What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...) higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...) and well-ordering -- and implying an ordinal re-creation of the continuum. During the last hundred years, the mainstream set-theoretical research -- all insights and adjustments due to Kurt G\"odel's revolutionary insights and discoveries notwithstanding -- has compliantly centered its efforts on ad hoc axiomatizations of Cantor's intuitive transfinite design. We demonstrate here that the ontological and epistemic sustainability} of this design has been irremediably compromised by the underlying peremptory, Reductionist mindset of the XIXth century's ideology of science. (shrink)

We present here a biblical exegesis of the value of Pi, PI_{Hebrew} = 3.141509 ..., from the well known verse 1 Kings 7:23. This verse is then compared to 2 Chronicles 4:2; the comparison provides independent supporting evidence for the exegesis.

Guessing the outcome of iterations of even most simple arithmetical functions could be an extremely hazardous experience. Not less harder, if at all possible, might be to prove the veracity of even a "sure" guess concerning iterations : this is the case of the famous 3x+1 conjecture. Our purpose here is to study and conceptualize some intuitive insights related to the ultimate (un)solvability of this conjecture.

The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear.

The enigma of the Emergence of Natural Languages, coupled or not with the closely related problem of their Evolution is perceived today as one of the most important scientific problems. The purpose of the present study is actually to outline such a solution to our problem which is epistemologically consonant with the Big Bang solution of the problem of the Emergence of the Universe}. Such an outline, however, becomes articulable, understandable, and workable only in a drastically extended epistemic and scientific (...) oecumene, where known and habitual approaches to the problem, both theoretical and experimental, become distant, isolated, even if to some degree still hospitable conceptual and methodological islands. The guiding light of our inquiry will be Eugene Paul Wigner's metaphor of ``the unreasonable effectiveness of mathematics in natural sciences'', i.e., the steadily evolving before our eyes, since at least XVIIth century, ``the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics''. Kurt Goedel's incompleteness and undecidability theory will be our guardian discerner against logical fallacies of otherwise apparently plausible explanations. John Bell's ``unspeakableness'' and the commonplace counterintuitive character of quantum phenomena will be our encouragers. And the radical novelty of the introduced here and adapted to our purposes Big Bang epistemological paradigm will be an appropriate, even if probably shocking response to our equally shocking discovery in the oldest among well preserved linguistic fossils of perfect mathematical structures outdoing the best artifactual Assemblers. (shrink)

Scientific enterprise is a part and parcel of the contemporaneous to it general human cultural and, even more general, existential endeavor. Thus, the fundamental for us notion of evolution, in the modern sense of this characteristically Occidental term, appeared in the 19-th century, with its everything pervading, irreversible cultural and technological change and the existential turmoil. Similarly, a formerly relatively recherché word emergence, became a widely used scientific term only in the 20-th century, with its cultural, economical, political, and national (...) sagas of emergence and destruction played against a background of the universe emerging from the Big Bang and disappearing into its black holes, if not into its ultimate Big Collapse. Today, the rules of engagement in scientific emergence-evolution games, steadily spreading from natural to cognitive sciences, and beyond, are dominated by the 19-th century concept of natural selection which has inverted the time-arrow of the classical creationist dogma, with its rarely spelled out pessimistic implication that the life is moving from the highest biological organization to an entropic chaos. In its turn, the natural selection’s excessively contagious, “do-it-yourself” optimism might ultimately turn out to be its undoing : the natural selection conjecture, when transposed to such fields as linguistics from the strictly biological scene, with its times of engagement ranging from at most hundred years of life expectancy for an individual organism to at least millions and even billions of years for evolutionary processes to bring this or that organism to existence, becomes for the first time verifiable and even falsifiable. The present paper studies some implications of the well-known but almost universally disregarded tight combinatorial morphological-semantic structure of the verbal system of Biblical Hebrew, to show that this linguistic fossil testifies to the existence of a now extinct Proto-Language whose extremely tight verbal organization and meaningful architecture made it both structurally strikingly similar and expressively vastly superior to humanly designed Assembler languages, – an absolutely novel, paradoxical phenomenon, never before and nowhere else observed and apparently incompatible with the basic tenets of modern linguistic natural selection theories and, at the very least, crying out for new explanatory linguistic paradigms. (shrink)

"The definitive clarification of the nature of the infinite has become necessary, not merely for the special interests of the individual sciences, but rather for the honour of the human understanding itself. The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have ; but also the infinite, more than other notion, is in need of clarification." (David Hilbert 1925).

Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: algorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their cyclic and divergent properties.

The problem of the emergence and evolution of natural languages is seen today by many specialists as one of the most difficult problems in the cognitive sciences. We believe that a key to unravelling this enigma is the close relationship of language to mathematics.

Biblical Hebrew, BH, could be seen as primarily a verbal language [1], with an average verse of the Hebrew Bible containing no less than three verbs and with the biggest part of its vocabulary representing morphological derivations from verbal roots, almost entirely triliteral, or triconsonantal, – the feature BH shares with all Semitic and a few other Afro- Asiatic languages. The unique peculiarity of this triconsonantal morphological pervasiveness did not completely escape the attention of previous generations of Western linguists, as (...) shows the following “methodological” warning opening a popular Hebrew grammar edited more than a century ago: «The roots, whatever may have been their original form, are in the Old Testament almost entirely triliteral, ... thus imposing upon the memory a very heavy strain. ... Every verb has to be learned separately; the verbs to go out, to go up, to go down are quite different, having nothing in common with one another and being quite unrelated to the verb to go.» This amusing résumé has the merit to recognize, even if under the guise of an earnestly banal pedagogical clueing in, two extraordinary fundamental linguistic phenomena common to all Semitic languages, the very objects of the present study. (shrink)

In the search of new approaches to the problem of emergence and evolution of natural languages, Mathematics, Theoretical Computer Science, as well as Molecular Biology and Neuroscience, both deeply penetrated and profoundly inspired by concepts originated in Mathematics and Computer Science, represent today the richest pools of formal concepts, structures, and methods to borrow and to adapt.

In the search of new approaches to the problem of emergence and evolution of natural languages, Mathematics, Theoretical Computer Science, as well as Molecular Biology and Neuroscience, both deeply penetrated and profoundly inspired by concepts originated in Mathematics and Computer Science, represent today the richest pools of formal concepts, structures, and methods to borrow and to adapt.

As organizational leaders worry about the appalling low percentage of people who feel engaged in their work, academics are trying to understand what causes an increase in engagement. We collected survey data from 231 team members from two organizations. We examined the impact of team members’ emotional intelligence (EI) and their perception of shared personal vision, shared positive mood, and perceived organizational support (POS) on the members’ degree of organizational engagement. We found shared vision, shared mood, and POS have a (...) direct, positive association with engagement. In addition, shared vision and POS interact with EI to positively influence engagement. Besides highlighting the importance of shared personal vision, positive mood, and POS, our study contributes to the emergent understanding of EI by revealing EI’s amplifying effect on shared vision and POS in relation to engagement. We conclude by discussing the research and practical implications of this study. (shrink)

What Science Offers the Humanities examines some of the deep problems facing the study of culture. It focuses on the excesses of postmodernism, but also acknowledges serious problems with postmodernism's harshest critics. In short, Edward Slingerland argues that in order for the humanities to progress, its scholars need to take seriously contributions from the natural sciences - and particular research on human cognition - which demonstrate that any separation of the mind and the body is entirely untenable. The author (...) provides suggestions for how humanists might begin to utilize these scientific discoveries without conceding that science has the last word on morality, religion, art, and literature. Calling into question such deeply entrenched dogmas as the 'blank slate' theory of nature, strong social constructivism, and the ideal of disembodied reason, What Science Offers the Humanities replaces the human-sciences divide with a more integrated approach to the study of culture. (shrink)

Introduction §1. 1s PHILOSOPHY FINISHED? Has philosophy now nearly completed its twenty-five hundred years of service to humanity? Has it only a few last remaining tasks of analysis and clarification to perform before its career is ...

Mind and Body in Early China critiques Orientalist accounts of early China as a radical "holistic" other, which saw no qualitative difference between mind and body. Drawing on knowledge and techniques from the sciences and digital humanities, Edward Slingerland demonstrates that seeing a difference between mind and body is a psychological universal, and that human sociality would be fundamentally impossible without it. This book has implications for anyone interested in comparative religion, early China, cultural studies, digital humanities, or science-humanities (...) integration. (shrink)

CHAPTER I INTRODUCTION: A NEW UNIVERSITY AND THE CHALLENGE OF THE NEW SCIENCE Despite the recent and continuing controversy concerning the proper role of ...

When Heidegger's influence was at its zenith in Germany from the early fifties to the early sixties, most serious students of philosophy in that country were deeply steeped in his thought. His students or students of his students filled many if not most of the major chairs in philosophy. A cloud of reputedly Black Forest mysticism veiled the perspective of many of his critics and admirers at home and abroad. Droves of people flocked to hear lectures by him that most (...) could not understand, even on careful reading, much less on one hearing. He loomed so large that Being and Time frequently could not be seen as a highly imaginative, initial approach to a strictly limited set of questions, but was viewed either as an all-embracing first order catastrophy incorporating at once the most feared consequences of Boehme, Kierkegaard, Rilke, and Nietzsche, or as THE ANSWER. But most of that has past. Heidegger's dominance of German philosophy has ceased. One can now brush aside the larger-than-life images of Heidegger, the fears that his language was creating a cult phenomenon, the convictions that only those can understand him who give their lives to his thought. His language is at times unusually difficult, at times simple and beautiful. Some of his insights are obscure and not helpful, others are exciting and clarifying. One no longer expects Heidegger to interpret literature like a literary critic or an academic philologist. (shrink)

Aesthetics, fledgling of the philosophic brood, is the most suspect of that family. It is suspected of all the philosophical sins: vagueness, disorder, dogmatism, emotionalism, reductionism, compartmentalization. Sometimes its youth is thought to be a sufficient excuse for these divagations. Sometimes the very nature of its content, involving the waywardness of genius, the remoteness of feeling from intellect, the surd of inspiration in even the mildest appreciation, are believed to condemn aes thetics irrevocably to the underside of the civilized man's (...) domain. Some philosophers have gloried in this apparently mystical and a-rational quality and have seen in it the very nature of the beautiful; others have come to regard it, rather, as evidence of the unskillfulness of our minds and have turned away from aesthetic problems to the task of sharpening the aesthetician's language and logic. The laughter of the gods is not difficult to discern through the poetry of the more mystical aesthetician or through the prose of the analysts. Meanwhile the manifold complexities and problems of aesthetic experience invite our understanding. For aesthetic experience is a present fact of human life and may, perhaps, be understood by men. Such, at least, will be the present assumption. This is the reason why the title of this book mentions art together with analysis; for if art is intelligible, the work of art and the experience of it may be analyzed into its functional parts. (shrink)

There can be no question but that Lachelier exercised great influence over French philosophy. Gabriel Séailles notes it as do others. Boutroux remarked "il fut un excitateur singulièrement puissant des intelligences," and Benrubi places him with Ravaisson in initiating the tradition of spiritualistic positivism in France. Bergson also recognized and acknowledged his debt to Lachelier, although the tradition which Lachelier helped to father was opposed to Bergsonianism in many important respects. The two traditions can, I suggest, be recognized as dialectical (...) opposites of one another. (shrink)

The dual responsibility of maintaining our copies of ancient writings in a state in which they reflect their originals intelligibly and authentically and of reinterpreting these writings in a manner which is both faithful and useful to later generations and their problems is so demanding that it has very frequently seemed justly to call forth a division of labor. But the divorce between the scholar and the philosophical interpreter has not always been fertile, as the more pedantic and frantic interpretations (...) of Plato demonstrate. Professor Brumbaugh seeks to avoid the specialist's isolation by uniting the two functions in his Plato on the One. The result is the unusual combination of the soundest and most elaborate work on the text of the second part of the Parmenides, so far as I can determine, yet done in this country, and in addition some very imaginative and varied philosophical interpretations. (shrink)