The being that knew too much

International Journal for Philosophy of Religion

Volumn 47, Issue 3, 2000, Pages 141-154

  Grim, Patrick ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52849087847     PISSN: 00207047     EISSN: 15728684     Source Type: Journal    
DOI: 10.1023/A:1004091304240     Document Type: Review

References (33)

1. John Abbruzzese, "The coherence of Omniscience: A defense", International Journal for Philosophy of Religion 41 (1997): 25-34.
2. See particularly chapter 4 of Grim, The Incomplete Universe (Cambridge, MA: MIT Press, 1991),
3. and Alvin Plantinga and Patrick Grim, "Truth, Omniscience and Cantorian Arguments: An Exchange", Philosophical Studies 71 (1993): 267-306.
4. Hector-Neri Castañeda, "'He': A Study of the Logic of Self-Consciousness", Ratio 8 (1966): 130-157,
5. John Perry, "The Problem of the Essential Indexical", Noûs 13 (1979): 3-21,
6. David Lewis, "Attitudes De Dicto and De Se", The Philosophical Review 88 (1979): 513-543,
7. Steven Boër and William Lycan, "Who, Me?", Philosophical Review 88 (1980): 427-466.
8. Here I don't address Castañeda's proposal in "Omniscience and Indexical Reference", Journal of Philosophy 64 (1967): 203-210, which relies on the roundly rejected principle P: that if X knows that Y knows that..., X knows what is expressed in situ by the phrase...
9. Castañeda had at any rate given up such an approach, and any associated defense of omniscience, by the time of Perry's "The Problem of the Essential Indexical", Journal of Philosophy op. cit.
10. For further discussion of Castañeda with regard to omniscience see Grim, "Against Omniscience: The Case From Essential Indexicals", Noûs 29 (1985): 151-180.
11. See particularly Grim, "Some Neglected Problems of Omniscience", American Philosophical Quarterly 20 (1983): 265-277.
12. The Swinburne approach that Abbruzzese quotes with approval is a propositionalist response to the Liar. But difficulties for propositionalist approaches also continue well beyond this point. See particularly The Incomplete Universe, chapter 1, section 6.
13. For details see David Kaplan and Richard Montague, "A Paradox Regained", Notre Dame Journal of Formal Logic I (1960): 79-90;
14. C. Anthony Anderson, "The Paradox of the Knower", Journal of Philosophy 80 (1983): 338-355,
15. and Grim, "Truth, Omniscience, and the Knower", Philosophical Studies 54 (1988): 9-41. In the present context I have passed over several arguments against omniscience related to Godel's results that appear in chapter 3 of The Incomplete Universe.
16. See Grim, "There Is No Set of All Truths", Analysis 44 (1984): 206-208.
17. Richard Cartwright, "Speaking of Everything", Noûs 28 (1994): 1-20;
18. D.A. Martin, "Sets versus Classes",
19. quoted in Keith Simmons, "On an argument Against Omniscience", Noûs 27 (1993): 22-33.
20. The full diagonal argument isn't given here. For details see chapter 4 of Grim, The Incomplete Universe (Cambridge, MA: MIT Press, 1991),
21. and Alvin Plantinga and Patrick Grim, "Truth, Omniscience and Cantorian Arguments: An Exchange", Philosophical Studies 71 (1993): 267-306.
22. Gary Mar, "Why 'Cantorian' Arguments against the Existence of God Do Not Work", International Philosophical Quarterly 33 (1993): 429-442.
23. A less formal presentation, though with precisely the same central difficulty, appeared as Keith Simmons, "On an Argument Against Omniscience", APA Central Division, April 1990.
24. The importance of that particular objection is significantly reduced in the published form (Simmons, "On an Argument Omniscience", Noûs 27 (1993): 22-33).
25. System NF, for 'New Foundations', first appears in W. V. O. Quine, "New Foundations for Mathematical Logic", American Mathematical Monthly 44(1937): 70-80.
26. Quine, Set Theory and its Logic (Cambridge, MA: Harvard University Press, 1969).
27. J. B. Rosser and Hao Wang showed that no interpretation of '∈' compatible with the axioms of NF could make well-orderings of both the lesser-to-greater relation among ordinals and that among finite cardinals except by interpreting '=' as something other than identity ("Non-standard Models for Formal Logic", Journal of Symbolic Logic 15 (1950): 113-129).
28. Ernest Specker went on to show that the non-Cantorian sets of NF cause the relations of lesser to greater among cardinals to fail of a well-ordering, entailing the falsehood of the axiom of choice ("The Axiom of choice in Quine's New Foundations for Mathematical Logic", Proceedings of the National Academy of Sciences 39 (1953): 972-975).
29. A consideration of other alternative set theories appears in cahpter 4 of The Incomplete Universe.
30. See esp. The Incomplete Universe, pp. 119ff.
31. Here I assume classical logic throughout. An intriguing alternative is to borrow elements of the formal structure of intuitionistic logics, which limit the consequences to be drawn from the negation of a universal quantification.
32. In Plantinga and Grim, op. cit., Alvin Plantinga charges that the premises of the Cantorian argument might also fall victim to the same objection: that if the argument were sound, they couldn't be true. This seems irrelevant from the perspective of the 'logic bomb'. It is the defender of omniscience who buys into the notion of a proposition about all propositions, and he can hardly object to the premises on the grounds that they invoke such a notion. The person who builds the bomb, on the other hand, need himself have no such commitments regarding the coherence of the premises. It is thus only the defender of omniscience who ends up making the universal claim, buying the premises, and facing contradiction and consternation as a result. Plantinga's other alternative - to deny the diagonal - seems to me a much better option in this case, but it is not one that Abbruzzese pursues.
33. I am grateful to members of the Disproof Atheism Society for helpful comments on an earlier draft: John Bach, Larry Ford, Lev Levitin, Michael Martin, Ricki Monnier, Alan O'Connor, Ruth O'Connor, and Vladimir Oytser. I am also grateful for helpful comments to an anonymous referee for the International Journal for Philosophical of Religion.