Plotinus on the Soul's Omnipresence in Body
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
How Dualists Should (Not) Respond to the Objection from Energy
c 2019 Imprint Academic Mind & Matter Vol. 17(1), pp. 95–121 How Dualists Should (Not) Respond to the Objection from Energy Conservation Alin C. Cucu International Academy of Philosophy Mauren, Liechtenstein and J. Brian Pitts Faculty of Philosophy and Trinity College University of Cambridge, United Kingdom Abstract The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. 1. The Objection from Energy Conservation Formulated Among philosophers of mind and metaphysicians, it is widely believed that the principle of energy conservation poses a serious problem to inter- actionist dualism. Insofar as this objection afflicts interactionist dualisms, it applies to property dualism of that sort (i.e., not epiphenomenalist) as much as to substance dualism (Crane 2001, pp. -
Philosophy of Science and Philosophy of Chemistry
Philosophy of Science and Philosophy of Chemistry Jaap van Brakel Abstract: In this paper I assess the relation between philosophy of chemistry and (general) philosophy of science, focusing on those themes in the philoso- phy of chemistry that may bring about major revisions or extensions of cur- rent philosophy of science. Three themes can claim to make a unique contri- bution to philosophy of science: first, the variety of materials in the (natural and artificial) world; second, extending the world by making new stuff; and, third, specific features of the relations between chemistry and physics. Keywords : philosophy of science, philosophy of chemistry, interdiscourse relations, making stuff, variety of substances . 1. Introduction Chemistry is unique and distinguishes itself from all other sciences, with respect to three broad issues: • A (variety of) stuff perspective, requiring conceptual analysis of the notion of stuff or material (Sections 4 and 5). • A making stuff perspective: the transformation of stuff by chemical reaction or phase transition (Section 6). • The pivotal role of the relations between chemistry and physics in connection with the question how everything fits together (Section 7). All themes in the philosophy of chemistry can be classified in one of these three clusters or make contributions to general philosophy of science that, as yet , are not particularly different from similar contributions from other sci- ences (Section 3). I do not exclude the possibility of there being more than three clusters of philosophical issues unique to philosophy of chemistry, but I am not aware of any as yet. Moreover, highlighting the issues discussed in Sections 5-7 does not mean that issues reviewed in Section 3 are less im- portant in revising the philosophy of science. -
Matter and Minds: Examining Embodied Souls in Plato's Timaeus
Matter and Minds: Examining Embodied Souls in Plato’s Timaeus and Ancient Philosophy By Emily Claire Kotow A thesis submitted to the Graduate Program in Philosophy in conformity with the requirements for the Master of Arts Queen’s University Kingston, Ontario, Canada September, 2018 Copyright © Emily Claire Kotow, 2018 Abstract With the rise of Platonism influenced by Plotinus and Descartes, philosophers have largely overlooked the fact that Plato directly acknowledges that there is a practical and valuable role for the body. The Timaeus clearly demonstrates that Plato took the idea of embodied minds seriously, not just as an afterthought of the immortal soul. Ultimately this research demonstrates that Plato did not fundamentally have a problem with the mind-body relationship. In offering an argument for Plato’s positive ideas of embodied minds and the necessity thereof, I will also demonstrate, through a historical comparative, why I think the emphasis on mind rather than on embodied mind might have occurred. ii Acknowledgments I would like to thank Dr. Jon Miller and the Philosophy Department of Queen’s University for allowing me to pursue my interests freely -a great privilege that few are fortunate enough to experience. iii Table of Contents Abstract………………………………….………………………………….…………………………………. ii Acknowledgments………………………………….………………………………….………………….. iii Table of Contents………………………………….………………………………….…………………….iv Introduction………………………………….………………………………….……………………………5 Chapter One: Plato’s Embodied Soul.……………………………….……………………………12 i. Plato and -
The Modal Logic of Potential Infinity, with an Application to Free Choice
The Modal Logic of Potential Infinity, With an Application to Free Choice Sequences Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ethan Brauer, B.A. ∼6 6 Graduate Program in Philosophy The Ohio State University 2020 Dissertation Committee: Professor Stewart Shapiro, Co-adviser Professor Neil Tennant, Co-adviser Professor Chris Miller Professor Chris Pincock c Ethan Brauer, 2020 Abstract This dissertation is a study of potential infinity in mathematics and its contrast with actual infinity. Roughly, an actual infinity is a completed infinite totality. By contrast, a collection is potentially infinite when it is possible to expand it beyond any finite limit, despite not being a completed, actual infinite totality. The concept of potential infinity thus involves a notion of possibility. On this basis, recent progress has been made in giving an account of potential infinity using the resources of modal logic. Part I of this dissertation studies what the right modal logic is for reasoning about potential infinity. I begin Part I by rehearsing an argument|which is due to Linnebo and which I partially endorse|that the right modal logic is S4.2. Under this assumption, Linnebo has shown that a natural translation of non-modal first-order logic into modal first- order logic is sound and faithful. I argue that for the philosophical purposes at stake, the modal logic in question should be free and extend Linnebo's result to this setting. I then identify a limitation to the argument for S4.2 being the right modal logic for potential infinity. -
Cantor on Infinity in Nature, Number, and the Divine Mind
Cantor on Infinity in Nature, Number, and the Divine Mind Anne Newstead Abstract. The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristote- lian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian volunta- rist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Can- tor’s thought with reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspec- tives on the Actual Infinite”) (1885). I. he Philosophical Reception of Cantor’s Ideas. Georg Cantor’s dis- covery of transfinite numbers was revolutionary. Bertrand Russell Tdescribed it thus: The mathematical theory of infinity may almost be said to begin with Cantor. The infinitesimal Calculus, though it cannot wholly dispense with infinity, has as few dealings with it as possible, and contrives to hide it away before facing the world Cantor has abandoned this cowardly policy, and has brought the skeleton out of its cupboard. He has been emboldened on this course by denying that it is a skeleton. Indeed, like many other skeletons, it was wholly dependent on its cupboard, and vanished in the light of day.1 1Bertrand Russell, The Principles of Mathematics (London: Routledge, 1992 [1903]), 304. -
Leibniz and the Infinite
Quaderns d’Història de l’Enginyeria volum xvi 2018 LEIBNIZ AND THE INFINITE Eberhard Knobloch [email protected] 1.-Introduction. On the 5th (15th) of September, 1695 Leibniz wrote to Vincentius Placcius: “But I have so many new insights in mathematics, so many thoughts in phi- losophy, so many other literary observations that I am often irresolutely at a loss which as I wish should not perish1”. Leibniz’s extraordinary creativity especially concerned his handling of the infinite in mathematics. He was not always consistent in this respect. This paper will try to shed new light on some difficulties of this subject mainly analysing his treatise On the arithmetical quadrature of the circle, the ellipse, and the hyperbola elaborated at the end of his Parisian sojourn. 2.- Infinitely small and infinite quantities. In the Parisian treatise Leibniz introduces the notion of infinitely small rather late. First of all he uses descriptions like: ad differentiam assignata quavis minorem sibi appropinquare (to approach each other up to a difference that is smaller than any assigned difference)2, differat quantitate minore quavis data (it differs by a quantity that is smaller than any given quantity)3, differentia data quantitate minor reddi potest (the difference can be made smaller than a 1 “Habeo vero tam multa nova in Mathematicis, tot cogitationes in Philosophicis, tot alias litterarias observationes, quas vellem non perire, ut saepe inter agenda anceps haeream.” (LEIBNIZ, since 1923: II, 3, 80). 2 LEIBNIZ (2016), 18. 3 Ibid., 20. 11 Eberhard Knobloch volum xvi 2018 given quantity)4. Such a difference or such a quantity necessarily is a variable quantity. -
Theory of Forms 1 Theory of Forms
Theory of Forms 1 Theory of Forms Plato's theory of Forms or theory of Ideas[1] [2] [3] asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality.[4] When used in this sense, the word form is often capitalized.[5] Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt.[6] Plato spoke of Forms in formulating a possible solution to the problem of universals. Forms Terminology: the Forms and the forms The English word "form" may be used to translate two distinct concepts that concerned Plato—the outward "form" or appearance of something, and "Form" in a new, technical nature, that never ...assumes a form like that of any of the things which enter into her; ... But the forms which enter into and go out of her are the likenesses of real existences modelled after their patterns in a wonderful and inexplicable manner.... The objects that are seen, according to Plato, are not real, but literally mimic the real Forms. In the allegory of the cave expressed in Republic, the things that are ordinarily perceived in the world are characterized as shadows of the real things, which are not perceived directly. That which the observer understands when he views the world mimics the archetypes of the many types and properties (that is, of universals) of things observed. -
Lecture 9 Plato's Theory of Matter
Lecture 9 Plato's Theory of Matter Patrick Maher Scientific Thought I Fall 2009 Necessity and intellect Both play a role We must describe both types of causes, distinguishing those which possess understanding and thus fashion what is beautiful and good, from those which are devoid of intelligence and so produce only haphazard and disorderly effects every time. [46e] Timaeus calls these \intellect" and \necessity," respectively. Now in all but a brief part of the discourse I have just completed I have presented what has been crafted by Intellect. But I need to match this account by providing a comparable one concerning the things that have come about by Necessity. For this ordered world is of mixed birth: it is the offspring of a union of Necessity and Intellect. [47e] Contrast with Phaedo In Phaedo Socrates said he wanted to explain everything by showing it is for the best. In Timaeus's terminology, he wanted to explain everything by intellect. But Timaeus says that in addition to intellect there is necessity and we need to take account of both. Role of intellect in matter Use of Platonic solids The creator gave fire, air, earth, and water forms that make them as perfect as possible. The regular polyhedra are the best shapes, so he gave the elements those shapes. See diagrams. Tetrahedron: fire Octahedron: air Cube: earth Icosahedron: water Elementary triangles The faces of the tetrahedron, octahedron, and icosahedron are equilateral triangles. Timaeus says these triangles are composed of six smaller ones, each of which is half an equilateral triangle. The faces of the cube are squares. -
Ontologies and Representations of Matter
Ontologies and Representations of Matter Ernest Davis Dept. of Computer Science New York University [email protected] Abstract 2. Benchmarks We carry out a comparative study of the expressive We will use the following eleven benchmarks: power of different ontologies of matter in terms of the Part-Whole: One piece of matter can be part of another. ease with which simple physical knowledge can be rep- resented. In particular, we consider five ontologies of Additivity of Mass: The mass of the union of disjoint models of matter: particle models, fields, two ontolo- pieces of matter is the sum of their individual masses. gies for continuous material, and a hybrid model. We Rigid solid objects: A solid object moves continuously evaluate these in terms of how easily eleven benchmark and maintains a rigid shape. Two objects do not overlap. physical laws and scenarios can be represented. Continuous motion of fluids: The shape of a body of fluid deforms continuously. 1. Introduction Chemical reactions. One combination of chemicals can Physical matter can be thoughtof, and is thoughtof, in many transform into a different combination of chemicals. Chem- different ways. Determining the true ontology of matter is ical reactions obey the law of definite proportion. a question for physicists; determining what ontologies are Continuity at chemical reactions: In a chemical reac- implicit in the way people think and talk is a question for tion, the products appear at exactly the same time and place cognitive scientists and linguists; determining the history of as the reactants disappear. views of the true ontology is a question for historians of sci- Gas equilibrium: A gas in a stationary or slowly moving ence. -
The Cosmos and Theological Reflection: the Priority of Self-Transcendence Paul Allen
Document generated on 09/30/2021 12:09 p.m. Théologiques The Cosmos and Theological Reflection: The Priority of Self-Transcendence Paul Allen Les cosmologies Article abstract Volume 9, Number 1, printemps 2001 In this article, I argue that the primary significance of cosmology for theology is through a notion of self-transcendence. It is an inherently theological notion URI: https://id.erudit.org/iderudit/005683ar arising within cosmology. It points to the realm of interiority claimed by DOI: https://doi.org/10.7202/005683ar contemporary theology. Employing the thought of Ernan McMullin in particular, I claim that self-transcendence emerges within cosmological See table of contents inquiry when it becomes philosophy, and when extrapolation is involved. A theological thrust to cosmology is confirmed when one understands the limits of cosmology as an empirical discipline amidst the existential questions that can be posed about the meaning of the universe, a development well illustrated Publisher(s) by the anthropic principle. Faculté de théologie de l'Université de Montréal ISSN 1188-7109 (print) 1492-1413 (digital) Explore this journal Cite this article Allen, P. (2001). The Cosmos and Theological Reflection: The Priority of Self-Transcendence. Théologiques, 9(1), 71–93. https://doi.org/10.7202/005683ar Tous droits réservés © Faculté de théologie de l’Université de Montréal, 2001 This document is protected by copyright law. Use of the services of Érudit (including reproduction) is subject to its terms and conditions, which can be viewed online. https://apropos.erudit.org/en/users/policy-on-use/ This article is disseminated and preserved by Érudit. -
Measuring Fractals by Infinite and Infinitesimal Numbers
MEASURING FRACTALS BY INFINITE AND INFINITESIMAL NUMBERS Yaroslav D. Sergeyev DEIS, University of Calabria, Via P. Bucci, Cubo 42-C, 87036 Rende (CS), Italy, N.I. Lobachevsky State University, Nizhni Novgorod, Russia, and Institute of High Performance Computing and Networking of the National Research Council of Italy http://wwwinfo.deis.unical.it/∼yaro e-mail: [email protected] Abstract. Traditional mathematical tools used for analysis of fractals allow one to distinguish results of self-similarity processes after a finite number of iterations. For example, the result of procedure of construction of Cantor’s set after two steps is different from that obtained after three steps. However, we are not able to make such a distinction at infinity. It is shown in this paper that infinite and infinitesimal numbers proposed recently allow one to measure results of fractal processes at different iterations at infinity too. First, the new technique is used to measure at infinity sets being results of Cantor’s proce- dure. Second, it is applied to calculate the lengths of polygonal geometric spirals at different points of infinity. 1. INTRODUCTION During last decades fractals have been intensively studied and applied in various fields (see, for instance, [4, 11, 5, 7, 12, 20]). However, their mathematical analysis (except, of course, a very well developed theory of fractal dimensions) very often continues to have mainly a qualitative character and there are no many tools for a quantitative analysis of their behavior after execution of infinitely many steps of a self-similarity process of construction. Usually, we can measure fractals in a way and can give certain numerical answers to questions regarding fractals only if a finite number of steps in the procedure of their construction has been executed. -
Claudius Ptolemy: Tetrabiblos
CLAUDIUS PTOLEMY: TETRABIBLOS OR THE QUADRIPARTITE MATHEMATICAL TREATISE FOUR BOOKS OF THE INFLUENCE OF THE STARS TRANSLATED FROM THE GREEK PARAPHRASE OF PROCLUS BY J. M. ASHMAND London, Davis and Dickson [1822] This version courtesy of http://www.classicalastrologer.com/ Revised 04-09-2008 Foreword It is fair to say that Claudius Ptolemy made the greatest single contribution to the preservation and transmission of astrological and astronomical knowledge of the Classical and Ancient world. No study of Traditional Astrology can ignore the importance and influence of this encyclopaedic work. It speaks not only of the stars, but of a distinct cosmology that prevailed until the 18th century. It is easy to jeer at someone who thinks the earth is the cosmic centre and refers to it as existing in a sublunary sphere. However, our current knowledge tells us that the universe is infinite. It seems to me that in an infinite universe, any given point must be the centre. Sometimes scientists are not so scientific. The fact is, it still applies to us for our purposes and even the most rational among us do not refer to sunrise as earth set. It practical terms, the Moon does have the most immediate effect on the Earth which is, after all, our point of reference. She turns the tides, influences vegetative growth and the menstrual cycle. What has become known as the Ptolemaic Universe, consisted of concentric circles emanating from Earth to the eighth sphere of the Fixed Stars, also known as the Empyrean. This cosmology is as spiritual as it is physical.