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Logos, logic and maximal infinity

Published online by Cambridge University Press:  10 March 2021

A. C. Paseau Open the ORCID record for A. C. Paseau [Opens in a new window]
A. C. Paseau*
Affiliation:
Wadham College, Oxford, OX1 3PN, UK
*
email: alexander.paseau@philosophy.ox.ac.uk
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Abstract

Recent developments in the philosophy of logic suggest that the correct foundational logic is like God in that both are maximally infinite and only partially graspable by finite beings. This opens the door to a new argument for the existence of God, exploiting the link between God and logic through the intermediary of the Logos. This article explores the argument from the nature of God to the nature of logic, and sketches the converse argument from the nature of logic to the existence of God.

Keywords

LogosLogicGod's InfinityGod and LogicMaximal Infinity
Type
Original Article
Information
Religious Studies , Volume 58 , Issue 2 , June 2022 , pp. 420 - 435
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

Achtner, W (2011) Infinity as a transformative concept in science and theology. In Heller S and Woodin WH (eds), Infinity: New Research Frontiers. Cambridge: Cambridge University Press, 19–51.CrossRefGoogle Scholar
Adam, C and Tannery, P (1897–1913) (eds), Oeuvres de Descartes. Paris: Léopold Cerf.Google Scholar
Alston, W (1991) Perceiving God: The Epistemology of Religious Experience. Ithaca, NY: Cornell University Press.Google Scholar
Anselm (1094–1098/1858) Cur Deus homo, trans. as Why God was made man. London: J. H. & J. Parker.Google Scholar
Aquinas, T (1273/1955) Summa Theologica Fathers of the English Dominican Province (trans.). London: Christian Classics.Google Scholar
Aristotle (4th century bc/1984) The Complete Works of Aristotle, J. Barnes (ed.). Princeton: Princeton University Press.Google Scholar
Bonnay, D (2008) Logicality and invariance. The Bulletin of Symbolic Logic 14, 29–68.CrossRefGoogle Scholar
Branson, B (2019) No new solutions to the logical problem of the Trinity. Journal of Applied Logic 6, 1051–1092.Google Scholar
Brunner, E (1952) The Christian Doctrine of Creation and Redemption. Philadelphia: The Westminster Press.Google Scholar
Burnett, C (1984) (ed. and trans.), Peter Abelard: Soliloquium: a critical edition. Studi Medievali 25, 885–891.Google Scholar
Cantor, G (1883) Grundlagen einer allgemeinen Mannigfaltigkeitslehre, trans. by Parpart, U. as ‘Foundations of the theory of manifolds’ in The Campaigner 9 (1976), 69–96. Page references are to Cantor (1932) Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, Zermelo E (ed.). Berlin: Springer.Google Scholar
Clark, GH (1980) God and logic. The Trinity Review, 1–7.Google Scholar
Craig, WL (2016) God Over All: Divine Aseity and the Challenge of Platonism. Oxford: Oxford University Press.CrossRefGoogle Scholar
Cullmann, O (1963) The Christology of the New Testament, 2nd Edn. Norwich: SCM.Google Scholar
Dauben, JW (1977) Georg Cantor and Pope Leo XIII: mathematics, theology, and the infinite. Journal of the History of Ideas 38, 85–108.CrossRefGoogle Scholar
Dauben, JW (1979/1990) Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton: Princeton University Press.Google Scholar
Feferman, S (1999) Logic, logics and logicism. Notre Dame Journal of Formal Logic 40, 31–54.CrossRefGoogle Scholar
Feferman, S (2010) Set-theoretical invariance criteria for logicality. Notre Dame Journal of Formal Logic 51, 3–20.CrossRefGoogle Scholar
Goldschmidt, T (2018) The argument from (natural) numbers. In Walls, J and Dougherty, T (eds), Two Dozen (or so) Arguments for God: The Plantinga Project. Oxford: Oxford University Press, 59–75.Google Scholar
Griffiths, O and Paseau, AC (forthcoming) One True Logic. Oxford: Oxford University Press.Google Scholar
Hart, DB (2011) Notes on the concept of the infinite in the history of western metaphysics. In Heller, S and Woodin, WH (eds), Infinity: New Research Frontiers. Cambridge: Cambridge University Press, 255–274.CrossRefGoogle Scholar
Hedman, BA (2019) Cantor and the infinity of God. In Göcke, BP and Tapp, C (eds), The Infinity of God. Notre Dame, IN: University of Notre Dame Press, 167–183.Google Scholar
Hick, J (2004) An Interpretation of Religion: Human Responses to the Transcendent, 2nd Edn. New Haven, CT: Yale University Press.CrossRefGoogle Scholar
Jané, I (1995) The role of the absolute infinite in Cantor's conception of set. Erkenntnis 42, 375–402.CrossRefGoogle Scholar
Kelly, JND (2014) Early Christian Doctrines, 5th Edn. London: Bloomsbury.Google Scholar
Krainer, F (2019) The concept of the infinity of God in ancient Greek thought. In Göcke, BP and Tapp, C (eds), The Infinity of God. Notre Dame, IN: University of Notre Dame Press, 21–36.Google Scholar
Kynaston, GR (2018) Jesus as God's word: a comparative study in Islamic and Christian theologies. Australian Journal of Islamic Studies 3, 68–85.CrossRefGoogle Scholar
Leftow, B (2012) God and Necessity. Oxford: Oxford University Press.CrossRefGoogle Scholar
Louth, A (2007) The Origins of the Christian Mystical Tradition, 2nd Edn. Oxford: Oxford University Press.CrossRefGoogle Scholar
Mawson, TJ (2001) Eternal truths and Cartesian circularity. British Journal for the History of Philosophy 9, 197–220.CrossRefGoogle Scholar
Menzel, C (2018) The argument from collections. In Walls, J and Dougherty, T (eds), Two Dozen (or so) Arguments for God: The Plantinga Project. Oxford: Oxford University Press, 29–58.Google Scholar
Millican, P (2019) Logic: atheism. In Kotersky, JW and Oppy, G (eds), Theism and Atheism: Opposing Arguments in Philosophy. New York: Macmillan, 81–101.Google Scholar
Minns, D and Parvis, P (2009) Justin, Philosopher and Martyr. Oxford: Oxford University Press.Google Scholar
Moore, AW (2019) The Infinite, 3rd Edn. London: Routledge.Google Scholar
Morris, TV (1991) The Logic of God Incarnate. Eugene, OR: Wipf and Stock.Google Scholar
Oppy, G (2011) God and infinity: directions for future research. In Heller, S and Woodin, WH (eds), Infinity: New Research Frontiers. Cambridge: Cambridge University Press, 233–254.CrossRefGoogle Scholar
Plantinga, A (1998) Christian philosophy at the end of the twentieth century. In Sennett, JF (ed.), The Analytic Theist: An Alvin Plantinga Reader. Grand Rapids, MI: William B. Eerdmans, 296–315.Google Scholar
Russell, RJ (2011) God and infinity: theological insights from Cantor's mathematics. In Heller, S and Woodin, WH (eds), Infinity: New Research Frontiers. Cambridge: Cambridge University Press, 75–89.Google Scholar
Sher, G (1991) The Bounds of Logic. Cambridge, MA: MIT Press.Google Scholar
Sher, G (2013) The Foundational Problem of Logic. Bulletin of Symbolic Logic 19, 145–198.CrossRefGoogle Scholar
Sober, E (2018) The Design Argument. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Steinberger, F and Murzi, J (2017) Inferentialism. In Hale, B, Wright, C and Miller, A (eds), Blackwell Companion to Philosophy of Language. Oxford: Wiley Blackwell, 197–224.Google Scholar
Strickland, L (2014) Leibniz's Monadology: A New Translation and Guide. Edinburgh: Edinburgh University Press.CrossRefGoogle Scholar
Swinburne, R (1990) The Existence of God, rev. Edn. Oxford: Clarendon Press.Google Scholar
Tarski, A (1936) Über den Begriff der logischen Folgerung. Actes du Congrès International de Philosophie Scientifique, 7, 1–11. Trans. by Woodger, J as On the Concept of Logical Consequence and repr. in J. Corcoran (ed.), Logic, Semantics, Metamathematics, 2nd Edn. Oxford: Clarendon Press, 1983, 409–420.Google Scholar
Tarski, A (1986) What are logical notions? History and Philosophy of Logic 7, 143–154.Google Scholar
Tarski, A and Vaught, R (1956) Arithmetical extensions of relational systems. Compositio Mathematica 13, 81–102.Google Scholar
Thomasius, G (1857) Christi Person und Werk, 2nd Edn., trans. as Christ's Person and Work and excerpted in Ford, DE and Higton, M (eds), Jesus Oxford: Oxford University Press, 2003, 353–355.Google Scholar
Tuggy, D (2018) Metaphysics and identity of the Trinity. Oxford Handbooks Online. doi: 10.1093/oxfordhb/9780199935314.013.27.Google Scholar
Williamson, T (2007) The Philosophy of Philosophy. Oxford: Blackwell.CrossRefGoogle Scholar