Faith and Philosophy: Journal of the Society of Christian Philosophers Volume 30 | Issue 2 Article 6 4-1-2013 On Whitcomb's Grounding For Atheism Andrew Cullison Daniel Howard Snyder Follow this and additional works at: https://place.asburyseminary.edu/faithandphilosophy This Article is brought to you for free and open access by ePLACE: preserving, learning, and creative exchange. It has been accepted for inclusion in Faith and Philosophy: Journal of the Society of Christian Philosophers by an authorized editor of ePLACE: preserving, learning, and creative exchange. Recommended Citation Cullison, Andrew and Snyder, Daniel Howard (2013) "On Whitcomb's Grounding For Atheism," Faith and Philosophy: Journal of the Society of Christian Philosophers: Vol. 30 : Iss. 2 , Article 6. Available at: https://place.asburyseminary.edu/faithandphilosophy/vol30/iss2/6 FAITH AND PHILOSOPHY Vol. 30 No. 2 April 2013 198 All rights reserved ON WHITCOMB'S GROUNDING ARGUMENT FOR ATHEISM Joshua Rasmussen, Andrew Cullison, and Daniel Howard-Snyder Dennis Whitcomb argues that there is no God on the grounds that (i) God is supposed to be omniscient, yet (ii) nothing could be omniscient due to the nature of grounding. We give a formally identical argument that concludes that one of the present co-authors does not exist. Since he does exist, Whitcomb's argument is unsound. But why is it unsound? That is a difficult question. We venture two answers. First, one of the grounding principles that the argument relies on is false. Second, the argument equivocates between two kinds of grounding: instance-grounding and quasi-mereological grounding. Happily, the equivocation can be avoided; unhappily, avoidance comes at the price of a false premise. I. Parody One way to argue for atheism is to argue that one of the properties God is supposed to have could not be had by anything. Thus, for example, one might argue that there is no God because God is supposed to be omni potent and nothing could be omnipotent due to a suitably subtle version of the paradox of the stone. And there are other well-known arguments of this form. Continuing in this grand tradition, Dennis Whitcomb argues that there is no God because God is supposed to be omniscient and nothing could be omniscient due to the nature of grounding and its relation to knowledge.1 Whitcomb offers two versions of his argument, one informal and the other formal. In what follows we assess both versions. The informal version goes like this: Suppose for reductio that someone is omniscient. Then his being omniscient is partly grounded by his knowing that he is omniscient (which is one of the knowings that helps make him all-knowing). And his knowing that he is omniscient is partly grounded by his being omniscient (for knowledge is partly grounded by the truth of what is known). Since partial grounding is transitive, it follows that his being omniscient is partly grounded by his being omniscient. But this result is absurd, for nothing can partly ground itself. Hence our reductio assumption is false. That is to say, it is false that 1Dennis Whitcomb, "Grounding and Omniscience," forthcoming, Oxford Studies in Philosophy of Religion 4 (2012). ON WHITCOMB'S GROUNDING ARGUMENT FOR ATHEISM 199 someone is omniscient. But if God exists, then he is omniscient. Therefore, God does not exist.2 Is the informal version of Whitcomb's grounding argument for atheism sound? To answer that question, consider the following definition and assumption: Definition. "X is daniscient" =df. "X knows all and only whatever propositions Dan Howard-Snyder happens to know." Assumption. One of the propositions that Dan Howard-Snyder happens to know is that Dan Howard-Snyder is daniscient. Now consider the following parody argument: Suppose for reductio that Dan Howard-Snyder is daniscient. Then his being daniscient is partly grounded by his knowing that he is daniscient (which is one of the knowings that helps make him daniscient). And his knowing that he is daniscient is partly grounded by his being daniscient (for knowledge is partly grounded by the truth of what is known). Since partial grounding is transitive, it follows that his being daniscient is partly grounded by his being daniscient. But this result is absurd, for nothing can partly ground itself. Hence our reductio assumption is false. That is to say, it is false that Dan Howard-Snyder is daniscient. But if Dan Howard-Snyder exists, then he is daniscient.3 Therefore, Dan Howard-Snyder does not exist. It appears that if the informal version of Whitcomb's grounding argument for atheism is sound, then Dan Howard-Snyder does not exist. But he does exist. (If you doubt this, run the argument using your own name.) Therefore, the informal version of Whitcomb's argument is unsound. Informal versions of an argument are often bettered by their formal versions. Here is Whitcomb's formal version of the argument, ever so slightly altered: Let "↤" abbreviate "is partly grounded by" and let "[P]" abbreviate "the fact that P." Now consider the following four true principles: TRANSITIVITY: For all facts X, Y, and Z: if X ↤ Y and Y ↤ Z, then X ↤ Z. IRREFLEXIVITY: For every fact F, it is not the case that F ↤ F. TRUTH GROUNDS KNOWLEDGE (TGK): For every fact F of the form S knows that K, F ↤ [K]. ∃∀ GROUNDING: Every existential-universal (∃∀) fact ↤ each of its instances. 2Ibid., 5 (manuscript). 3This is true because both the antecedent and the consequence are true (which is not to say, of course, that the conditional is necessarily true). 200 Faith and Philosophy To illustrate ∃∀ GROUNDING, suppose that it is a fact that someone is loved by everyone: ∃x∀y(y loves x). Call that fact "L." Further, suppose that Igor is loved by everyone, and that Sam and Pat are among the people who exist. Then ∃∀ GROUNDING tells us that L is partly grounded by [Sam loves Igor], and partly grounded by [Pat loves Igor]. That is to say, it tells us that L is partly grounded by both of these two instances it has-these two as well as many others. (We trust the intended meaning of "instance" is sufficiently clear from the examples. For a more precise definition, see Whitcomb's Appendix 2.) These four principles are inconsistent with OMNISCIENCE: It is a fact that there is some being x such that for every fact f, x knows f. Proof: Let "G" name one of the individuals who knows every fact, according to OMNISCIENCE, and let "O" name [there is some being x such that for every fact f, x knows f]. Then: 1. [G knows O] is an instance of O (by OMNISCIENCE) 2. O ↤ [G knows O] (by 1 and ∃∀ GROUNDING) 3. [G knows O] ↤ O (by OMNISCIENCE and TGK) 4. O ↤ O (by 2, 3, and TRANSITIVITY) 5. ¬(O ↤ O) (by IRREFLEXIVITY) Contradiction (4, 5) Since God exists only if OMNISCIENCE is true, and OMNISCIENCE is inconsistent with our four true principles of grounding, God does not exist.4 What should we make of this argument? Well, consider the following parody argument: TRANSITIVITY, IRREFLEXIVITY, TGK, and ∃∀ GROUNDING are all true and inconsistent with DANISCIENCE: It is a fact that there is some being x such that for every fact f known by Dan Howard-Snyder, x knows f. Proof: Let "Dan Howard-Snyder" name one of the individuals who knows every fact that Dan Howard-Snyder knows, according to DANISCIENCE, and let "D" name [there is some being x such that for every fact f known by Dan Howard-Snyder, x knows f]. Then: 1. [Dan Howard-Snyder knows D] is an instance of D (by DANISCIENCE) 4Ibid., 6–7, 14 (manuscript). ON WHITCOMB'S GROUNDING ARGUMENT FOR ATHEISM 201 2. D ↤ [Dan Howard-Snyder knows D] (by 1 and ∃∀ GROUNDING) 3. [Dan Howard-Snyder knows D] ↤ D (by DANISCIENCE and TGK) 4. D ↤ D (by 2, 3, and TRANSITIVITY) 5. ¬(D ↤ D) (by IRREFLEXIVITY) Contradiction (4, 5) Since Dan Howard-Snyder exists only if DANISCIENCE is true, and DANISCIENCE is inconsistent with our four true principles of grounding, Dan Howard-Snyder does not exist. It appears that if the formal version of Whitcomb's grounding argument for atheism is sound, then Dan Howard-Snyder does not exist. But he does exist. Therefore, the formal version of Whitcomb's argument is unsound. II. Diagnosis We conclude that Whitcomb's grounding argument for atheism, in both its informal and formal versions, is unsound. But why is it unsound? This is not an easy question to answer. Still, we venture an answer. In fact, we venture two. It is unsound because ∃∀ GROUNDING is false and/or because it commits the fallacy of equivocation. We explain each answer in turn. Recall that, according to ∃∀ GROUNDING, every ∃∀ fact is partly grounded by each of its instances. It's not too difficult, however, to get in a frame of mind where one might well think one can see that there are some ∃∀ facts that are not partly grounded by each of their instances. Indeed, we only need look to omniscience's near neighbor omnipotence to find a candidate. Omnipotence, as one might expect, has to do with power, particularly the ability to bring about every metaphysically possible state of affairs (roughly). Suppose, just for the sake of illustration, that OMNIPOTENCE: It is a fact that there is some being x such that for every metaphysically possible state of affairs s, x is able to bring about s. OMNIPOTENCE is an ∃∀ fact. Thus, if, as ∃∀ GROUNDING tells us, every ∃∀ fact is partly grounded by each of its instances, then (say) Theia's ability to bring about every metaphysically possible state of affairs is partly grounded by, for example, her ability to bring it about that the freezing level drops at Goat Rocks tonight.5 But this implication seems false. Indeed, the reverse seems true: Theia's ability to bring it about that the freezing level drops at Goat Rocks tonight is partly grounded by her ability to bring 5See http://en.wikipedia.org/wiki/Goat_Rocks. "The Goat Rocks are a series of rugged volcanic peaks in the Cascade Range, roughly between Mount Rainier and Mount Adams in southern Washington state. They are named after the numerous mountain goats which live in the area, and are at the core of the eponymous Goat Rocks Wilderness." 202 Faith and Philosophy about every metaphysically possible state of affairs. In that case, if we add IRREFLEXIVITY-according to which, for every fact F, it is not the case that F is partly grounded by F-∃∀ GROUNDING turns out false. One might agree that ∃∀ GROUNDING is false in its full generality and that omnipotence shows that this is so, but nevertheless insist that it applies to omniscience. This would be a mistake, however. For suppose that omnipotence shows that ∃∀ GROUNDING is false in its full generality. Now, just as omnipotence has to do with power, so does omniscience- cognitive power, particularly the ability to know all facts (roughly, and in keeping with Whitcomb's usage). It seems that what we said about omnipotence is rightly said about omniscience. Theia's ability to know all facts is not partly grounded by, for example, her ability to know that the freezing level will drop at Goat Rocks tonight. Rather, her ability to know that the freezing level will drop at Goat Rocks tonight is partly grounded by her ability to know all facts. Add IRREFLEXIVITY and ∃∀ GROUNDING turns out false with respect to omniscience. So much for ∃∀ GROUNDING. We now turn to equivocation. TGK and ∃∀ GROUNDING seem to be about different grounding relations. Recall that according to TGK, for every fact F of the form S knows that K, F is partly grounded by [K]. Here the grounding relation seems to involve something being grounded by its parts or constituents. Knowledge is partly grounded by the fact known in that it is a part or constituent of knowledge. Part of what it is to for us to know that the Knife's Edge is in the Goat Rocks Wilderness is for it to be the case that the Knife's Edge is in the Goat Rocks Wilderness; it's being the case that the Knife's Edge is in the Goat Rocks Wilderness is a constituent of our knowing that the Knife's Edge is in the Goat Rocks Wilderness. The grounding here appears to be mereological or, better, quasi-mereological.6 (We leave the quasi-qualification implicit from here on out.) Not so for ∃∀ GROUNDING. According to ∃∀ GROUNDING, every ∃∀ fact is partly grounded by each of its instances. Here the grounding relation seems to involve facts being grounded by their instances. For example, [∃x(x is a person)] is partly grounded by [Barack Obama is a person]; and, to draw on Whitcomb's illustrative hypothetical case, [∃x∀y(y loves x)] is partly grounded by [Sam loves Igor], [Pat loves Igor], and so on. Now, it might be tempting to think of instances as in some sense parts of the facts they instance. Perhaps this temptation underwrites some of the appeal of ∃∀ GROUNDING. However, some instances cannot be so thought of. Take, for example, [∃x(x is a fact)]. Call it "E." Notice that [E is a fact] is an instance of E but [E is a fact] is not a part or constituent of E. If anything, it's the other way around: E is a part or constituent of [E is a 6Karen Bennett calls this sort of relation a "building" grounding relation in "Construction Area (No Hard Hat Required)," Philosophical Studies 154:1, 79–104. See also Whitcomb's commentary on TGK, pages 11–13 (manuscript), where he characterizes the grounding relation involved in TGK in mereological, or quasi-mereological, terms. ON WHITCOMB'S GROUNDING ARGUMENT FOR ATHEISM 203 fact]. Thus, from a mereological point of view, [E is a fact] might well be partly grounded by E, but E is not an instance of [E is a fact]. The same goes for the ∃∀ facts on the table. [Dan Howard-Snyder knows D] is an instance of D but it is not a part or constituent of D. That is, [Dan Howard-Snyder knows D] is an instance of [there is some being x such that for every fact f known by Dan Howard-Snyder, x knows f], but the former is not a part or constituent of the latter. Likewise, [G knows O] is an instance of O but it is not a part or constituent of O. That is, [G knows O] is an instance of [there is some being x such that for every fact f, x knows f], but the former is not a part or constituent of the latter. The upshot, then, is this: the instance grounding relation is not identical with the mereological grounding relation. Whitcomb's grounding argument for atheism and our parody argument make use of both types of grounding. Here's the relevant portion of the formal version of Whitcomb's argument: 2. O ↤ [G knows O] (by 1 and ∃∀ GROUNDING) 3. [G knows O] ↤ O (by OMNISCIENCE and TGK) 4. O ↤ O (by 2, 3, and TRANSITIVITY) Here's the relevant portion of our parity argument: 2. D ↤ [Dan Howard-Snyder knows D] (by 1 and ∃∀ GROUNDING) 3. [Dan Howard-Snyder knows D] ↤ D (by OMNISCIENCE and TGK) 4. D ↤ D (by 2, 3, and TRANSITIVITY) The relation expressed by "↤" in each version of (2) is the instance grounding relation, whereas the relation expressed by "↤" in each version of (3) is the mereological grounding relation. Thus, each argument equivocates. Consequently, (4) of each argument doesn't follow from (2) and (3), at least not by TRANSITIVITY, whose application demands a single relation and not just a single symbol or form of words. Can equivocation be avoided? We think so, but only if there is a general grounding relation that encompasses both mereological grounding and instance grounding. However, if there is such a general grounding relation, then-since mereological grounding (or whatever grounding is involved in TGK) dictates that [Dan Howard-Snyder knows D] is partly grounded by D, which, recall, is [there is some being x such that for every fact f known by Dan Howard-Snyder, x knows f], and instance grounding dictates that D is partly grounded by [Dan Howard-Snyder knows D]-it grounds in both directions, from D to [Dan Howard-Snyder knows D] and from [Dan Howard-Snyder knows D] to D. Now: either this general grounding relation is transitive or it is not. If it is transitive, then D is partly grounded by D, in which case it is not irreflexive and Whitcomb's IRREFLEXIVITY is false. If, on the other hand, it is not transitive, then Whitcomb's TRANSITIVITY is false. Equivocation can be avoided in our 204 Faith and Philosophy parity argument, therefore, but only at the usual price: a false premise. Mutatis mutandis, the same goes for Whitcomb's grounding argument for atheism.7 Azusa Pacific University SUNY Fredonia Western Washington University 7For comments on previous drafts, thanks to Ben Corey, Tom Flint, Frances HowardSnyder, Hud Hudson, Ryan Wasserman, Dennis Whitcomb, and an anonymous referee.