It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein’s equations. The fact that Einstein’s general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in \ for both (...) the \ invariant and the Euler invariant can only be achieved for N-extended supergravity multiplets with \. (shrink)

Die folgende Darstellung geht davon aus: I) so sehr die Sprache der Dichtung ein ernst zu nehmendes Problem der Sprachphilosophie ist, so darf doch nicht umgekehrt unter der letzteren ein Dichten und Raunen über die Sprache ver­ standen werden. Kants Entscheidung für prosaische, nicht für poetische Philosophie bleibt Vorbild. Einzig und allein das Nüchterne zählt. 2) Wenn es scheinen könnte, dass verschie­ dene deutsche Darstellungen der Sprachphilosophie aus den letzten ] ahren ausgerechnet auf diesem Gebiet der Philoso­ phie dem, was (...) nach den Klassikern und nicht von ihnen her kommt, relativ wenig Raum und Gewicht geben, so liegt es im Sinn dieses Buches, gerade umgekehrt zu verfahren. 3) Ein Verhältnis befremdlich und betrüblich geringer gegenseitiger Berücksichtigung zwischen deutschsprachiger Literatur über Sprache und der ins riesenhafte angewachsenen nichtdeut­ schen Literatur darüber ruft nach Abhilfe. Es werden im fol­ genden die Brücken zwischen deutschsprachigen und in der nichtdeutschen westlichen Welt dominanten Darstellungen bevorzugt gewürdigt. 4) Die Abgrenzung der Schrift gegen Logistik und Informationstheorie, die sich als selbständige Gebiete mit eigenen Methoden konstituiert haben, ist klar. Ebenso, dass umfassende Philosophien des zwanzigsten] ahr­ hunderts - wie diejenigen Husserls, Whiteheads, Moores, Russells, Croces, Heideggers, ] aspers', Nicolai Hartmanns- in ihrer Ganzheit an anderer Stelle zu behandeln sind, mögen sie auch gleichzeitig spezifische Quellen der Sprach-Philo­ sophie unseres] ahrhunderts sein. (shrink)

The semantic confusion in Europe about the term “anthropology” has of late been considerable. On the one hand there is meant by it, and quite justifiably, human biology and medical anthropology. On the other hand, the work of some contemporary thinkers, under the name of “philosophical anthropology,” has recently gone beyond the narrower compass. This has been noticeable at both the German and the international European philosophical conventions since the last war. In addition to this, there appeared the term “Kulturanthropologie,”—for (...) the first time probably as the title of E. Rothacker's contribution to Systematische Philosophie, a collection of essays edited by Nicolai Hartmann and published in 1942. But “Kulturanthropologie,” in Rothacker's sense, is not a translation of “cultural anthropology,” which has in recent years grown to such eminence among scholarly fields in England and America. In the United States, “anthropology” designates a group of scholarly fields ranging on the one hand from biological anthropology to archaeology and the study of the beginnings of history on the other, often including history, linguistics, and other realms of research; it is neither one of the natural sciences nor of the humanities but one of the social sciences; and the actually new results of this young discipline, especially at Harvard, Yale, and the University of Chicago, are arrived at by means of team work by anthropologists, psychologists, and sociologists, which in Germany has not been the case so far. (shrink)

This article is of both a historical and philosophical nature. It aims to present the intellectual relationship between the Spanish philosopher José Ortega y Gasset and one of the most influential German thinkers of the first half of the twentieth century, Nicolai Hartmann. It is based on hitherto unknown and unpublished correspondence that the philosophers conducted intermittently between 1907 and 1912. The correspondence was found in the archives of the José Ortega y Gasset – Gregorio Marañón Foundation in Madrid (...) along with other letters that show the relationship between the Spanish author and representatives of the neo-Kantian Marburg School, including its founder Hermann Cohen, as well as Paul Natorp, Ernst Cassirer, and Heinz Heimsoeth. (shrink)

The founders of the Marburger Schule of Neo-Kantianism, Hermann Cohen and Paul Natorp, laid an emphasis upon a Platonic understanding of mathematics and logic as the paradigmatic epistemological basis of philosophy. Their successors, namely Ernst Cassirer and Nicolai Hartmann, made obvious, however, that new biological thinking can have a strong influence on ontology as well as on the theory of knowledge. They could show that biology was no longer to be treated as a metaphysical system in that pejorative (...) meaning of metaphysics which Kant had so severely been opposing. Against the anti-realistic approach of the older neo-Kantians who wanted to eliminate Kant's thing-in-itself (Ding an sich), both Cassirer and Hartmann returned to a form of realism by way of Hegel's philosophical results and reflections on his method. This makes clear that their realism is still to be taken as a more of less monistic idealism. However, considering that modern biology as an antimetaphysical force became influential in their system for the first time and that it did so in two different but - on second thoughts - complementary ways, it becomes clear that it was necessary to change the paradigms of any neo-Kantian philosophy. Cassirer proved this by his development as a philosopher with a strong historical impetus while Hartmann as a more systematical philosopher only pointed in that direction. (shrink)

There is considerable evidence that listeners’ understanding of a spoken sentence need not always follow from a full analysis of the words and syntax of the utterance. Rather, listeners may instead conduct a superficial analysis, sampling some words and using presumed plausibility to arrive at an understanding of the sentence meaning. Because this latter strategy occurs more often for sentences with complex syntax that place a heavier processing burden on the listener than sentences with simpler syntax, shallow processing may represent (...) a resource conserving strategy reflected in reduced processing effort. This factor may be even more important for older adults who as a group are known to have more limited working memory resources. In the present experiment, 40 older adults and 20 younger adults were tested for comprehension of plausible and implausible sentences with a simpler subject-relative embedded clause structure or a more complex object-relative embedded clause structure. Dilation of the pupil of the eye was recorded as an index of processing effort. Results confirmed greater comprehension accuracy for plausible than implausible sentences, and for sentences with simpler than more complex syntax, with both effects amplified for the older adults. Analysis of peak pupil dilations for implausible sentences revealed a complex three-way interaction between age, syntactic complexity, and plausibility. Results are discussed in terms of models of sentence comprehension, and pupillometry as an index of intentional task engagement. (shrink)

Nicolai Bachman explores the key principles and concepts of yoga philosophy through the Yoga Sutras offering an opportunity to learn and practice the sutras in Sanskrit, revealing the essence of yoga philosophy. The Yoga Sutras is a comprehensive and modern approach to working with Patanjali's seminal text for guidance and inspiration on your own journey toward clarity and happiness.

Philosophy &Public Affairs, Volume 51, Issue 2, Page 140-165, Spring 2023.

Any account of “what is special about the human brain” (Passingham 2008) must specify the neural basis of our unique ability to produce speech and delineate how these remarkable motor capabilities could have emerged in our hominin ancestors. Clinical data suggest that the basal ganglia provide a platform for the integration of primate-general mechanisms of acoustic communication with the faculty of articulate speech in humans. Furthermore, neurobiological and paleoanthropological data point at a two-stage model of the phylogenetic evolution of this (...) crucial prerequisite of spoken language: (i) monosynaptic refinement of the projections of motor cortex to the brainstem nuclei that steer laryngeal muscles, presumably, as part of a “phylogenetic trend” associated with increasing brain size during hominin evolution; (ii) subsequent vocal-laryngeal elaboration of cortico-basal ganglia circuitries, driven by human-specificFOXP2mutations.;>This concept implies vocal continuity of spoken language evolution at the motor level, elucidating the deep entrenchment of articulate speech into a “nonverbal matrix” (Ingold 1994), which is not accounted for by gestural-origin theories. Moreover, it provides a solution to the question for the adaptive value of the “first word” (Bickerton 2009) since even the earliest and most simple verbal utterances must have increased the versatility of vocal displays afforded by the preceding elaboration of monosynaptic corticobulbar tracts, giving rise to enhanced social cooperation and prestige. At the ontogenetic level, the proposed model assumes age-dependent interactions between the basal ganglia and their cortical targets, similar to vocal learning in some songbirds. In this view, the emergence of articulate speech builds on the “renaissance” of an ancient organizational principle and, hence, may represent an example of “evolutionary tinkering” (Jacob 1977). (shrink)

RésuméL'idée d'un “monde des images” situé quelque part entre les mondes immatériel et matériel est un pivot de la spéculation eschatologique dans l'Islam médiéval tardif. Comme cela a déjà été reconnu, le concept a été inauguré par al-Suhrawardī. Cependant, ses fondements plus proprement philosophiques et en particulier la notion d'images “suspendues” – des images dotées d'un statut en quelque manière objectif plutôt que purement mental ou subjectif – méritent d’être davantage clarifiés; et c'est ce que cet article entend faire. Puisque (...) le concept de “formes suspendues”, tout en étant appliqué par al-Suhrawardī à des questions eschatologiques dans le dernier traité de sa Philosophie de l'illumination, apparaît pour la première fois dans une discussion sur la vision spéculaire, j'examine assez en détail la conception avicennienne de la vision spéculaire telle qu'elle est présentée dans le Shifāʾ, ouvrage contre lequel al-Suhrawardī réagit. J'entreprends ensuite une reconstruction détaillée de deux paragraphes de la Philosophie de l'illumination en accordant une attention particulière à la question du statut ontologique des images “suspendues” ou “auto-subsistantes” ainsi qu’à l'idée selon laquelle les miroirs servent non pas de lieux dans lesquels les images résideraient, mais de lieux où elles deviennent manifestes. (shrink)

English summary: With his research on early Greek philosophy, Hermann Diels created the definitive works of his era, and his Fragments of the Presocratics remains the standard work on the topic. However, the scholar never published a panorama of his unmatched knowledge. For the first time, a transcript of the lecture in which Diels represented his vision of Hellenic thought is now available. The script from the 1897/98 winter semester documents the oratory and pedagogy of the great Hellenist and (...) was provided by one of his exceptional students, the Munich-based Egyptologist Friedrich Wilhelm von Bissing. Diels proved himself as a clear-headed thinker discussing the historical course of early proverbial wisdom, the natural and political theory of Plato, and the conceptual precision of Aristotle. Central figures such as Anaximander, Heraclitus, Parmenides, and Democritus are concisely drawn and colored. Thus the text offers an absorbing picture of the origins of theoretical consciousness in Europe. German text. German description: Mit seinen Forschungen zur fruehgriechischen Philosophie hat Hermann Diels Epoche gemacht; seine aFragmente der Vorsokratiker sind weiterhin das Standardwerk zum Thema. Nie jedoch hat der Gelehrte ein Panorama seines unerreichten Wissens veroffentlicht. Erstmals wird nun eine Mitschrift jener Vorlesung zuganglich, in der Diels seine Sicht des hellenischen Denkens darstellte. Das Skript aus dem Wintersemester 1897/98 dokumentiert vorzueglich Sprachkraft und Padagogik des grossen Grazisten; es stammt von einem Ausnahme-Studenten, dem spateren Muenchner Agyptologen Friedrich Wilhelm von Bissing.Im historischen Gang von frueher Spruchweisheit bis zur Natur- und Staatslehre Platons und der begrifflichen Prazisionsarbeit des Aristoteles hebt Diels besonders das Fortwirken grosser Denkmuster hervor. Zentrale Gestalten wie Anaximander, Heraklit, Parmenides oder Demokrit sind pragnant und farbig gezeichnet. So bietet der Text ueber seinen fachhistorischen Wert hinaus ein fesselndes Bild der Urspruenge theoretischen Bewusstseins in Europa. (shrink)

Conscious existence is the product of a neural brain mechanism, which is largely identical with Immanuel Kant's Oneness Function, a service performed by 200 million neurons in the prefrontal lobe, & makes possible our interior cosmos, the record of our interconnected, or general, experience. Essential for us humans is the well-being of our interior cosmos, or Saint Teresa of Avila's interior castle, in all interactions with each other \& the greater environment. Any disorders of our cosmos are liable to make (...) us fall ill, setting our existence on a path of psychosomatic etiology of a large class of mysterious undiagnosed diseases. (shrink)

Recent advances in neuroscience lead to a wider realm for philosophy to include the science of the Darwinian-evolved computational brain, our inner world producing organ, a non-recursive super- Turing machine combining 100B synapsing-neuron DNA-computers based on the genetic code. The whole system is a logos machine offering a world map for global context, essential for our intentional grasp of opportunities. We start from the observable contrast between the chaotic universe vs. our orderly inner world, the noumenal cosmos. So far, philosophy (...) has been rehearsing our thoughts, our human-internal world, a grand painting of the outer world, how we comprehend subjectively our experience, worked up by the logos machine, but now we seek a wider horizon, how humans understand the world thanks to Darwinian evolution to adapt in response to the metaphysical gap, the chasm between the human animal and its environment, shaping the organism so it can deal with its variable world. This new horizon embraces global context coded in neural structures that support the noumenal cosmos, our inner mental world, for us as denizens of the outer environment. Kant’s inner and outer senses are fundamental ingredients of scientific philosophy. Several sections devoted to Heidegger, his lizard debunked, but his version of the metaphysical gap & his doctrine of the logos praised. Rorty and others of the behaviorist school discussed also. (shrink)

Impressions, energy radiated by phenomena in the momentary environmental scene, enter sensory neurons, creating in afferent nerves a data stream. Following Kant, by our inner sense the mind perceives its own thoughts as it ties together sense data into an internalized scene. The mind, residing in the brain, logically a Language Machine, processes and stores items as coded grammatical entities. Kantian synthetic unity in the linguistic brain is able to deliver our experience of the scene as we appear to see (...) it. Uniquely, the brain records its own history, synthesizing a Movie-in-the-Brain, called the Noumenal Cosmos. Attempting thereby to represent the actual Universe, this makes for a sovereign brain that governs itself. The brain is domicile of an Ego, with its selfhood at stake at all times. Yet, it can know itself only by its actions, in which it appears as an actor in its own movie. Phenomena enter garbled, as confused apparitions, and must be put in good form using top–down feedback control by Ego, so that each movie frame makes rational sense within the overall context of the Noumenal Cosmos. A stack of frames is processed typically in 40 Hz rhythm with 300 ms process time each, for about 12 in the stack at any time. Successive neural centers are processing the stack in the brain assembly line, based on data from increasingly global receptive fields. Ego stitches together the movie frames, but only the top frame is in consciousness for 25 ms. The top frame contains the whole scene where the Ego makes an appearance as the actor that imposes Kantian synthetic unity on the scene, merely an assembly of grammatical texts, in a system-internal coded process language, fitting the scene into the Noumenal Cosmos. But Ego observes Ego only to the extent permitted by the objectivity rule, only what it does and thinks, not its true face. From the Noumenal Cosmos, the Ego receives grammatical messages in the internal sense code. They are integrated into a whole in the reaction of the Ego to the momentary scene. The voluntary nature of Ego’s decisions is explained, based on its ability to code in advance its own actions sequentially in time, as it sees fit with a view to an orderly Noumenal Cosmos, records of code being arranged spatially in neural structures. (shrink)

Das Gewissen spielt im Leben und Werk von John Henry Newman eine zentrale Rolle. Seine Lehre uber das Gewissen ist im allgemeinen bekannt und anerkannt. Ebenso charakteristisch ist fur ihn aber das Streben nach dem Licht der Wahrheit. Der Autor behandelt in dieser Studie das Verhaltnis von Gewissen und Wahrheit bei Newman: ein Thema, das in dieser Weise in der Newman-Forschung bisher nicht erortert worden ist; ein Thema, das im Kontext der heute um sich greifenden Subjektivierung und Autonomisierung des Gewissens (...) von grundlegender Bedeutung ist.". (shrink)

This book is the scholarly & fully annotated edition of the award-winning _The Illustrated To Think Like God.__ _To Think Like God_ focuses on the emergence of philosophy as a speculative science, tracing its origins to the Greek colonies of Southern Italy, from the late 6th century to mid-5th century B.C. Special attention is paid to the sage Pythagoras and his movement, the poet Xenophanes of Colophon, and the lawmaker Parmenides of Elea. In their own ways, each thinker held that (...) true insight, whether as wisdom or certainty, belonged not to mortal human beings but to the gods. The Pythagoreans sought to approach this otherwordly knowledge by studying numerical relationships, believing them to govern the universe, and that those who know the number of a thing know its true nature. Yet their quest was a hopeless one, bogged down by cultism, numerology, political conspiracies, bloody uprisings, and exile. Above all, number did not turn out as the most reliable of mediums; it was certainly not a key to the realm of the divine. Thus, their contributions to philosophy's inception, while much better-publicized, was not the most significant. That particular role was reserved for an unusual challenge and the elaborate reaction it provoked. The challenge came from Xenophanes, who had argued that reliable truth was beyond mortal reach, because even if by accident a human being should state what is exactly the case, he had no way of knowing that he did, all things being susceptible to opinion. This dilemma is sure to have bothered a legislative mind like that of Parmenides, and we find him introducing techniques for testing the veracity of statements. These methods were meant to be carried out by reasoning and argument alone, without relying in physical evidence or mortal sense-perception, which was deemed untrustworthy. Reason was that one faculty shared by gods and humans alike. In time, Parmenides' ingenious arguments have earned him the titled of the first logician and metaphysician whose influence on subsequent thinkers was immeasurable. Parmenides taught us that philosophy was not about claims but about proof, which also makes him the father of theoretical science -- which, curiously, began as a quest into the mind of God. "Arnold Hermann makes a genuine contribution to Presocratics studies. This book, which is both an introduction to Pythagoras and Parmenides and a scholarly study, will interest novices and experts alike. Hermann's multi-leveled approach and his careful analyses of alternate views make his work a useful teaching tool, while his systematic inquiry into Pythagoreanism, the poem of Parmenides, and the development of early Greek thought will well repay the attention of scholars. — Patricia Curd_,_ _Purdue University_ "_To Think Like God_ is a highly ambitious book... Hermann's approach deserves to be taken seriously as an alternative to standard interpretations." — Richard D. McKirahan, Jr.,___ __Edwin Clarence Norton Professor of Classics and Professor of Philosophy, Pomona College_ "Arnold Hermann brings fresh life into the specialists' debates... a blow of wind that dissipates much fog." — Walter Burkert_, Professor Emeritus of Classical Philology, University of Zurich_ ARNOLD HERMANN_ is pursuing independent research on the origins of philosophy and methods of thinking. He specialices on subjects connected with Parmenides and Plato's _Parmenides._. (shrink)

Drawing on recent phenomenological discussions of collective intentionality and existential phenomenological accounts of agency, this article proposes a novel interpretation of shared action. First, I argue that we should understand action on the basis of how an environment pre-reflectively solicits agents to behave based on (a) the affordances or goals inflected by their abilities and dispositions and (b) their self-referential commitment to a project that is furthered by these affordances. Second, I show that this definition of action is sufficiently flexible (...) to account for not only individual action (in which both (a) and (b) refer only to an individual) but also several distinct subtypes of shared action. My thesis is that behaviour counts as shared action if and only if it is caused by a solicitation in which either (a) the goals, or (b) the commitments, or both (a) goals and (b) commitments are joint, i.e., depend on several individuals. We thereby get three distinct subtypes of shared actions: (i) jointly coordinated individually committed action, (ii) individually coordinated jointly committed action, and (iii) jointly coordinated jointly committed action. (shrink)

Outlines of Metaphysic - dictated portions of the lectures of Hermann Lotze is an unchanged, high-quality reprint of the original edition of 1884. Hansebooks is editor of the literature on different topic areas such as research and science, travel and expeditions, cooking and nutrition, medicine, and other genres. As a publisher we focus on the preservation of historical literature. Many works of historical writers and scientists are available today as antiques only. Hansebooks newly publishes these books and contributes to (...) the preservation of literature which has become rare and historical knowledge for the future. (shrink)

Name der Zeitschrift: Archiv für Geschichte der Philosophie Jahrgang: 98 Heft: 3 Seiten: 272-301.

This essay reviews two recent volumes containing editions of important early quranic codices. One of these is the so-called Sanaa Palimpsest, whose lower text at present remains our only known material witness to a recension of the quranic text that is different from the canonical one; the other is the Codex Amrensis. The essay devotes particular attention to the question of the textual relationship between the Quran’s standard text and that documented by the lower layer of the Sanaa Palimpsest, and (...) to Asma Hilali’s claim that the Sanaa Palimpsest never constituted a full quranic codex but only “a collection of disparate leaves.”. (shrink)

This article proposes to interpret Surah 97 based on research undertaken in the framework of the Corpus Coranicum project. The first part scrutinizes Christopn Luxenberg’s seriously flawed argument that Surah 97 can be understood as a Qur’anic hymn on the Nativity of Jesus if some of its key expressions are read against the semantic background of Syriac, while the remainder of the article endeavours to develop a more tenable understanding of the text. This involves an attempt to date Surah 97 (...) relative to other Qur’anic texts and to detect possible additions to it. In addition, the article discusses the meaning and reference of its most central term, laylat al-qadr. Finally, special attention is given to the question whether the text might not, in spite of the circularity of Luxenberg’s reading, contain implicit references to the Nativity. (shrink)

What is commonly referred to as the Adoption Problem is a challenge to the idea that the principles of logic can be rationally revised. The argument is based on a reconstruction of unpublished work by Saul Kripke. As the reconstruction has it, Kripke extends the scope of Willard van Orman Quine's regress argument against conventionalism to the possibility of adopting new logical principles. In this paper we want to discuss the scope of this challenge. Are all revisions of logic subject (...) to the Adoption Problem? If not, are there significant cases of logical revision that are subject to the Adoption Problem? We will argue that both questions should be answered negatively. (shrink)

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...) of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

In this essay, our goal is to discover science in Martin Heidegger's Introduction to Metaphysics, lecture notes for his 1935 summer semester course, because, after all, his subject is metaphysica generalis, or ontology, and this could be construed as a theory of the human brain. Here, by means of verbatim quotes from his text, we attempt to show that indeed these lectures can be viewed as suggestion for an objective scientific theory of human perception, the human capacity for deciphering phenomena, (...) ie. hermeneutics in its broadest sense. His added notes from the 1953 edition, all of which are comments, not corrections, imply that he never abandoned these thoughts on metaphysics, despite all of his utterances about a need to overcome it, and their popular interpretations to that effect. In his presentation, he further develops the colorful and intuitive style, an hermeneutic language, that he had created in his earlier work Being and Time. Of human existence he speaks in such expressions as being-there -- ``Dasein" -- and being-in-the-world, the latter term no longer explicit in the 1935 lectures. The lectures can be read as a pre-scientific analysis of how man, being-there, perceives his environment, artfully managing to deal with the manifold challenges posed by the phenomenal structures of the universe. Man attentively recognizes and deciphers their pre-linguistic contents and, while trying to make sense of it all, puts into words his awareness. There are numerous passages in Heidegger's work where he in fairly concrete terms provides us with hints for a perceptive science that, as it turns out and is demonstrated below in this essay, can be explained in terms of recent advances in neuroscience. It would be implausible, even unthinkable, unimaginable, for there not to be found essential agreement between on one hand his philosophical insights gained by hermeneutics of Dasein, into how our brain functions to let us know what's happening & on the other hand, scientific discoveries obtained through anatomy, EEG, fMRI, TMS, electrode implants, etc, of brain structures & functions employed in perception of the momentary scene. A nexus between science and philosophy is provided in Heidegger's definitive treatment of the Logos, here interpreted as a structural version of Platonic forms (Burchard, 2014). This allows for neurolinguistic brain functions to serve as meta-context for Heidegger's being-in-the-world. The logical functions of Dasein's anatomical brain are performed by the logos machine, formerly the human soul, using top-down processing based on a global context, the noumenal cosmos which humans maintain internally. Heidegger's 1942/43 winter semester lectures Parmenides extend in unbroken fashion his 1935 work, proving that he never abandoned, as is widely claimed, his metaphysical avenue of thought. (shrink)

The ancient dualism of a sensible and an intelligible world important in Neoplatonic and medieval philosophy, down to Descartes and Kant, would seem to be supplanted today by a scientific view of mind-in-nature. Here, we revive the old dualism in a modified form, and describe mind as a symbolic language, founded in linguistic recursive computation according to the Church-Turing thesis, constituting a world L that serves the human organism as a map of the Universe U. This methodological distinction of L (...) vs. U helps to understand how and why structures of phenomena come to be opposed to their nature in human thought, a central topic in Heideggerian philosophy. U is uncountable according to Georg Cantor’s set theory but Language L, based on the recursive function system, is countable, and anchored in a Gray Area within U of observable phenomena, typically symbols, prelinguistic structures, genetic-historical records of their origins. Symbols, the phenomena most familiar to mathematicians, are capable of being addressed in L-processing. The Gray Area is the human Environment E, where we can live comfortably, that we manipulate to create our niche within hostile U, with L offering overall competence of the species to survive. The human being is seen in the light of his or her linguistic recursively computational mind. Nature U, by contrast, is the unfathomable abyss of being, infinite labyrinth of darkness, impenetrable and hostile to man. The U-man, biological organism, is a stranger in L-man, the mind-controlled rational person, as expounded by Saint Paul. Noumena can now be seen to reside in L, and are not fully supported by phenomena. Kant’s noumenal cause is the mental L-image of only partly phenomenal causation. Mathematics occurs naturally in pre-linguistic phenomena, including natural laws, which give rise to pure mathematical structures in the world of L. Mathematical foundation within philosophy is reversed to where natural mathematics in the Gray Area of pre-linguistic phenomena can be seen to be a prerequisite for intellectual discourse. Lesser, nonverbal versions of L based on images are shared with animals. (shrink)

Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice function. (...) This results in a concise and uncomplicated proof of the Well-Ordering Theorem. (shrink)