Abstract
Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefinite extensibility, and show how Grim’s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim’s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity.
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References
Abbruzzese J. E. (1997) The coherence of omniscience: A defense. International Journal for Philosophy of Religion 41(1): 25–34
Aquinas. De veritate. Corpus Thomisticum. www.corpusthomisticum.org. Accessed 3 June 2010.
Aquinas. Summa theologiae. Corpus Thomisticum. www.corpusthomisticum.org. Accessed 4 June 2010.
Beall J. C. (2000) A neglected response to the Grim result. Analysis 60(1): 38–41
Ferreirós J. (1999) Matemáticas y platonismo(s). La Gaceta de la Real Sociedad Española de Matemáticas 2: 446–473
Fine K. (2006) Relativey unrestricted quantification. In: Rayo A., Uzquiano G. (eds) Absolute generality. Oxford University Press, Oxford, pp 22–40
Grim P. (1991) The incomplete universe: Totality, knowledge, and truth. The MIT Press, Cambridge, MA
Grim P. (2003) Logic and the limits of knowledge and truth. In: Martin M., Monnier R. (eds) The impossibility of God. Prometheus, New York, pp 381–407
Grim P., Plantinga A. (1993) Truth, omniscience, and Cantorian arguments: An exchange. Philosophical Studies 71(3): 267–306
Lavine S. (2006) Something about everything: Universal quantification in the universal sense of universal quantification. In: Rayo A., Uzquiano G. (eds) Absolute generality. Oxford University Press, Oxford, pp 98–148
Luna L. (2008) Can we consistently say that we cannot speak about everything?. The Reasoner 2(9): 5–7
Luna L., Small C. (2009) Intentionality and computationalism. A diagonal argument. Mind and Matter 7(1): 81–90
Mar G. (1993) Why ‘Cantorian’ arguments against the existence of God do not work. International Philosophical Quarterly 33(4): 429–442
Parsons C. (2006) The problem of absolute universality. In: Rayo A., Uzquiano G. (eds) Absolute generality. Oxford University Press, Oxford, pp 203–219
Post J. F. (2003) Omniscience, weak PSR, and method. Philo 6(1): 33–48
Rayo, A., Uzquiano, G. (eds) (2006) Absolute generality. Oxford University Press, Oxford
Shapiro S., Wright C. (2006) All things indefinitely extensible. In: Rayo A., Uzquiano G. (eds) Absolute generality. Oxford University Press, Oxford, pp 255–304
Simmons K. (1993) On an argument against omniscience. Noûs 27(1): 22–33
Wang H. (1958) Eighty years of foundational studies. Dialectica 12(3–4): 466–497
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Luna, L. Grim’s arguments against omniscience and indefinite extensibility. Int J Philos Relig 72, 89–101 (2012). https://doi.org/10.1007/s11153-011-9301-x
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DOI: https://doi.org/10.1007/s11153-011-9301-x