Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

eferences 253contested philosophical domains. If this is right, then, for example, the adoption ofstandard theological hypotheses has important consequences for the debates aboutformalism, finitism, intuitionism, and Platonism in the philosophy of mathematics forthose who take these theological hypotheses seriously.Eighth, there are issues that cluster around the application of the results of mathematicalinvestigations of infinity to specific parts of Christian theology and doctrine –for example, to discussions of trinity, incarnation, immortality, and so forth. To theextent that there has been prior discussion of the application of the results of mathematicalinvestigations of infinity to theology, this discussion has tended to focus onquestions about generic divine attributes, that is, divine attributes as these are conceivedon most monotheistic conceptions of God. However, it seems to me that thereare bound to be questions that are quite specific to Christian theology and doctrine forwhich investigation of “limits” and “bounds” as a subject matter in its own right hasimportant consequences. 11Although the examination of infinity in theological contexts is doubtless not itself aninfinite task, it is abundantly clear – even from this relatively superficial and incompleteoverview – that there is plenty of work to be done.AcknowledgmentsI am grateful to all of the participants in the “New Frontiers in Research on Infinity”Conference, San Marino, August 18 to 20, 2006. In particular, I am grateful to WolfgangAchtner, Denys Turner, and Marco Bersanelli for their detailed comments on an earlierdraft of this paper; to Ed Nelson, Hugh Woodin, Anthony Aguirre, and Michael Hellerfor discussion of relevant points in mathematics, set theory, and theoretical physics;and to Charles Harper, Bob Russell, and Melissa Moritz for their feedback, enthusiasm,and extraordinary organizational skills.ReferencesBarrow, J. 2005. The Infinite Book. London: Vintage.Benardete, J. 1964. Infinity: An Essay in Metaphysics. Oxford: Oxford University Press.Conway, J. 1976. On Numbers and Games. London: Academic.Grim, P. 1991. The Incomplete Universe: Totality, Knowledge and Truth. Cambridge: MIT Press.Lavine, S. 1994. Understanding the Infinite. Cambridge: Harvard University Press.Lewis, D. 1991. Parts of Classes. London: Blackwell.Meyer, R. 1987. God exists! Nous 21: 345–61.Moore, A. W. 1990. The Infinite. London: Routledge.Moore, A. W. 1998. Infinity. In Routledge Encyclopaedia of Philosophy, E. Craig (ed.), pp. 772–78.London: Routledge.11 Perhaps because of the nature of my own interests, I have focused here particularly on considerations fromlogic, philosophy of language, and metaphysics. There are also interesting epistemological issues that areraised by questions about the infinite (for some introduction to these considerations, see, e.g., Thomson 1967;Lavine 1994) and, in particular, by questions about the infinite in the context of theology.