AUGUSTINE of HIPPO and HANNAH ARENDT Antonio Calcagno
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St. Augustine and St. Thomas Aquinas on the Mind, Body, and Life After Death
The University of Akron IdeaExchange@UAkron Williams Honors College, Honors Research The Dr. Gary B. and Pamela S. Williams Honors Projects College Spring 2020 St. Augustine and St. Thomas Aquinas on the Mind, Body, and Life After Death Christopher Choma [email protected] Follow this and additional works at: https://ideaexchange.uakron.edu/honors_research_projects Part of the Christianity Commons, Epistemology Commons, European History Commons, History of Philosophy Commons, History of Religion Commons, Metaphysics Commons, Philosophy of Mind Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Please take a moment to share how this work helps you through this survey. Your feedback will be important as we plan further development of our repository. Recommended Citation Choma, Christopher, "St. Augustine and St. Thomas Aquinas on the Mind, Body, and Life After Death" (2020). Williams Honors College, Honors Research Projects. 1048. https://ideaexchange.uakron.edu/honors_research_projects/1048 This Dissertation/Thesis is brought to you for free and open access by The Dr. Gary B. and Pamela S. Williams Honors College at IdeaExchange@UAkron, the institutional repository of The University of Akron in Akron, Ohio, USA. It has been accepted for inclusion in Williams Honors College, Honors Research Projects by an authorized administrator of IdeaExchange@UAkron. For more information, please contact [email protected], [email protected]. 1 St. Augustine and St. Thomas Aquinas on the Mind, Body, and Life After Death By: Christopher Choma Sponsored by: Dr. Joseph Li Vecchi Readers: Dr. Howard Ducharme Dr. Nathan Blackerby 2 Table of Contents Introduction p. 4 Section One: Three General Views of Human Nature p. -
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. -
Post-Continental Philosophy: Its Definition, Contours, and Fundamental Sources
Post-continental Philosophy: Its Definition, Contours, and Fundamental Sources NELSON MALDONADO-TORRES It is no accident that the global geographical framework in use today is essentially a cartographic celebration of European power. After centuries of imperialism, the presumptions of a worldview of a once-dominant metropole has become part of the intellectual furniture of the world…. Metageography matters, and the attempt to engage it critically has only begun. Martin W. Lewis and Kären W. Wigen, The Myth of Continents.1 or several decades now the contours of legitimate philosophy have been drawn by advocates of F so-called analytic and continental philosophies. Analytic philosophy is often referred to as a style of thinking centered on the question of whether something is true, rather than, as continental philosophy, on the multiple factors that constitute meaning.2 Analytic philosophy is also said to be closer to the sciences, while continental philosophy has more affinity with the humanities.3 One of the reasons for this lies in that while analytic philosophy tends to dismiss history from its reflections, continental philosophy typically emphasizes the relevance of time, tradition, lived experience, and/or social context. Fortunately, this situation is slowly but gradually changing today. A variety of intellectuals are defying the rigid boundaries of these fields. Some of the most notable are Afro- American, Afro-Caribbean, and Latina/o scholars using the arsenal of these bodies of thought to analyze and interpret problems related to colonialism, racism, and sexism in the contemporary world.4 These challenges demand a critical analysis of the possibilities and limits of change within the main coordinates of these different styles or forms of philosophizing. -
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. -
Book Review: Gadamer's Ethics of Play: Hermeneutics and the Other
Eastern Illinois University The Keep Faculty Research and Creative Activity Kinesiology, Sport & Recreation January 2013 Book Review: Gadamer’s Ethics of Play: Hermeneutics and the Other Chad R. Carlson Eastern Illinois University, [email protected] Follow this and additional works at: https://thekeep.eiu.edu/kss_fac Part of the Kinesiology Commons Recommended Citation Carlson, Chad R., "Book Review: Gadamer’s Ethics of Play: Hermeneutics and the Other" (2013). Faculty Research and Creative Activity. 19. https://thekeep.eiu.edu/kss_fac/19 This Article is brought to you for free and open access by the Kinesiology, Sport & Recreation at The Keep. It has been accepted for inclusion in Faculty Research and Creative Activity by an authorized administrator of The Keep. For more information, please contact [email protected]. BOOK REVIEW Chad Carlson Eastern Illinois University Gadamer’s ethics of play: Hermeneutics and the other, by Monica Vilhauer, Lanham, MD, Lexington Books, 2010, 166 pp., £37 (hardback), ISBN 978-0739139141 As a naıve graduate student, I remember signing up for a course in the Philosophy Department entitled, ‘Art and Truth’. Although I was studying sport and play in a different department, I was intrigued by the title – art seemed closely related to play and sport in the landscape of human experiences. Further, the course was offered at a convenient time and it fulfilled a deficiency I had toward graduation. Unfortunately, I had no idea what I was getting into. The course readings, which included Martin Heidegger, Friedrich Nietzsche, Maurice Merleau- Ponty, Jacques Derrida, Jurgen Habermas, and, most prominently, Hans-Georg Gadamer, seemed so dense that they necessitated long hours of introduction and prior training that I did not have. -
Galileo and Leibniz: Different Approaches to Infinity
Arch. Hist. Exact Sci. 54 (1999) 87–99. c Springer-Verlag 1999 Galileo and Leibniz: Different Approaches to Infinity Eberhard Knobloch Communicated by J. J. Gray Introduction “God exists since mathematics is consistent, and the devil exists since we cannot prove it.” In this way Andre´ Weil, one of the leading mathematicians of this century, characterized the mathematics of our time (Meschkowski 1969, p. 112; Rosenbloom 1950, p. 72). This connection between mathematics, God and the devil is not new: I would like to recall here only the study scene in Goethe’s Faust: Faust has the devil temporarily in his hand, because the pentagram is badly drawn. What is new in Weil’s saying is the insight that even mathematics cannot provide complete foundations for itself. Metamathematics and Hilbert’s proof theory are disciplines of our century. When Hilbert set about showing how the antinomies of the set theory created by Cantor could be avoided without betraying mathematics, as described in his lecture “On the Infinite” in 1925, he emphasized the necessity of clarifying the nature of the infinite (Hilbert 1926, p. 188). The infinite plays a crucial role in analysis, this most ingenious product of mathematical science, being ramified in the most refined way. As Hilbert fittingly formulated, mathematical analysis is, so to speak, a pure symphony on the infinite (Hilbert 1926, p. 184). No wonder that three years after Hilbert’s lecture his pupil Hermann Weyl character- ized mathematics as the science of the infinite (Weyl 1925–1927, p. 1; Laugwitz 1986, p. 233). He thus defined mathematics in a completely different way than his predecessors of earlier centuries. -
Analytic and Continental Philosophy, Science, and Global Philosophy
CHAPTER SIX ANALYTIC AND CONTINENTAL PHILOSOPHY, SCIENCE, AND GLOBAL PHILOSOPHY Richard Tieszen There are many references in the philosophical literature to the division between analytic and Continental philosophy but it is not easy to provide a simple formulation of what it is that distinguishes these approaches to or styles of philosophy. There have been significant subdivisions within what has been considered analytic philosophy, such as that between for- mal philosophy, ordinary language philosophy, and conceptual analysis, and there have of course also been many variations within the general grouping of Continental philosophy, extending from eidetic phenomenol- ogy, existential phenomenology, existentialism, structuralism and semiot- ics, and neo-Freudian analysis to deconstruction. Philosophers who have written about the split between the analytic and Continental traditions have often focused on the work of particular figures who seem to embody much of what is involved in the division. In The Origins of Analytic Philoso- phy, for example, Michael Dummett looks to Frege and Husserl and holds that Frege took a turn into the philosophy of language but that Husserl did not, thus initiating a split in modern philosophy. Michael Friedman, to take another example, writes a book entitled A Parting of the Ways in which he focuses on Carnap, Cassirer, and Heidegger. Over the years I have heard or read a host of characterizations of the two traditions, such as the following: Analytic philosophy strives for clarity, exactness, precision and Continental philosophy does not. Con- tinental philosophy instead tends toward the use of poetic or dramatic language. The methodology of analytic philosophy is argumentation while Continental philosophy, if it has a methodology at all, is concerned with description or narrative or literary quality. -
Hermeneutical Phenomenology and the Philosophy of Science Patrick A
Fordham University Masthead Logo DigitalResearch@Fordham Hermeneutic and Phenomenological Philosophies Research Resources of Science 1991 Hermeneutical Phenomenology and the Philosophy of Science Patrick A. Heelan Georgetown University, [email protected] Follow this and additional works at: https://fordham.bepress.com/phil_research Part of the Continental Philosophy Commons, and the Philosophy of Science Commons Recommended Citation Heelan, Patrick A., "Hermeneutical Phenomenology and the Philosophy of Science" (1991). Research Resources. 11. https://fordham.bepress.com/phil_research/11 This Article is brought to you for free and open access by the Hermeneutic and Phenomenological Philosophies of Science at DigitalResearch@Fordham. It has been accepted for inclusion in Research Resources by an authorized administrator of DigitalResearch@Fordham. For more information, please contact [email protected]. Hermeneutical Phenomenology and the Philosophy of Science Heelan, Patrick, “Hermeneutical Phenomenology and the Philosophy of Science,” in Silverman, Hugh (ed.), Gadamer and Hermeneutics: Science, Culture, and Literature, (New York: Routledge, 1991). pp. 213-228 HERMENEUTICAL PHENOMENOLOGY AND THE PHILOSOPHY OF SCIENCE PATRICK A. HEELAN PART I: Continental and Analytic Philosophy of Science Compared The two most characteristic interests of continental philosophy1 are (1) its preoccupation with the problem of the “constitution” of knowledge, and (2) the effect of the historical and cultural world context of science on the “social constitution” of scientific knowledge. Such constitution is “hermeneutical,” when it essentially involves language, natural and artifactual symbols, and historical communities of interpreters. Continental philosophy from the start sees science as an institution in a cultural, historical, and hermeneutical setting. The domain of its discourse is values, subjectivity, Life Worlds, history, and society, as these affect the constitution of scientific knowledge. -
Plotinus on the Soul's Omnipresence in Body
Plotinus on the Limitation of Act by Potency Gary M. Gurtler, S.J. Boston College The limitation of act by potency, central in the metaphysics of Thomas Aquinas, has its origins in Plotinus. He transforms Aristotle’s horizontal causality of change into a vertical causality of participation. Potency and infinity are not just unintelligible lack of limit, but productive power. Form determines matter but is limited by reception into matter. The experience of unity begins with sensible things, which always have parts, so what is really one is incorporeal, without division and separation. Unity is like the esse of Thomas, since it is the act that makes a thing what it is and has its fullness in God. 1. Introduction Over fifty years ago Norris Clarke, S.J., published “The Limitation of Act by Potency: Aristotelianism or Neoplatonism,” The New Scholasticism, 26 (1952) 167–194, which highlighted the role of Plotinus in formulating some of the fundamental distinctions operative in medieval philosophy. He singled out the doctrine of participation and the idea of infinity and showed how they went beyond the limits of classical Greek thought. At the same time, his work challenged some of the basic historical assumptions of Thomists about the relation of scholastic philosophy, especially St. Thomas’s, to Plato and Aristotle. I have appreciated more and more the unusual openness and self critical character of Fr. Clarke’s historical method, and am pleased to have the chance in this response to Sarah Borden’s paper to explore some of the issues raised by Fr. Clarke’s seminal article in light of my own work on Plotinus. -
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar Ve Yorumlar
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar ve Yorumlar David Pierce October , Matematics Department Mimar Sinan Fine Arts University Istanbul http://mat.msgsu.edu.tr/~dpierce/ Preface Here are notes of what I have been able to find or figure out about Thales of Miletus. They may be useful for anybody interested in Thales. They are not an essay, though they may lead to one. I focus mainly on the ancient sources that we have, and on the mathematics of Thales. I began this work in preparation to give one of several - minute talks at the Thales Meeting (Thales Buluşması) at the ruins of Miletus, now Milet, September , . The talks were in Turkish; the audience were from the general popu- lation. I chose for my title “Thales as the originator of the concept of proof” (Kanıt kavramının öncüsü olarak Thales). An English draft is in an appendix. The Thales Meeting was arranged by the Tourism Research Society (Turizm Araştırmaları Derneği, TURAD) and the office of the mayor of Didim. Part of Aydın province, the district of Didim encompasses the ancient cities of Priene and Miletus, along with the temple of Didyma. The temple was linked to Miletus, and Herodotus refers to it under the name of the family of priests, the Branchidae. I first visited Priene, Didyma, and Miletus in , when teaching at the Nesin Mathematics Village in Şirince, Selçuk, İzmir. The district of Selçuk contains also the ruins of Eph- esus, home town of Heraclitus. In , I drafted my Miletus talk in the Math Village. Since then, I have edited and added to these notes.