Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Acknowledgments
- Introduction
- I Perspectives on Infinity from History
- 1 Infinity as a Transformative Concept in Science and Theology
- II Perspectives on Infinity from Mathematics
- III Technical Perspectives on Infinity from Advanced Mathematics
- IV Perspectives on Infinity from Physics and Cosmology
- V Perspectives on Infinity from Philosophy and Theology
- Index
- References
1 - Infinity as a Transformative Concept in Science and Theology
Published online by Cambridge University Press: 07 June 2011
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Acknowledgments
- Introduction
- I Perspectives on Infinity from History
- 1 Infinity as a Transformative Concept in Science and Theology
- II Perspectives on Infinity from Mathematics
- III Technical Perspectives on Infinity from Advanced Mathematics
- IV Perspectives on Infinity from Physics and Cosmology
- V Perspectives on Infinity from Philosophy and Theology
- Index
- References
Summary
Introduction
As finite human beings in space, time, and matter, our thinking and feeling about infinity have always been associated with religious awe, whether in terms of wondering, being frightened, or being inspired. In this sense, infinity has a very strong affective-emotional component. At the same time, infinity is a scientific concept, and it has a strong intellectual-rational component that is mostly intertwined with a kind of intuitive and even ecstatic grasp of the infinite God. The affective-emotional component is emphasized in many records. One of the most famous is the text of Blaise Pascal (1623–62). He was writing when modern Europe, with its drive for infinite scientific progress, was about to emerge.
If I consider the short period of time in which my life is intertwined with the eternity preceding and following it, and if I consider the small space in which I dwell, and if I consider just that which I see, which is lost in infinite space, of which I know nothing, and which knows nothing of me, then I am struck with wonder that I live here and not there.
(Pascal 1978, pp. 114–15)However, the rational structure of infinity still needs to be clarified. Many philosophers and mathematicians have struggled to give a rational account of infinity. The most famous quotation derives from the German mathematician David Hilbert (1862–1943).
- Type
- Chapter
- Information
- InfinityNew Research Frontiers, pp. 19 - 52Publisher: Cambridge University PressPrint publication year: 2011
References
1934. Summa Theologica, bd. 1, Gottes Dasein und Wesen. Salzburg, Leipzig, and Regensburg: Verlag Anton Pustet.Google Scholar
. 1993. Physics, books I–IV, Loeb Classical Library, (ed.). Translated by and . Cambridge: Harvard University Press.Google Scholar
. 1997. Metaphysics, books X–XIV, Loeb Classical Library, (ed.). Translated by . Cambridge: Harvard University Press.Google Scholar
. 2003. Metaphysics, books I–IX, Loeb Classical Library, (ed.). Translated by . Cambridge: Harvard University Press.Google Scholar
1954–1955. Plotinus' doctrine of the infinite and its significance for Christian thought. Downside Review 73: 47–58.CrossRefGoogle Scholar
. 1988. City of God, vol. 4, books XII–XV, Loeb Classical Library, (ed.). Translated by . Cambridge: Harvard University Press.Google Scholar
1966. Metousia Theou: Man's Participation in God's Perfections According to Saint Gregory of Nyssa. Rome: Pontificium Institutum S. Anselmi, Studia Anselmiana 55.Google Scholar
1992. Die Unendlichkeit des Seins. Cantor's Transfinite Mengenlehre und ihre metaphysischen Wurzeln. Frankfurt: Verlag Peter Lang.Google Scholar
1975. Grundlagen der Mathematik in geschichtlicher Entwicklung. Frankfurt: Suhrkamp Verlag.Google Scholar
1996. Theoria, Unendlichkeit, Aufstieg. Philosophische Implikationen zu De Vita Moysis von Gregor von Nyssa. Leiden and New York, Köln: E. J. Brill.Google Scholar
1889. Die mandäische Religion. Ihre Entwicklung und geschichtliche Bedeutung. Erforscht, dargestellt und beleuchtet. Leipzig: J. C. Hinrich'sche Buchhandlung (reprint: Amsterdam, 1973).Google Scholar
1973. Apophatic theology and divine infinity in St. Gregory of Nyssa. Greek Orthodox Theological Review 18: 97–114.Google Scholar
1883. Grundlagen einer allgemeinen Mannichfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen. Leipzig: Teubner Verlag.Google Scholar
1932. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Berlin: Verlag Julius Springer (reprint: 1980).Google Scholar
1892. Vorlesungen über die Geschichte der Mathematik, bd. II. Leipzig: Teubner Verlag.Google Scholar
1991. Das Erkenntnisproblem, bd. I. Darmstadt: Wissenschaftliche Buchgesellschaft (reprint).Google Scholar
1960. Geschichte des Unendlichkeitsproblems im abendländischen Denken bis Kant. Hildesheim: Georg Olms Verlagsbuchhandlung.Google Scholar
1980. Stretching forth to infinity: The mystical doctrine of Gregory of Nyssa. In Prayer and Contemplation, (ed.), pp. 331–48. Bangalore: Asian Trading Corporation.Google Scholar
2002. Johannes Duns Scotus. Die Unverfügbarkeit Gottes. In Theologen des Mittelalters. Eine Einführung, U. KÖpf (ed.). Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
. 1956. Mystische Theologie, (ed.) Schriftenreihe “Weisheitsbücher der Menschheit.” Translated by . München-Planegg: O. W. Barth Verlag.Google Scholar
2001. Schleiermacher's Wissenschaftslehre als Entwurf einer prozessualen Metaphysik in semiotischer Perspektive. Triadizität im Werden. Berlin and New York: de Gruyter.Google Scholar
1974. Gregory of Nyssa and Nicholas of Cusa: Infinity, anthropology and the via negativa. Downside Review 92: 102–8.CrossRefGoogle Scholar
2002. Unendlichkeit und All-Einheit. Zum Unendlichkeitsgedanken in der philosophischen Theologie des Cusanus. In Nikolaus Cusanus zwischden Deutschland und Italien, (ed.), pp. 383–441. Berlin: Akademieverlag.Google Scholar
1973. God's infinity and man's mutability: Perpetual progress according to Gregory of Nyssa. Greek Orthodox Theological Review 18: 59–78.Google Scholar
1955. Die Begründung der mathematischen Naturwissenschaft durch Eudoxos. In Knowledge, Will, and Belief: Collected Essays, (ed.), pp. 134–57. Chicago and Zürich: Artemis Verlag.Google Scholar
1936a. Die Widerspruchsfreiheit der reinen Zahlentheorie. Mathematische Annalen 112: 493–565.CrossRefGoogle Scholar
1936b. Die Widerspruchsfreiheit der Stufenlogik. Mathematischde Zeitschrift 41: 357–66.CrossRefGoogle Scholar
. 1960a. Gregorii Nysseni Opera, vol. I, Contra Eunomius Libros I–II, (ed.). Leiden: E. J. Brill.Google Scholar
. 1960b. Gregorii Nysseni Opera, vol. II, Contra Eunomius Liberum III, (ed.). Leiden: E. J. Brill.Google Scholar
. 1964. Gregorii Nysseni Opera, vol. VII, pars I, Gregorii Nysseni De Vita Moysis, , , and (eds.). Leiden: E. J. Brill.Google Scholar
1963. “The Background, Sources and Meaning of Divine Infinity in St. Gregory of Nyssa.” Ph.D. thesis, Fordham University, ETD Collection for Fordham University. Paper AAI6305594.
1925. Über das Unendliche. Mathematische Annalen 95: 161–90. Reprint in From Frege to Gödel, A Source Book in Mathematical Logic, 1879–1931, J. van Heijenoort (ed.), pp. 367–92. Lincoln, NE: iUniverse.com, Inc. (1967).CrossRefGoogle Scholar
. 1955. De fide orthodoxa, Saint John Damascene. In Versions of Burgundio and Cerbanus, (ed.). St. Bonaventure, NY: The Franciscan Institute.Google Scholar
1962. Plotin über Zeit und Eweigkeit. In Politische Ordnung und menschliche Existenz, et al. (eds.). Festgabe für Eric Voegelin, pp. 295–319. München: Verlag C. H. Beck.Google Scholar
2001. Die Unendlichkeit Gottes und der unendliche Weg des Menschen nach Gregor von Nyssa. Sacris Erudiri (Brugge) 40: 47–81.CrossRefGoogle Scholar
2002. Unendlichkeit und Mathematik bei Nikolaus von Kues. In Chemie-Kultur-Geschichte, Festschrift für Hans-Werner Schütt, and (eds.). Berlin: Verlag für Geschichte der Naturwissenschaften und der Technik (GNT-Verlag).Google Scholar
1966. Die Fragmente des Eudoxos von Knidos (Texte und Kommentare 4). Berlin: de Gruyter.Google Scholar
1913. Die Begriffe Zeit und Ewigkeit im späteren Platonismus, Beiträge zur Geschichte der Philosophie des Mittelalters XIII 4. Münster: Aschendorff.Google Scholar
1975. “An Historical Analysis of Grassmann's Ausdehnungslehre of 1844.” Ph.D. thesis, University of Texas.
1977. H. Grassmann's Ausdehnungslehre and Schleiermacher's Dialektik. Annals of Science 34: 103–62.CrossRefGoogle Scholar
1981. Friedrich Schleiermacher's influence on H. Grassmann's Mathematics. In Social History of Nineteenth Century Mathematics. Papers from a Workshop Held in Berlin, July 5–9, 1979, , , and (eds.), pp. 246–54. Basel and Boston: Birkhäuser.Google Scholar
1997. Kirche und bildende Kunst der Moderne. Ein an F.D.E. Schleiermacher orientierter Beitrag zur theologischen Urteilsbildung. Tübingen: Mohr Siebeck.Google Scholar
1960. The life of Eudoxos. In Studies in Epicurus and Aristotle, Klassisch philologische Studien 22, pp. 98–104. Wiesbaden: Harrassowitz Verlag.Google Scholar
1966. Die Unendlichkeit Gottes bei Gregor von Nyssa: Gregors Kritik am Gottesbegriff der klassischen Metaphysik. FKDG 16; Göttingen: Vandenhoeck & Ruprecht.Google Scholar
. 1964. Philosophisch-Theologische Schriften, vol. I, Lateinisch-Deutsch,. L. Gabriel (ed.). Wien: Herder Verlag.Google Scholar
. 1966. Philosophisch-Theologische Schriften, vol. II, Lateinisch-Deutsch, L. Gabriel (ed.). Wien: Herder Verlag.Google Scholar
. 1967. Philosophisch-Theologische Schriften, vol. III, Lateinisch-Deutsch, L. Gabriel (ed.). Wien: Herder Verlag.Google Scholar
. 1979. Die mathmatischen Schriften, übersetzt von Josepha Hofmann und mit einer Einführung versehen von Josef Ehrenfried Hofmann. Hamburg: Meiner Verlag.Google Scholar
. 1992. Vier Bücher von den Prinzipien (Origenis De Principiis Libri IV), and (eds.). Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
1978. Pensées. Über die Religion und über einige andere Gegenstände. Heidelberg: Verlag Lambert Schneider.Google Scholar
. 1956–71. Plotins Schriften, bd. I–VI, R. Harder and R. Beutler (eds. and trans.). Hamburg: Felix Meiner Verlag.Google Scholar
. 1958. Über Plotins Leben und die Ordnung seiner Schriften. Hamburg: Felix Meiner Verlag.Google Scholar
1967. Über die Religion. Reden an die Gebildeten unter ihren Verächtern. Göttingen: Vandenhoeck & Ruprecht.Google Scholar
1978. Monologen. In Neujahrspredigt von 1792. Über den Wert des Lebens, (ed.). Hamburg: Felix Meiner Verlag.Google Scholar
1984. Spinozismus, Spinoza betreffend aus Jacobi. In Kritische Gesamtausgabe, bd. I, Jugendschriften 1787–96, (ed.), pp. 515–58. Berlin and New York: de Gruyter.Google Scholar
1978. Zahl, Proportion, Analogie. Eine Untersuchung zur Metaphysik und Wissenschaftshaltung des Nikolaus von Kues, Buchreihe der Cusanusgesellschaft, bd. VII. Münster: Aschendorff Verlag.Google Scholar
. 1954. Aristotelis Physicorum libros quattuor posteriors commentaria (Commentaria in Aristotelum Graeca 10), (ed.). Berlin: de Gruyter (reprint).Google Scholar
, and 1980. Lexicon Plotinianum, Ancient and Medieval Philosophy Series. Leiden, Leuven: E. J. Brill.Google Scholar
1989. Tractatus de Intellectus Emendatione. Ethica, bd. II, (ed.). Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
1992a. Bonaventure and Aquinas on the divine being as infinite. In Divine Infinity and Medieval Thought, (ed.), pp. 413–37. Frankfurt and New York: Peter Lang Verlag.Google Scholar
(ed.). 1992b. Divine Infinity in Greek and Medieval Thought. Frankfurt and New York: Peter Lang Verlag.
1992c. Infinity in Plotinus. In Divine Infinity in Greek and Medieval Thought, (ed.), pp. 167–222. Frankfurt and New York: Peter Lang Verlag.Google Scholar
1980. Journeys to Selfhood, Hegel & Kierkegaard. Berkeley: University of California Press.Google Scholar
1895. Die mathematischen Schriften des Nikolaus Cusanus. In Philosophisches Jahrbuch der Görres Gesellschaft, no. 8, pp. 301–17, 403–22.
1896. Die mathematischen Schriften des Nikolaus Cusanus. In Philosophisches Jahrbuch der Görres Gesellschaft, no. 9, pp. 54–66, 391–410.
1897. Die mathematischen Schriften des Nikolaus Cusanus. In Philosophisches Jahrbuch der Görres Gesellschaft, no. 10, pp. 144–59.
1978. God's infinity and his relationship to creation in the theologies of Gregory of Nyssa and Jonathan Edwards. Foundations 21: 305–21.Google Scholar
1963. Die Philosophie der Griechen in ihrer geschichtlichen Entwicklung: Drei Teile, jeder in zwei Abteilungen. Hildesheim: Georg Olms Verlag.Google Scholar
- 5
- Cited by