In this article it is shown that a careful analysis of Kant 's Gedanken von der wahren Schätzung der lebendigen Kräfte und Beurtheilung der Beweise leads to a conclusion that does not match the usually accepted interpretation of Kant 's reasoning in 1747, according to which the young Kant supposedly establishes a relationship between the tridimensionality of space and Newton's law of gravitation. Indeed, it is argued that this text does not yield a satisfactory explanation of space dimensionality, and actually (...) restricts itself to justifying the tridimensionality of extension. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 106 Heft: 4 Seiten: 547-560.

Ever since Copernicus, scientists have continually adjusted their view of human nature, moving it further and further from its ancient position at the center of Creation. But in recent years, a startling new concept has evolved that places it more firmly than ever in a special position. Known as the Anthropic Cosmological Principle, this collection of ideas holds that the existence of intelligent observers determines the fundamental structure of the Universe. In its most radical version, the Anthropic Principle asserts that (...) "intelligent information-processing must come into existence in the Universe, and once it comes into existence, it will never die out." This wide-ranging and detailed book explores the many ramifications of the Anthropic Cosmological Principle, covering the whole spectrum of human inquiry from Aristotle to Z bosons. Bringing a unique combination of skills and knowledge to the subject, John D. Barrow and Frank J. Tipler--two of the world's leading cosmologists--cover the definition and nature of life, the search for extraterrestrial intelligence, and the interpretation of the quantum theory in relation to the existence of observers. The book will be of vital interest to philosophers, theologians, mathematicians, scientists, and historians, as well as to anyone concerned with the connection between the vastness of the universe of stars and galaxies and the existence of life within it on a small planet out in the suburbs of the Milky Way. (shrink)

Comprehensive coverage of the special theory (frames of reference, Lorentz transformation, relativistic mechanics of mass points, more), the general theory ...

And the first step of the Peripatetick argument is that, where Aristotle proveth the integrity and perfection of the World, telling us, that it is not a simple line, nor a bare superficies, but a body adorned with Longitude, Latitude and Profundity; and because there are no more dimensions but these three; the World having them, hath all, and having all, is to be concluded perfect. And again, that by simple length, that magnitude is constituted, which is called a line, (...) to which adding breadth, there is formed a Superficies, and yet further adding the altitude or profundity, there results the Body, and after these three the dimensions there is no passing farther, so that in these three the integrity, and to so speak, totality is terminated, which I might but with justice have required Aristotle to have proved to me by necessary consequences, the rather in regard he was able to do it very plainly and speedily. *Received 9. iii. 54. (shrink)

Some brief remarks are made on the relation between the ordering and dimensionality properties of time and the laws of physics. Time is defined as the ordinal of the set of photographs describing the configuration of the Universe associated with each collision of a test particle. This set of pictures is ordered by a parameter which appears in simple physical laws, and it is these laws which determine the ordering. Time is one-dimensional because these snapshots can be ordered with a (...) single parameter. The signature of space-time appears to be related to the measurement process. If there were no time dimension, there would probably be no physical laws, because there would seem to be nothing to predict: while if there were more than one timelike dimension, then the extra dimensions may be unobservable and so physically nonexistent. (shrink)

Introduction.--Thoughts on the true estimation of living forces (selected passages)--On the first ground of the distinction of regions in space.--Dissertation on the form and principles of the sensible and intelligible world.

Part two of the proceedings of the fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada, August 27 - September 2, 1975.

Why is space 3-dimensional? The fi rst answer to this question, entirely based on Physics, was given by Ehrenfest, in 1917, who showed that the stability requirement for n-dimensional two-body planetary system very strongly constrains space dimensionality, favouring 3-d. This kind of approach will be generically called "stability postulate" throughout this paper and was shown by Tangherlini, in 1963, to be still valid in the framework of general relativity as well as for quantum mechanical hydrogen atom, giving the same constraint (...) for space{dimensionality. In the present work, before criticizing this methodology, a brief discussion has been introduced, aimed at stressing and clarifying some general physical aspects of the problem of how to determine the number of space dimensions. Then, the epistemological consequences of Ehrenfest's methodology are critically reviewed. An alternative procedure to get at the proper number of dimensions, in which the stability postulate - and the implicit singularities in three-dimensional physics - are not an essential part of the argument, is proposed. In this way, the main epistemological problems contained in Ehrenfest's original idea are avoided. The alternative methodology proposed in this paper is realized by obtaining and discussing the n-dimensional quantum theory as expressed in Planck's law, de Broglie relation and the Heisenberg uncertainty relation. As a consequence, it is possible to propose an experiment, based on thermal neutron di raction by crystals, to directly measure space dimensionality. Finally the distinguished role of Maxwell's electromagnetic theory in the determination of space dimensionality is stressed. (shrink)

The catchy term "anthropic cosmological principle" embraces a medley of arguments ranging from a mere observation selection effect (the universe must not be such to rule out our existence) to design arguments and an explicit cosmic teleology. This narrow focus neglects that anthropic reasoning reaches back even to late 19th century pre-relativistic physics--at about the same time when there was renewed interest in the principle of least action--and that it emerged in the context of speculations about the cosmological consequences of (...) the second law of thermodynamics. Stefano Bettini’s contribution offers a historical tour through the various applications of the design argument until Carter enunciated the anthropic principle in the context of a very specific physical problem. Subsuming anthropic reasoning under formal teleology, accordingly, does not require invoking any kind of cosmic purpose. Rather, fine-tuning represents a variation argument that distinguishes the actual universe am. (shrink)

L'idea di relazionare la dimensionalità dello spazio ad una legge fisica, contenuta nel primo scritto di Kant "Pensieri sulla veridica estima delle forze vive", svela un modo di guardare i rapporti tra Fisica e Matematica così nuovo ed originale che potè essere sviluppato e compreso nella sua plenitudine soltanto nel secolo XX. Ci riferiamo qui ala prospettiva aperta da Ehrenfest nel suo "In what way does it become manifest in the fundamental laws of physics that space has three dimensions?". In (...) questo saggio si cerca di comprendere alcune delle radici fisiche, filosofiche e teologiche dell’approccio di Kant a questo problema, e la sua inserzione nel dibattito delle idee che sostengono la concezione meccanicista del Mondo. In primo luogo, si sottolinea che da una lettura attenta del suo Gedanken von der wahren Schätzung der lebendigen Kräfte si può concludere che - al contrario di quanto viene normalmente creduto - Kant non riuscì a dimostrare la sua congettura che la tridimensionalità dello spazio possa essere fondata sulla legge di gravitazione di Newton, secondo la quale la forza tra due corpi va come l'inverso del quadrato della distanza che li separa; in realtà, egli si limitò a giustificare la tridimensionalità della estensione. Dopo aver considerato la distinzione fra estensione e spazio, si fa notare che la catena logica della congettura del giovane Kant, presuppone la forza come concetto basilare, intrinseco alle sostanze. È mediante questa forza che si stabiliscono le relazioni tra le sostanze, le quali, a sua volta, creano l'ordine su cui viene basato il concetto di spazio. Si deve badare che la coerenza del suo argomento richiede, in ultima analisi, concepire la percezione, cioè, l'interazione fra le sostanze e l'anima, come risultato della medesima forza di lunga portata. Inoltre, si dimostra che l'argomento di Kant non poteva essere costrutto su una intelaiatura puramente newtoniana nel 1747. Infatti, egli costruì sua dimostrazione a partire da una concezione del mondo basata sul legato di Cartesio (soprattutto l'idea di um ordine cosmico) e Leibniz (l'esistenza di una forza che precede l'estensione e l'idea di spazio relativo) alla quale sovrappone, in modo ibrido, la legge di gravitazione di Newton. Si argomenta che questa scelta fu fortemente influenzata da alcune idee teologiche del Giovane Kant che divergono da quelle di Cartesio, Newton e Leibniz. Fu questo carattere ibrido del suo approccio che permise a Kant di trattare la questione della dimensionalità dello spazio come un problema di fisica, ma, che, allo stesso tempo, a causa delle sue limitazioni intrinsiche, portò Kant a provare appena la tridimensionalità della estensione. (shrink)

Metascientific criteria used for explaining or constraining physical space dimensionality and their historical relationship to prevailing causal systems are discussed. The important contributions by Aristotle, Kant and Ehrenfest to the dimensionality of space problem are considered and shown to be grounded on different causal explanations: causa materialis for Aristotle, causa efficiens for young Kant and an ingenious combination of causa efficiens and causa formalis for Ehrenfest. The prominent and growing rôle played by causa formalis in modern physical approaches to this (...) problem is emphasized. (shrink)