are governed by institutional rules, John R. Searle introduces the notion of a mental “background” that is supposed to explain how persons can acquire the capacity of following such rules. I argue that Searle’s internalism about the mind and the resulting poverty of his conception of the background keep him from putting forward a convincing explanation of the normative features of institutional action. Drawing on competing conceptions of the background of Heidegger and (...) Wittgenstein, I propose to revise Searle’s conception. The background of institutional agency can only provide a convincing explanation if it includes the context of actions and intersubjective structures of a shared life-world. I suggest that a further development of this idea would lead to the identification of the background with a web of social recognition. (shrink)

Psychopathy refers to a range of complex behaviors and personality traits, including callousness and antisocial behavior, typically studied in criminal populations. Recent studies have used self-reports to examine psychopathic traits among noncriminal samples. The goal of the current study was to examine the underlying factor structure of the Self-Report of Psychopathy Scale–Short Form (SRP-SF) across complementary samples and examine the impact of gender on factor structure. We examined the structure of the SRP-SF among 2,554 young adults from three undergraduate samples (...) and a high-risk young adult sample. Using confirmatory factor analysis, a four-correlated factor model and a four-bifactor model showed good fit to the data. Evidence of weak invariance was found for both models across gender. These findings highlight that the SRP-SF is a useful measure of low-level psychopathic traits in noncriminal samples, although the underlying factor structure may not fully translate across men and women. (shrink)

Suppose that a scientific theory X is well confirmed, and either states or implies a statement like “classes exist”. Suppose, if the statement is not explicit but implied, that the specified systems are ‘accepted’ by two individuals, R and F, as the ‘best available'. Suppose, finally, that both R and F, in some yet to be explained sense of the word, ‘accept’ and use theory X to regulate their experience. Then we have something very like the situation discussed by Putnam (...) and van Fraassen in their debate over ‘fictionalism'. I will argue that, in this situation, there is a great mystery over what would separate a fictionalist F from a realist R. Neither Putnam nor van Fraassen seems to be conscious of the problems involved.Fictionalism, according to its opponent, Putnam, statesvarious entities presupposed by scientific and common sense discourse [are] merely “useful fictions”, or that we cannot, at any rate, possibly know that they are more than “useful fictions”. (shrink)

In 1932, John von Neumann argued for the equivalence of the thermodynamic entropy and −Trρlnρ, since known as the von Neumann entropy. Meir Hemmo and Orly R. Shenker recently challenged this argument by pointing out an alleged discrepancy between the two entropies in the single-particle case, concluding that they must be distinct. In this article, their argument is shown to be problematic as it allows for a violation of the second law of thermodynamics and is based on an (...) incorrect calculation of the von Neumann entropy. (shrink)

In this work R. M. Martin carries his semiotical studies into the fields of intensional semantics and pragmatics, dealing with such philosophically important concepts as meaning, preference, reasonableness and indifference. The crucial notion is that of the meaning or intension of an expression. Two major categories are distinguished, objective intensions and subjective intensions. To deal with objective intensions an intensional semantics is developed as an extension of denotational semantics in the tradition of Tarski, Carnap and Martin's earlier Truth and Denotation. (...) In the treatment of subjective intensions Martin makes an advance over his earlier study of pragmatics by utilizing the work of von Neumann and Morgenstern in their Theory of Games and Economic Behavior.—R. H. K. (shrink)

A revised and expanded version of studies by McKinsey, Winet and the authors, in axiomatic theories of value, together with a report of experiments designed to test the formal theories. This volume makes an important contribution to the theoretical and experimental investigation of values and decision-making, both of which subjects are still in their infancy. Experimental studies by Mosteller and Nogee and theoretical discussions of von Neumann and Morgenstern are criticized and improved. Ch. IV contains original suggestions for a (...) theory of utility involving incomparable values. -- A. R. A. (shrink)

In this work R. M. Martin carries his semiotical studies into the fields of intensional semantics and pragmatics, dealing with such philosophically important concepts as meaning, preference, reasonableness and indifference. The crucial notion is that of the meaning or intension of an expression. Two major categories are distinguished, objective intensions and subjective intensions. To deal with objective intensions an intensional semantics is developed as an extension of denotational semantics in the tradition of Tarski, Carnap and Martin's earlier Truth and Denotation. (...) In the treatment of subjective intensions Martin makes an advance over his earlier study of pragmatics by utilizing the work of von Neumann and Morgenstern in their Theory of Games and Economic Behavior.—R. H. K. (shrink)

This paper addresses the doubts voiced by Wigner about the physical relevance of the concept of geometrical points by exploiting some facts known to all but honored by none: Almost all real numbers are transcendental; the explicit representation of any one will require an infinite amount of physical resources. An instrument devised to measure a continuous real variable will need a continuum of internal states to achieve perfect resolution. Consequently, a laboratory instrument for measuring a continuous variable in a finite (...) time can report only a finite number of values, each of which is constrained to be a rational number. It does not matter whether the variable is classical or quantum-mechanical. Now, in von Neumann’s measurement theory (von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, [1955]), an operator A with a continuous spectrum—which has no eigenvectors—cannot be measured, but it can be approximated by operators with discrete spectra which are measurable. The measurable approximant F(A) is not canonically determined; it has to be chosen by the experimentalist. It is argued that this operator can always be chosen in such a way that Sewell’s results (Sewell in Rep. Math. Phys. 56: 271, [2005]; Sewell, Lecture given at the J.T. Lewis Memorial Conference, Dublin, [2005]) on the measurement of a hermitian operator on a finite-dimensional vector space (described in Sect. 3.2) constitute an adequate resolution of the measurement problem in this theory. From this follows our major conclusion, which is that the notion of a geometrical point is as meaningful in nonrelativistic quantum mechanics as it is in classical physics. It is necessary to be sensitive to the fact that there is a gap between theoretical and experimental physics, which reveals itself tellingly as an error inherent in the measurement of a continuous variable. (shrink)

The object of this article is to set forth certain evidence that emerges from a study of three of Plutarch's Lives, the Titus, the Paullus, and the Cato Maior, evidence which indicates that these Lives are based upon a definite type of biographical composition, and to suggest its possible origin and date. Since E. Meyer's article on the Cimon of Nepos and Plutarch, biographical sources have generally been assumed for the Greek Lives, and there has been a tendency to (...) make the same assumption for the Roman Lives also, without, however, setting forth the evidence that might justify it. Uxkull Gyllenband maintained that biographies of Greeks and Romans, the sources of Plutarch, were written in the second century b.c., but he gives no evidence for his contention, which is indeed refuted by the observations of Jacoby. Mühl argued with some force that Plutarch's source for the Marcellus was a biography. There is good reason to doubt his conclusion that Plutarch has used a biography of Poseidonius; but the arguments advanced by Klotz for the thesis that the source was the annalist Valerius Antias are still less convincing. Liedmeier postulates a biographical source for the Paullus, but without doing more than asserting the general improbability that Plutarch here used a multiplicity of sources. It seems therefore desirable to collect such evidence as there is of a biographical source in these three Roman Lives of the second century b.c., and it is with such an attempt rather than with a priori considerations that I am here concerned. (shrink)

I have taken such pains to indicate the scope, terms, and foci of Neumann's analysis because he provides one of the main pillars on which any further systematic study of the woman hero must rest. By showing Psyche's relation to the mythic or archetypal structure of heroism, by demonstrating the particular ways in which the hero is a figure distinguished primarily by involvement in particular patterns of action and psychological development, Neumann provides an invaluable service to further studies (...) of literature, heroism, and women. Without belaboring the distinction between the hero and the heroine, Neumann validates the claim that a woman can be a hero and eliminates the awkward distinction between the heroine as heroic figure and the heroine as conventional woman that has perplexed so much recent literary, especially feminist, analysis.1 He is also very good at locating the details in Psyche's dilemma that constitute significant associative images within a narrative representing heroism by means of a female character. Specifically, he indicates how Psyche's beauty is as much a burden as a boon, shows the importance of her relationship to other female characters, and points out the ways in which the apparent hostility of other women acts as a necessary goad to Psyche's own developing independence. Neumann's analysis is also suggestive in showing the appropriateness of archetypal criticism to material which is not myth in the narrow sense. To be sure, Apuleius' Amor and Psyche results from the distillation of narratives whose origins are clearly to be found in the folklore and functioning mythologies of Greek and Roman culture; just as clearly, however, Apuleius is telling his tale as part of a highly self-conscious, complexly structured narrative2 analogous, in some ways, to Chaucer's Canterbury Tales, Bunyan's Pilgrim's Progress, Milton's great religious epics, and even that seemingly least mythic set of narrative structures, the novel. · 1. See, e.g., Ellen Moers' long discussion of "heroinism" in Literary Women: The Great Writers , pp. 113-242. Moers' use of this awkward term, the female version of the presumably masculine heroism, perpetuates the idea that only men can be true heroes, while extraordinary women remain "special cases" necessitating special terminology.· 2. See P. G. Walsh, The Roman Novel: The 'Satyricon' of Petronius and the 'Metamorphoses' of Apuleius , pp. 141-223. Lee R. Edwards is an editor of The Massachusetts Review and an associate professor of English at the University of Massachusetts at Amherst. She is presently completing The Labors of Psyche: Female Heroism and Fictional Form. (shrink)

Elsasser outlines in an informal but meticulous fashion an organismic biology which promises, in his opinion, to combine the best features of epigenetic vitalism and preformationist mechanism. Mechanistic reductionism is for Elsasser an unverifiable metaphysical hypothesis; i.e., if the postulate of infinite homogenous classes is dropped from the axiomatics of Van Neumann's proof that the state of any system is, in principle, Quantum Mechanically determinable, it becomes combinatorically obvious that biological systems and classes are radically inhomogenous [[sic]], a fact (...) which operationally bars the way to any complete reductionism. The door is thus opened to an open-ended theoretical biology in which all questions do not have a truth-functional equivalent answer according to the axioms and laws of the science, and prediction in the science becomes statistical in a nonabsolute way. Elsasser is a physicist with more than a casual acquaintance with biology and his argument benefits by his obvious expertise in both of these areas. Philosophically, however, he is a lightweight and relies, in particular, too much on the ontological ice that might be cut by operationalism. Theories are not verified in the stringent operational sense; they are confirmed in a way which is not logically tied to the requirement that all laws be inductively established. Elsasser, however, has so much to say on the problem of reductionism in biology that is of obvious value that the book is easily recommended over these caveats.—E. A. R. (shrink)

For the probabilistic description of all the joint von Neumann measurements on a D-dimensional quantum system, we present the specific example of a context-invariant quasi hidden variable model, proved in Loubenets to exist for each Hilbert space. In this model, a quantum observable X is represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual model, each of these random variables equivalently models X under all joint von (...) class='Hi'>Neumann measurements, regardless of their contexts. This, in particular, implies the specific local qHV model for an N-qudit state and allows us to derive the new exact upper bound on the maximal violation of 2\2-setting Bell-type inequalities of any type under N-partite joint von Neumann measurements on an N-qudit state. For d = 2, this new upper bound coincides with the maximal violation by an N-qubit state of the Mermin–Klyshko inequality. Based on our results, we discuss the conceptual and mathematical advantages of context-invariant and local qHV modelling. (shrink)

We highlight methodological and theoretical limitations of the authors' Dirac formalism and suggest the von Neumann open systems approach as a resolution. The open systems framework is a generalization of classical probability and we hope it will allow cognitive scientists to extend quantum probability from perception, categorization, memory, decision making, and similarity judgments to phenomena in learning and development.

I must start with an apologia. My original paper, ``Minds, Machines and Gödel'', was written in the wake of Turing's 1950 paper in Mind, and was intended to show that minds were not Turing machines. Why, then, didn't I couch the argument in terms of Turing's theorem, which is easyish to prove and applies directly to Turing machines, instead of Gödel's theorem, which is horrendously difficult to prove, and doesn't so naturally or obviously apply to machines? The reason was that (...) Gödel's theorem gave me something more: it raises questions of truth which evidently bear on the nature of mind, whereas Turing's theorem does not; it shows not only that the Gödelian well-formed formula is unprovable-in-the-system, but that it is true. It shows something about reasoning, that it is not completely rule-bound, so that we, who are rational, can transcend the rules of any particular logistic system, and construe the Gödelian well-formed formula not just as a string of symbols but as a proposition which is true. Turing's theorem might well be applied to a computer which someone claimed to represent a human mind, but it is not so obvious that what the computer could not do, the mind could. But it is very obvious that we have a concept of truth. Even if, as was claimed in a previous paper, it is not the summum bonum, it is a bonum, and one it is characteristic of minds to value. A representation of the human mind which could take no account of truth would be inherently implausible. Turing's theorem, though making the same negative point as Gödel's theorem, that some things cannot be done by even idealised computers, does not make the further positive point that we, in as much as we are rational agents, can do that very thing that the computer cannot. I have however, sometimes wondered whether I could not construct a parallel argument based on Turing's theorem, and have toyed with the idea of a von Neumann machine. A von Neumann machine was a black box, inside which was housed John von Neumann.. (shrink)

We show that the so-called quantum probabilistic rule, usually introduced in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is commonly accepted, in contrast to the rule for the addition of probabilities of mutually exclusive events. The latter is valid under all experimental situations upon classical and quantum systems. We discuss also the quantum measurement situation that is similar to the classical one, described by the (...) Bayes formula. We show the compatibility of the description of this quantum measurement situation in the frame of purely classical and experimentally justified straightforward frequency arguments and in the frame of the quantum stochastic approach to the description of generalized quantum measurements. In view of derived results, we argue that even under experiments upon classical systems the classical Bayes formula describes particular experimental situations that are specific for context-independent measurements. The similarity of the forms of the relation between the transformation of probabilities, which we derive in the frame of the quantum stochastic approach and in the frame of the approach, based on straightforward frequency arguments, underlines once more that the projective (von Neumann) measurements represent only a special type of measurement situations in quantum physics. (shrink)

We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the map sending an L-structure R to the L-structure of definable functions from R n to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an extra (...) condition such as continuity. (shrink)

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG, it may be said to contain (...) “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas $\mathbb{R}$should merely be regarded as constituting an arithmetic continuum, No may be regarded as a sort of absolute arithmetic continuum, and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)

In order to understand the various strands of general equilibrium theory, why it has taken the forms that it has since the time of Léon Walras, and to appreciate fully a view of the state of general equilibrium theorising, it is essential to understand Walras's work and examine its influence. The first section of this book accordingly examines the foundations of Walras's work. These include his philosophical and methodological approach to economic modelling, his views on human nature, and the basic (...) components of his general equilibrium models. The second section examines how the influence of his ideas has been manifested in the theorising of his successors, surveying the models of theorists such as H. L. Moore, Vilfredo Pareto, Knut Wicksell, Gustav Cassel, Abraham Wald, John von Neumann, J. R. Hicks, Kenneth Arrow, and Gerard Debreu. The treatment also examines models of many types in which Walras's influence is explicitly acknowledged. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific (...) inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

contents -/- ONT vol 1 i. short review: Beyond the Black Rainbow ii. as you die, hold one thought iii. short review: LA JETÉE -/- ONT vol 2 i. maya means ii. short review: SANS SOLEIL iii. vocab iv. eros has an underside v. short review: In the Mood for Love -/- ONT vol 3 i. weed weakens / compels me ii. an Ender's Game after-party iii. playroom is a realm of the dead iv. a precise german History v. short (...) review: STATUES ALSO DIE vi. Kenneth Clark, curator for Fascism vii. a protest poem, in industry lit viii. Lawrence and the English Romance -/- ONT vol 4 i. short review: The Eyes of Tammy Faye ii. vR is efficient R iii. all thru Asia, robes for monks iv. same of God, and of the one God sent v. i thought of the Messiah / muse would be vi. conscience is strong vii. a monk's exalted end -/- ONT vol 5 -/- i. for Shakespeare's Richard the Third ii. the truth is i pass over so many words iii. the boori nazar / nadhar iv. i've awe for jihaad v. short review: Hail, Caesar! vi. a minute of Nothing, gone from YouTube vii. we were rivalrous friends, again viii. my bardo pdf ix. within i'm a weak old mandarin -/- ONT vol 6 i. short review: The Intern ii. the confusion of Chinatown iii. we'll remember water, in Theology iv. Respironics versus ResMed v. i'd bet my life for what vi. the Mad Max deity vii. they'd kill my rat, not heal him -/- ONT vol 7 i. Austen would eroticize all life ii. Merchant/Ivory, a name oddly right iii. Ellie Arroway / Agent Starling iv. abattoir / l’abattoir / laboratoire v. von Neumann's brain an anomaly vi. was terrified of death, delighted in the a-bomb vii. the Greatest Brain is variously named -/- ONT vol 8 i. the day they shot the sacrifice ii. Yay or Nay, on Animal Testing iii. an ought is an is / an is is an ought iv. Behaviorism is for zombies v. a finding from the neuro-lab, on empathy vi. i’ve never had discernible abs vii. a cowardice i'm assenting to perpetually -/- ONT vol 9 i. Day of the Locust / Triffids ii. we're wide on a Paramount soundstage iii. HOLLYWOOD, an ecologic history iv. yet one more site of end-time art v. he's "a bookworm with bulging lobes" vi. apartment is my state of being apart vii. enlightenment means a weight's release -/- ONT lates and xtras i. re Gödel's ontological argument ii. deep in pi's numeric noise iii. from Nothing, something iv. endless in the wrong direction, tragic v. they give you all Eternity to answer vi. what of God's mercy? vii. informed consent and prayer viii. i won't live on. a deed i've done may ix. my selective memory x. Janus means: in close-up foam, two faces xi. a liveable world is a readable world xii. what Supervenes from this? xiii. at each extreme our naming is anachronism xiv. Cat is a collapsing of the wave-function xv. diminishing returns in the history of Experiment xvi. all those undershared Nobels xvii. ice preserves the Cold from heat xviii. a desert spreads xix. Pinker's wit, on jokes xx. Rome surrounds St. Paul / Paul is now the center xxi. each is a gathering Ministry xxii. white boy shot execution-style xxiii. the McDonald's Statement of Claim xxiv. first & last: Don Quixote / Ulysses xxv. The Summer of Rave xxvi. this electro is intrinsically anonymous xxvii. all thru Asia, Drake-Rihanna xxviii. WHO IS BETTER: PLATON OR KANT? (shrink)

This book contains a collection of papers from the 1985, 1987 and 1989 Australian Lonergan Workshops. Contents: A Summary of Lonergan's Economic Diagram, S.P. Burley; How Lonergan Illuminates Aristotle, T.V. Daly, S.J.; Lonergan and the Philosophy of Science, Dr. W.J. Danaher; "Transubstantiation Over Transsignification": Giovanni Sala and Edward Schillebeeckx on the Eucharistic Presence, P. Beer, S.J.; Schillebeeckx's Philosophic Prologomenon: A Dialectic Analysis, Dr. N. Ormerod; Mutual Self-Mediation with Christ, F. Fletcher, M.S.C.; The Integration of Trinitarian Theology and Spirituality, Bishop J. (...) Bathersby; A Von Neumann Representation of Lonergan's Production Model, S.P. Burley; Chemistry and Insight, Dr. W.J. Danaher; Rediscovering Philosophies through Cognitional Models, T. Daly, S.J.; The Holy Spirit and Lonergan's Psychological Analogy, P. Beer, S.J.; Lonergan and Finnis on the Human Good, Dr. N. Ormerod; A Response to Lonergan and Finnis, Rev. G. Moses; Insight in Science, Dr. W.J. Danaher; Learning-Levels, T.V. Daly, S.J.; Lonergan as a Neo-Schumpeterian, S.P. Burley; Bernard Lonergan, Mechanism and Evolution, L. Drake, S.J.; Can I Be Certain That I Am Justified?, P. Beer, S.J.; The A Priori in Human Knowledge: A Critique of Kant from the Point of View of Lonergan's Insight, M. Brennan, R.C.S.J.; The Foundational Theologian as Prophet, F. Fletcher, M.S.C. (shrink)

An ancient tale retold, by R. M. MacIver.--On deceiving the public for the public good, by L. Bryson.--Fact, fiction, and reality, by F. E. Johnson.--On the justifiable grounds of disobedience to law, by R. N. Baldwin.--On the limits of justifiable disobedience, by F. L. Neumann.--On the enlistment of dubious allies, by H. Simons.--On "Making friends with the mammon of unrighteousness," by L. Pope.--The Hiroshima issue, by W. W. Waymack.--Institutionalism and the faith, by L. Finkelstein.--Freedom and interference in American education, (...) by O. Tead.--Private profit and public interest in mass communication, by R. Saudek.--The threat to privacy, by H. D. Lasswell. (shrink)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. (...) Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $\dot{\alpha}$ of the parameter α is the order of magnitude $\dot{\alpha}=-H_0 \alpha$ , where H0 is the instantaneous value of the Hubble constant: $H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$ . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. (shrink)

We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every infinite cardinal (...) κ, the class HCκ of all κ-hereditary sets is a set with von Neumann rank ϱ ≤ κ+. Moreover, ϱ = κ+ if and only if κ is singular, otherwise ϱ = κ. The statements of the corollary are well known in the presence of the axiom of choice . To prove them without AC - as carried through here - is, however, much harder. A special case of the corollary has been treated independently by T. JECH. (shrink)

Ethical mysticism, by S. Coit.--The ethical import of history, by D. S. Muzzey.--The tragic and heroic in life, by W. M. Salter.--Distinctive features of the ethical movement, by A. W. Martin.--Ethical experience as the basis of religious education, by H. Neumann.--"All men are created equal," by G. E. O'Dell.--How far is art an aid to religion? by P. Chubb.--Evolution and the uniqueness of man, by H. J. Bridges.--The spiritual outlook on life, by H. J. Golding.--The ethics of Abu'l Ala (...) al Ma'arri, by N. Schmidt.--Life's unused moral force, by H. Snell.--Is the ideal real? by G. A. Smith.--Some ethical tendencies in the professions, by R. D. Kohn.--On the art of living, by W. Boerner.--The relation of the ethical ideal to social reform, by J. L. Elliott.--Concerning tolerance, by R. F. Dewey.--Ethical culture in Germany after the war, by R. Penzig.--A confession of faith, by S. B. Weston.--"Hearing the witnesses," by J. Gutmann. (shrink)