NEW PUZZLES ABOUT DIVINE ATTRIBUTES Forthcoming in European Journal for Philosophy of Religion MOTI MIZRAHI St. John's University, New York Abstract: According to traditional Western theism, God is maximally great (or perfect). More explicitly, God is said to have the following divine attributes: omnipotence, omniscience, and omnibenevolence. In this paper, I present three puzzles about this conception of a maximally great (or perfect) being. The first puzzle about omniscience shows that this divine attribute is incoherent. The second puzzle about omnibenevolence and omnipotence shows that these divine attributes are logically incompatible. The third puzzle about perfect rationality and omnipotence shows that these divine attributes are logically incompatible. I. INTRODUCTION According to traditional Western theism, God is maximally great (or perfect). More explicitly, God is said to have the following divine attributes: omnipotence, omniscience, and omnibenevolence (Everitt 2010). In other words, God is supposed to be omnipotent (allpowerful), omniscient (all-knowing), and omnibenevolent (all-good). (See, e.g., Plantinga 1974, 1980; Morris 1987; Wierenga 1989; Adams 1983; MacDonald 1991; Rogers 2000.) The familiar puzzles about omnipotence include the following (Hoffman and Rosenkrantz 2006):  Could an omnipotent being create a stone so massive that that being could not move it?  Could an omnipotent being create a spherical cube? Paradoxically, it appears that however we answer these questions, an omnipotent being turns out not to be all-powerful (Cf. Campbell and Nagasawa 2005). In what follows, I present three puzzles about the conception of God as a maximally great (or perfect) being. The first puzzle about omniscience shows that this divine attribute is incoherent. The second puzzle about omnibenevolence and omnipotence shows that these divine attributes are logically incompatible. The third puzzle about perfect rationality and omnipotence shows that these divine attributes are logically incompatible. The puzzles presented in this paper are different from the arguments outlined by Michael Martin (1990) in two important respects. First, these puzzles are presented as puzzles vis-à-vis the conception of God as a maximally great 2 (or perfect) being rather than arguments for atheism. Second, these puzzles are immune to the objections raised by Beyer (2004) (Cf. Nagasawa 2005). II. A PUZZLE ABOUT OMNISCIENCE God is said to be omniscient (all-knowing). For present purposes, the divine attribute of omniscience is understood as follows (Wierenga 2010): B is omniscient =df for any proposition p, if p is true, then B knows that p. Now, omniscience, thus understood, seems incoherent. To see why, consider the following question: Could an omniscient being know what it is like not to know that p? On the one hand, if we answer yes, then that means that there must be some p that an omniscient being does not know, and hence an omniscient being turns out not to be all-knowing (Cf. Grim 1983). It might seem as if the generalization on which this claim rests is not clearly true. For example, can't I know modal logic, say, and know what it is like not to know modal logic? Even if one thinks that this is a rhetorical question, and so the answer is clearly yes, this move will not work for the following reason. Presumably, a human person needs to learn modal logic before he or she knows modal logic. So a human person can know what it was like not to know modal logic before he or she has learned it. For an omniscient being, however, that cannot be the case, for, presumably, an omniscient being does not need to learn anything. So, presumably, an omniscient being does not need to learn modal logic. Rather, an omniscient being just knows modal logic (or anything else, for that matter). Surely, if an omniscient being needs to learn anything, then that being is not really omniscient. On the other hand, if we answer no, then there is something that an omniscient being could not know, namely, an omniscient being could not know what it is like not to know that p, and hence an omniscient being turns out not to be all-knowing. 3 It might be objected that 'knowing what it is like' is not propositional knowledge. And since omniscience has been characterized in terms of propositional knowledge, there is no problem with saying that an omniscient being still has maximal propositional knowledge. This objection, however, raises two further problems. First, an omniscient being, presumably, should have perfect knowledge of all sorts, including propositional knowledge, as well as knowledge of skills (e.g., knowing how to write a paper) and knowledge by acquaintance (e.g., knowing the Prime Minister of England). Restricting omniscience to propositional knowledge, then, seems arbitrary. But, in this paper, omniscience has been characterized in terms of propositional knowledge, since this is the common way in which omniscience is characterized in the literature. (See, e.g., Plantinga 1974: 68; Davis 1983: 26; Gale 1991: 57; Zagzebski 2007: 262.) Second, 'knowing what it is like' can be easily couched in terms of propositional knowledge. For instance, in order to know what it is like not to know that p, an omniscient being would have to know the following proposition: (L) This is what it is like not to know that p. or (L*) Not knowing that p feels like F. For (L) or (L*) to be true, however, there must be some p that an omniscient being does not know. That is to say, in order to know that (L) or (L*), there must be some p that an omniscient being does not know, and hence an omniscient being turns out not to be all-knowing. On the other hand, if an omniscient being does not know that (L) or (L*), then an omniscient being turns out not to be all-knowing. Some might think that the Christian doctrine of Incarnation might provide a way out of this puzzle. According to this doctrine, God took human form in the body of Christ. Accordingly, some might argue, while incarnated in the body of Christ, God could know that (L) or (L*), since Christ qua human being is not all-knowing. However, while incarnated in the body of Christ, God could know what it is like for God to behave like a human being who does not know that p, but God could not know what it is like 4 for Christ qua human being not to know that p. In other words, the following two propositions could be the object of the Christian God's knowledge in this case: (L1) This is what it is like for the Christian God to behave like a human being who does not know that p. (L2) This is what it is like for a human being not to know that p. Arguably, the Christian God could know that (L1) is true, since God is incarnated in the body of Christ, but God could not know that (L2) is true, since, while incarnated in the body of Christ, God has the subjective experience of what it is like for God to behave like a human being, not the subjective experience of what it is like to be a human being who does not know that p, just as if one were to have bat sonar, one would be able to know what it is like for one to echolocate like a bat does, but not what it is like for a bat to echolocate using bat sonar (Nagel 1974). To this reply to the Incarnation move it might be objected that an underlying, and unwarranted, assumption here is that God assuming human form involves nothing more than engaging in human behaviour (the so-called Apollinarian heresy). However, this objection is also mistaken, since there is another way of putting the puzzle that circumvents this worry. Consider the following question: Could an omniscient being know what it is like to be finite? As an answer to this question, the Incarnation move does not work because God cannot know what it is like to be finite while being infinite. Furthermore, assuming God could know what it is like for God to be finite, that is not the same as knowing what it is like for a finite being to be finite. Indeed, it seems incoherent to say that God could know what it is like for God to be finite because that would require that God be finite, and hence not God in the sense of a maximally great (or perfect) being. Finally, one might think that it is not the case that, in order to know that (L) or (L*), there must be some p that an omniscient being does not know. Rather, one might argue, an omniscient being can simply imagine what it is like not to know that p. This objection, however, is also mistaken. First, clearly, imagining what it is like not to know that p is different from knowing what it is like not to know that p. Second, resorting to imagination simply pushes the puzzle one 5 level up. For then one could ask: Can an omniscient being know that it is like to imagine what it is like not to know that p? The aforementioned puzzle about omniscience can be summed up in the form of a dilemma as follows: 1. Either God can know what it is like not to know that p or God cannot know what it is like not to know that p. 2. If God can know what it is like not to know that p, then God is not omniscient (since to know what it is like not to know that p, there must be some p that God does not know). 3. If God cannot know what it is like not to know that p, then God is not omniscient (since there is some p-i.e., (L) or (L*)-that God cannot know). 4. (Therefore) Either way, God is not omniscient. Alternatively, the second formulation of the puzzle can be summed up in the form of a dilemma as follows: 1. Either God can know what it is like to be finite or God cannot know what it is like to be finite. 2. If God can know what it is like to be finite, then God is not omniscient (since to know what it is like to be finite, God must be finite). 3. If God cannot know what it is like to be finite, then God is not omniscient (since there is something that God cannot know, namely, what it is like to be finite). 4. (Therefore) Either way, God is not omniscient. Like the familiar puzzles about omnipotence, it appears that however we answer the aforementioned question about omniscience, an omniscient being turns out not to be omniscient. This puzzle, then, shows that the divine attribute of omniscience, like the divine attribute of omnipotence, is incoherent. 6 III. A PUZZLE ABOUT OMNIBENEVOLENCE AND OMNIPOTENCE God is said to be omnibenevolent (all-good). For present purposes, the divine attribute of benevolence is understood along the following Leibnizian lines (1989, 35): (1) 'God is an absolutely perfect being.' (2) '[P]ower and knowledge are perfections, and, insofar as they belong to God, they do not have limits.' (3) (Therefore) 'God, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking.' Now, it has already been suggested that the divine attributes of benevolence and omnipotence are logically incompatible. For example, according to Pike (1969), since doing evil is a possible thing to do, if an omnipotent being lacks the power to do evil, then that being lacks the power to do something possible, and hence that being is not omnipotent (Cf. Hoffman 1979). Accordingly, in more recent literature, the concept of omnipotence has been understood in terms of the power to bring about certain possible states of affairs, where states of affairs are propositional entities that either obtain or fail to obtain (Hoffman and Rosenkrantz 1980; Wierenga 1989). Nevertheless, even if omnipotence is construed in terms of the power to bring about certain possible state of affairs, it seems that the divine attributes of benevolence and omnipotence are still logically incompatible. To see why, consider the following question: Could a being that is both omnipotent and omnibenevolent choose the lesser of two evils? By 'choose the lesser of two evils', I mean a state of affairs in which there are two options-E1 and E2-and both are bad but not equally bad (e.g., E2 is worse than E1). Now, on the one hand, if we answer yes, then that means that an omnipotent and omnibenevolent being has the power to bring about a state of affairs where that being chooses the lesser of two evils. But then that means that an omnipotent and omnibenevolent being is capable of choosing evil, and hence an omnipotent and omnibenevolent being turns out not to be all-good. One might think that, if one chooses E1 simply because it is not as bad as E2, then one hasn't chosen evil. But this is mistaken, for, by stipulation, E1 and E2 are both evil, just not 7 equally so. If E1 is evil, then by choosing E1, one chooses evil, even if E1 is less evil than E2 ('less evil' is still evil, only less so), just as if one chooses to drink a cup of tea with one sugar cube, then one is still choosing sweet tea, even if a cup of tea with one sugar cube is not as sweet as a cup of tea with two sugar cubes ('less sweet' is still sweet, only less so). On the other hand, if we answer no, then there is a possible state of affairs that an omnipotent and omnibenevolent being cannot bring about, namely, the state of affairs where an omnipotent and omnibenevolent being chooses the lesser of two evils, and thus an omnipotent and omnibenevolent being turns out not to be all-powerful. Some might think that if we distinguish between metaphysical possibility and moral possibility, then we could say that an omnipotent and omnibenevolent being can bring about the state of affairs where an omnipotent and omnibenevolent chooses the lesser of two evils metaphysically, since this state of affairs is metaphysically possible, but not morally, since this state of affairs is not morally possible. But this is equivalent to saying that there is a state of affairs that an omnipotent and omnibenevolent being is morally prevented from bringing about, which is why this move fails. In other words, it does not make a difference to the puzzle whether an omnipotent and omnibenevolent being lacks the metaphysical power or the moral power (or any kind of power, for that matter) to bring about a possible state of affairs. As long as an omnipotent and omnibenevolent being lacks any kind of power whatsoever to bring about a possible state of affairs, whether that state of affairs is metaphysically possible or morally possible, the problem is to say how this being could still be said to be all-powerful in any meaningful sense. One might also try to respond to this puzzle about omnipotence and omnibenevolence by appealing to the notion of evil as a privation. In other words, if evil is not real, but rather a privation of good, then one could argue that, in choosing the lesser of two evils, an omnipotent and omnibenevolent being may be choosing the lesser good, but it is still choosing something good rather than evil. This response, however, seems to amount to a denial of conclusion (3) in the Leibnizian argument outlined above. Admittedly, it might seem coherent to say that it is not the case that God always acts in the most perfect manner, both metaphysically and morally (Cf. Rowe 2004). But then it is difficult to see how God can be said to be a maximally great (or 8 perfect) being in the moral sense, i.e., an omnibenevolent being, for one would then be admitting that God can choose something that is less than maximally good. The aforementioned puzzle about omnibenevolence and omnipotence can be summed up in the form of a dilemma as follows: 1. Either God can choose the lesser of two evils or God cannot choose the lesser of two evils. 2. If God can choose the lesser of two evils, then God is not omnibenevolent (since God can choose evil). 3. If God cannot choose the lesser of two evils, then God is not omnipotent (since there is a possible state of affairs that God cannot bring about). 4. (Therefore) Either God is not omnibenevolent or God is not omnipotent. Unlike the familiar puzzles about omnipotence, and the aforementioned puzzle about omniscience, this puzzle about omnibenevolence and omnipotence is not intended to show that the divine attribute of benevolence is incoherent. Rather, this puzzle shows that the divine attributes of benevolence and omnipotence are logically incompatible. IV. A PUZZLE ABOUT DIVINE RATIONALITY AND OMNIPOTENCE God is also said to be a perfectly rational being. This idea can be traced back to Leibniz, whose Principle of Sufficient Reason (PSR) implies that God must have a reason for acting as he does. In Principles of Nature and Grace (1714), Leibniz says that PSR means that things happen in such a way that an omniscient being would be able to give a reason (or reasons) why things are so and not otherwise. (See also Torrance 1981.) Now, divine rationality, thus understood, seems to be incompatible with the divine attribute of omnipotence. This is illustrated by the following puzzling question: Could a being that is both omnipotent and perfectly rational form a belief on the basis of fallacious reasoning? 9 On the one hand, if we answer yes, then a perfectly rational and omnipotent being is capable of forming a belief on the basis of fallacious reasoning, and hence this being turns out not to be perfectly rational. On the other hand, if we answer no, then there is a possible state of affairs that a perfectly rational and omnipotent being cannot bring about, namely, the state of affairs where a perfectly rational and omnipotent being forms a belief on the basis of fallacious reasoning, and thus this being turns out not to be all-powerful. Some might think that if we distinguish between metaphysical possibility and epistemic possibility (i.e., what an epistemic agent can do), then we could say that an omnipotent and perfectly rational being can bring about the state of affairs where an omnipotent and perfectly rational being forms a belief on the basis of fallacious reasoning metaphysically, since this state of affairs is metaphysically possible, but not epistemically, since this state of affairs is not epistemically possible. But this is equivalent to saying that there is a possible state of affairs that an omnipotent and perfectly rational being is epistemically prevented from bringing about, which is why this move fails. In other words, it does not make a difference to the puzzle whether an omnipotent and perfectly rational being lacks the metaphysical power or the epistemic power (or any kind of power, for that matter) to bring about a possible state of affairs. As long as an omnipotent and perfectly rational being lacks any kind of power whatsoever to bring about a possible state of affairs, whether the state of affairs is metaphysically possible or epistemically possible, the problem is to say how this being could still be said to be all-powerful in any meaningful sense. One might also try to respond to this puzzle about omnipotence and divine rationality by saying that, while God does not possess the maximum of every attribute (because some attributes have no maxima or because God's possession of the maximum of one attribute conflicts with that of another attribute), God may nevertheless be the greatest possible being because no set of compossible perfections is as great as the set of perfections God possesses (see, e.g., Schlesinger 1985). But even if one finds a principled and non-arbitrary way of individuating sets of compossible perfections and then ranking them from best to worst, one would still face the 10 following problem: how could one know that no set of compossible perfections is as great as the set of perfections God possesses unless God is simply a being with maximal perfections? To put it another way, suppose that omnipotence conflicts with omnibenevolence, as I have argued above, how do we decide whether the greatest set of compossible perfections includes omnipotence or omnibenevolence, given that it cannot include both? And then, what are the criteria for determining whether the set of the divine attributes is equivalent to the set that includes omnipotence but not omnibenevolence or the set that includes omnibenevolence but not omnipotence? Furthermore, even if one manages to solve the aforementioned problems, this move seems to amount to admitting that God is not really a maximally great (or perfect) being after all. For, presumably, a maximally great (or perfect) being is a being that has the maximum of all perfections. But the move outlined above proceeds by admitting that God does not have maximal perfections, since some of them are logically incompatible. The aforementioned puzzle about divine rationality and omnipotence can be summed up in the form of a dilemma as follows: 1. Either God can form a belief on the basis of fallacious reasoning or God cannot form a belief on the basis of fallacious reasoning. 2. If God can form a belief on the basis of fallacious reasoning, then God is not perfectly rational (since God can reason fallaciously). 3. If God cannot form a belief on the basis of fallacious reasoning, then God is not omnipotent (since there is a possible state of affairs that God cannot bring about). 4. (Therefore) Either God is not perfectly rational or God is not omnipotent. Unlike the familiar puzzles about omnipotence, and the aforementioned puzzle about omniscience, this puzzle about divine rationality and omnipotence is not intended to show that the divine attribute of perfect rationality is incoherent. Rather, this puzzle shows that the divine attributes of omnipotence and perfect rationality are logically incompatible. 11 V. CONCLUSION In conclusion, the aforementioned puzzles point to problems with the conception of God as a maximally great (or perfect) being. The first puzzle about omniscience shows that the divine attribute of omniscience is incoherent. The second puzzle about omnibenevolence and omnipotence shows that these two divine attributes are logically incompatible. The third puzzle about perfect rationality and omnipotence shows that these two divine attributes are logically incompatible. I have also considered several possible replies to these puzzles but found them wanting. REFERENCES Adams, R. 1983. 'Divine Necessity', Journal of Philosophy, 80: 741-746 Beyer, J. A. 2004. 'A Physicalist Rejoinder to Some Problems with Omniscience; Or, How God Could Know What We Know', Sophia, 43: 5-13 Campbell, B. and Nagasawa, Y. 2005. 'Anything You Can Do God Can Do Better', American Philosophical Quarterly, 42: 221-227 Davis, S. 1983. Logic and the Nature of God (Grand Rapids, MI: Wm. B. Eerdmans) Everitt, N. 2010. 'The Divine Attributes', Philosophy Compass, 5: 78-90 Gale, R. 1991. On the Existence and Nature of God (New York: Cambridge University Press) Grim, P. 1983. 'Some Neglected Problems of Omniscience', American Philosophical Quarterly, 20: 265277 Hoffman, J. 1979. 'Can God Do Evil?', Southern Journal of Philosophy, 17: 213-220 Hoffman, J. and Rosenkrantz, G. 1980. 'The Omnipotence Paradox, Modality, and Time', Southern Journal of Philosophy, 18: 473-479 Hoffman, J. and Rosenkrantz G. 2006. 'Omnipotence', The Stanford Encyclopedia of Philosophy. Edward N. Zalta (ed.). Available at: <http://plato.stanford.edu/entries/omnipotence/> [accessed 05/06/2013] Leibniz, G. W. 1989. Philosophical Essays, Roger Ariew and Dan Garber (Eds.) (Indianapolis: Hackett Publishing Co.) MacDonald, S., Ed. 1991. Being and Goodness (Ithaca: Cornell University Press) Martin, M. 1990. Atheism: A Philosophical Justification (Philadelphia: Temple University Press) Morris, T. 1987. 'Perfect Being Theology', Noûs, 21: 19-30 12 Nagasawa, Y. 2005. 'Omniscience and Physicalism: A Reply to Beyer', Sophia, 44: 55-58 Nagel, T. 1974. 'What Is It Like to Be a Bat?', The Philosophical Review, 83: 435-450 Pike, N. 1969. 'Omnipotence and God's Ability to Sin', American Philosophical Quarterly, 6: 208-216 Plantinga, A. 1974. God, Freedom, and Evil (Grand Rapids, MI: Wm. B. Eerdmans) --1980. Does God Have a Nature? (Milwaukee: Marquette University Press) Rogers, K. A. 2000. Perfect Being Theology (Edinburgh: Edinburgh University Press) Rowe, W. L. 2004. Can God be Free? (Oxford: Clarendon Press) Schlesinger, G. N. 1985. 'Divine Perfection', Religious Studies, 21: 147-158 Torrance, T. F. 1981. Divine and Contingent Order (Oxford: Oxford University Press) Wierenga, E. 1989. The Nature of God (Ithaca: Cornell University Press) --2010. 'Omniscience', The Stanford Encyclopedia of Philosophy. Edward N. Zalta (ed.). Available at: <http://plato.stanford.edu/entries/omniscience/> [accessed 05/06/2013] Zagzebski, L. 2007. 'Omniscience', in The Routledge Companion to Philosophy of Religion, C. Meister and P. Copans (Eds.), pp. 261-269 (New York: Routledge)