Gegenüber den Ansichten vonCharles Richet , sowie auch die gegensätzliche, die von E.Meyerson , bei Seite lassend, hebt der Verfasser hervor, dass gerade auf dem Gebiete der Biologie vollständig identische Gebilde, Merkmale oder Erscheinungen, so zu sagen mit mathematischer Notwendigkeit, auftreten müssen, falls die Verterbung der Merkmale, die sich auf dem Wege der geschlechtlichen Fortpflanzung abspielt und derMendel-Gesetzen unterworfen ist, auf das Verfahren desNewton'schen Binoms zurückzuführen ist. Die entwickelte Reihe dieses letzteren — in deren Gliedern vertreten — stellt dann ein (...) zusammengesetztes Beispiel einer eigenartigen biologischen Multiplizierung dar, die die Entstehung der natürlichen homogenen Gruppen von sogenannten Binomionen verursacht.Jede einzelne derselben setz sich bekanntlich aus vollständig identischen Individuen zusammen, die in durch die binomische Regel festgesetzten, genau bestimmten Häufigkeiten auftreten und lauter aus dem Verfahren der Multiplizierung der teilnehmenden Elementen in allen gegebenen Gliedern jeder beliebigen Reihe herrühren können.Die eventuelle Entstehung etwaiger kleinsten individuellen Differenzen in auf solche Weise entstandenen vollständig identischen Gebilden ist als Folge der allmählichen Vertiefung unseres Erkenntnissverfahrens, bzw. diagnostischer Analyse zu deuten, in welcher mit immer kleiner und kleiner werdenden — materiellen oder energetischen — Einheiten gearbeitet wird.Zum Schluss, sich auf wenige hauptsächlich beiläufig ausgewählte Beispiele aus den Gebieten der Astronomie, der Chemie, der Embryologie, der Anthropologie, der Soziologie, der Logik und der Philosophie stützend, sucht der Verfasser zu beweisen, dass in der modernen Wissenschaft überhaupt eine allgemeine Tendenz herrscht die Schlüsse auf die Wechselwirkung der Factoren, bzw. auf den Prinzip der Komplexität , als einer grundsetzlichen Eigenschaft jeder wissenschaftlichen Methode, zurückzuführen.While refuting the standpoint taken byCharles Richet and simultaneously setting aside the contrary view ofEmil Meyerson , the author argues that in biology the perfectly identical creatures, features or phenomena must occur, so to say by virtue of mathematical necessity, if the inheritance of features through the course of sexual propagation, governed by the laws ofMendel, is proceeding according to the rules ofNewton's binomial. Then the expanded series of the latter brings us the expression of some sort of biological multiplication, which — in their successive terms — leads to the origin of natural groups of so called binomions , each of which being composed of identical individuals, appearing in the exactly definite frequencies, issuing from the very procedure of multiplication of the factors, partaking in those series in any given term.Again, the possibility of ascertaining the eventual, if any, individualising differencies in the identical so originated beings is explained by the author as being actually due to the gradual deepening of our diagnosing analysis, by the use of which the more and more minute units, material or energetic ones, are introduced.Finally, referring to the few, mostly incidentally chosen, examples taken from astronomy, chemistry, embryology, anthropology, sociology, logic and philosophy, the author calls the attention to the fact that the modern science shows a general tendency towards the foundation of its conclusions on the interaction of factors and on the use of the general “principle of complexity” as an obligatory course of very scientific methodology. (shrink)

Using the results of the latest neurophysiological research on colour, the article rejects outright physicalism and dispositionalism as appropriate approaches to solving the problem of colour realism. Physicalism sees colour as a real property of objects, i.e. the reflectance profile, while dispositionalism takes subjects, objects and light as necessary elements for colour production. First, it briefly outlines the historical development of the theory of colour, pointing towards dispositionalism which, in some sense, considers colour as a real entity of the world, (...) and then introduces the problem of colour realism, focusing on objections to physicalism as well as dispositionalism. After delineating the neurophysiological mechanisms underlying the visual experience of colour, and with the help of the concrete results of practical neurophysiological experiments, the article points to why the physicalist and any dispositionalist theories of colour in the light of a new physiological objection do not present credible views on the nature of colour. (shrink)

In contrast to Christian theology that has ignored science, this essay suggests that a credible doctrine of God as creator must take into account scientific understandings of the world. The introduction of the principle of inertia into seventeenth‐century science and philosophy helped change the traditional idea of God as creator (which included divine conservation and governance) into a deist concept of God. To recapture the idea that God continually creates, it is important to affirm the contingency of the world as (...) a whole and of all events in the world. Reflecting on the interrelationship of contingency and natural law provides a framework for relating scientific theories of a universal field, the concept of emergent evolution, and the theological concept of eternal divine spirit active in all creation. (shrink)

In the following paper, the author will try to test the meaning of the transcendental approach in respect of the inner changes implied by the idea of quantum gravity. He will firstly describe the basic methodological Kant’s aim, viz. the grounding of a meta-science of physics as the a priori corpus of physical knowledge. After that, he will take into account the problematic physical and philosophical relationship between the theory of relativity and the quantum mechanics; in showing how the elementary (...) ontological and epistemological assumptions of experience result to be changed within them, he will also show the further modifications occurred in the development of the loop quantum gravity. He will particularly focus on the tough problem of the relationship space-matter, in order to settle the decisive question about the possibility of keeping a transcendental approach in the light of quantum gravity. He will positively answer by recalling Cassirer’s theory of the invariants of experience, although he will also add some problematic issues arising from the new physical context. (shrink)

The “unknown heritage” is the name usually given to a problem type in whose archetype a father leaves to his first son 1 monetary unit and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{n}}$$\end{document} (n usually being 7 or 10) of what remains, to the second 2 units and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{n}}$$\end{document} of what remains, and so on. In the end, all sons get the same, and nothing remains. The earliest known (...) occurrence is in Fibonacci’s Liber abbaci, which also contains a number of much more sophisticated versions, together with a partial algebraic solution for one of these and rules for all which do not follow from his algebraic calculation. The next time the problem turns up is in Planudes’s late thirteenth century Calculus according to the Indians, Called the Great. After that the simple problem type turns up regularly in Provençal, Italian and Byzantine sources. It seems never to appear in Arabic or Indian writings, although two Arabic texts (one from c. 1190) contain more regular problems where the number of shares is given; they are clearly derived from the type known from European and Byzantine works, not its source. The sophisticated versions turn up again in Barthélemy de Romans’ Compendy de la praticque des nombres (c. 1467) and, apparently inspired from there, in the appendix to Nicolas Chuquet’s Triparty (1484). Apart from a single trace in Cardano’s Practica arithmetice et mensurandi singularis, the sophisticated versions never surface again, but the simple version spreads for a while to German practical arithmetic and, more persistently, to French polite recreational mathematics. Close examination of the texts shows that Barthélemy cannot have drawn his familiarity with the sophisticated rules from Fibonacci. It also suggests that the simple version is originally either a classical, strictly Greek or Hellenistic, or a medieval Byzantine invention; and that the sophisticated versions must have been developed before Fibonacci within an environment (located in Byzantium, Provence, or possibly in Sicily?) of which all direct traces has been lost, but whose mathematical level must have been quite advanced. (shrink)

This paper examines the logical and metaphysical consequences of denying Leibniz's Law, the principle that if t1= t2, then φ(t1) if and only if φ(t2). Recently, Caie, Goodman, and Lederman (2020) and Bacon and Russell (2019) have proposed sophisticated logical systems permitting violations of Leibniz's Law. We show that their systems conflict with widely held, attractive principles concerning the metaphysics of individuals. Only by adopting a highly revisionary picture, on which there is no finest-grained equivalence relation, can a well-motivated metaphysics (...) for rejecting Leibniz's Law be developed. We sketch one such picture—a metaphysics of stuff. Stuff ontologies can be initially motivated through ordinary language: stuff stands to mass nouns as objects stand to count nouns. The stuff ontology we propose takes stuff to be fundamental and views the world as composed of an infinite descending hierarchy of kinds and portions of stuff. We defend the coherence of this picture and offer a model theory demonstrating that it can be consistently formalized. (shrink)