Introduction
Dennis Whitcomb has recently argued that the idea that there is an omniscient being is to be rejected, since, in conjunction with a few plausible principles about grounding, it leads to a contradiction.Footnote 1 However, on a classical, Anselmian, conception of God, which prevails in current analytic philosophy of religion, God is (necessarily) omniscient. Hence, if the argument is sound, it not only refutes the idea that there is an omniscient being, but also the thesis that God exists. In this paper, I argue that Whitcomb's argument should be rejected since it has certain unacceptable consequences that have nothing to do with the existence of God, and I show that the argument trades on an ambiguity in the pivotal notion of grounding.
The article is structured as follows. First, I define the principles that play a role in Whitcomb's argument and then briefly sketch that argument. Second, I argue that if this argument is sound, it has at least three dire consequences, namely that we do not know that we have knowledge; that, for most of us, all of our beliefs are false; and that there are no truths. This suggests that Whitcomb has not so much laid bare a problem with the idea of an omniscient being as discovered a problem with the notion of grounding that he uses. Finally, I try to show where the argument goes wrong by defending the view that Whitcomb's notion of grounding is ambiguous between two different kinds of relations and that if we keep these two kinds of relations apart, the argument turns out to be invalid.
The grounding objection to omniscience
Before I lay out Whitcomb's argument and the principles that it involves, let me say a word about grounding. Whitcomb does not actually define what it is for something to be grounded by something else. What he says is merely that he takes it that grounding is a relation and that the relata are facts, although he submits that it might also be cast in terms of a relation between the truth of different propositions. And although he does not define what it is for one fact to be grounded by another, he says that if some fact X is partially or fully grounded by some other fact Y, then X obtains partly or fully in virtue of or because of Y.
Moreover, he elucidates the notion of grounding by giving what he considers to be three examples of the grounding relation. First, Plato's famous question in his Euthyphro can correctly be understood as the following question: is the rightness of an act grounded by God's approval of that act, or is God's approval of an act grounded by that act's rightness? Second, the fact that I truly believe that I have hands is partly grounded by the fact that I believe that I have hands. The fact that I believe that I have hands is not partly grounded by the fact that I truly believe that I have hands. Third, the fact that some number or other is an even prime is partly grounded by the number 2's being an even prime. It is not the case that the number 2's being an even prime is partly grounded by there being some even prime number (pp. 173–174). Of course, much more could be said about grounding, but Whitcomb's rough characterization and these three examples give us at least some grip on this notion.
There are five principles – or maybe one premise and four principles – that play an important role in Whitcomb's argument against omniscience. They can be defined as follows, where ‘X ↤ Y’ stands for ‘X is at least partly grounded by Y’:
(i) There is some fact O such that O = <there is some being x such that for every fact F, x knows F > . [OMNISCIENCE]
(ii) For all facts X, Y, and Z: if X ↤ Y and Y ↤ Z, then X ↤ Z. [TRANSITIVITY]
(iii) For every fact F, it is not the case that F ↤ F. [IRREFLEXIVITY]
(iv) For every fact F of the form S knows that F*, F ↤ F*. [TRUTH GROUNDS KNOWLEDGE]
(v) Every ∃∀ fact ↤ each of its instances. [∃∀ GROUNDING]
Principle (v) requires some elucidation. For what is it for some fact to be an instance of some other fact? Here is how Whitcomb explains his use of this notion:
[T]he instances of any fact F are simply the facts we represent when, starting with a sentence adequately representing F, we remove the quantifiers and replace the variables with constants in such a way that the resulting sentence successfully represents a fact. (p. 178)Footnote 2
Thus, the fact that Berta, one of my uncle's cows, exists is an instance of the more general fact that there are cows. For we can replace ‘∃x(x is a cow)’ with ‘Berta is a cow’. And the fact that God is omniscient, if that is a fact, is an instance of the more general fact that there is some being who is omniscient, again, if that is a fact. For we can replace ‘∃x(x is omniscient)’ with ‘God is omniscient’. Throughout this section and the following section, I will assume with Whitcomb that his interpretation of the instantiation relation is viable. In the fourth and final section, I return to this issue.
Now, principle (v) uses the expression ‘∃∀ fact’. By an ‘∃∀ fact’ Whitcomb means a fact that can be represented in the sentence ‘∃x∀y(Rxy)’, where R is a relation that holds between x and y. Thus, an example of an ∃∀ fact is the fact, if it is fact, that there is someone who is loved by everyone. And another example is the fact, if it is a fact, that there is someone who knows the truth value of every proposition. Clearly, if God is omniscient, then that is an ∃∀ fact. This means that what ∃∀ GROUNDING says is that, for example, the fact that Igor is loved by everyone is grounded by the fact (one of its instances) that Igor is loved by Sam and by the fact (another of its instances) that Igor is loved by Pat; and that the fact that God is omniscient is grounded by the fact that God knows that p is true, by the fact that God knows that some other proposition q is true, and so forth.
Now, it is important for our purposes to note, as Whitcomb himself does (p. 178), that ∃∀ facts are a subcategory of the more general category of ∃ facts. ∃ facts are facts that can be represented in the sentence ‘∃x(Px)’. Thus the sentence ‘There are persons’ and the sentence ‘There are truths’ represent ∃ facts. Now, if ∃∀ facts are grounded by their instances, it seems plausible to say that all ∃ facts are grounded by their instances. Indeed, Whitcomb explicitly embraces this thought. He says, for example, that the ∃ fact that some persons exist is grounded by the fact that Bill Clinton is a person, by the fact that I am a person, and by the fact that you are a person (p. 177). This means that we can add the following principle which closely resembles ∃∀ GROUNDING to the above list:
(v′) Every ∃ fact ↤ each of its instances. [∃ GROUNDING]
Now, if both the more general ∃ facts and the more specific ∃∀ facts are grounded by each of their instances, then it seems plausible that ∃∃ facts, another subcategory of ∃ facts, are also grounded by each of their instances. Whitcomb does not mention ∃∃ facts in his paper, but given that he embraces (v) and (v′), it seems that he would have to embrace the following principle (v″) as well:
(v″) Every ∃∃ fact ↤ each of its instances. [∃∃ GROUNDING]
For example, the more general fact that there are people who have possessions is partly grounded by the fact that Jane has a house and the fact that Sam owns a bike. For these are facts that we represent when we remove the quantifiers and replace the variables with constants in the sentence ∃x∃y(x owns y). It is important to make this explicit, for both ∃ GROUNDING and ∃∃ GROUNDING are principles that will play a crucial role in my objections to Whitcomb's argument.
Now, according to Whitcomb, the argument against divine omniscience is simply this: (i)–(v) are jointly inconsistent, and each of (ii)–(v) is plausible, hence, (i) has to go. Here is his argument for his view that (i)–(v) are inconsistent:
(1) <God knows O> is an instance of O [by OMNISCIENCE]
(2) O ↤ <God knows O> [by (1) and ∃∀ GROUNDING]
(3) <G knows O> ↤ O [by OMNISCIENCE and TRUTH GROUNDS KNOWLEDGE]
(4) O ↤ O [by (2), (3), and TRANSITIVITY]
(5) ¬ (O ↤ O) [by IRREFLEXIVITY]
(6) ¬ (1) [RAA; by (1)–(5)]Footnote 3
Whitcomb gives a detailed defence of each of (ii)–(v). If we want to avoid the contradiction constituted by the conjunction of (4) and (5), Whitcomb says, we need to give up the idea that there is an omniscient being. But if there is no omniscient being, then the God of perfect being theology does not exist. Hence, the argument against omniscience also refutes theism.
A reduction
Whitcomb takes his argument to count against omniscience. However, if the four principles (ii)–(v′) that he subscribes to are correct, then we can run a similar argument against certain claims that are widely accepted among philosophers and non-philosophers alike. More specifically, if Whitcomb's argument is sound, then it also follows among other things that we do not know that we have knowledge, that we hold only false beliefs, and that there are no truths. Since these claims contradict widely accepted theses, this counts as a reductio of Whitcomb's strategy.
As to the first dire consequence, consider the following two propositions, where ‘K’ stands for the fact that <Someone has knowledge > :
(vi) Some person S knows that K.
(vii) If some person S knows that K, then S's knowing that K is an instance of K.
I will assume premise (vi) for the sake of argument. Premise (vii) follows from Whitcomb's definition of some fact's being an instance of another fact. For we can represent in a sentence the fact that S knows that K (where K is the proposition that someone has knowledge) by removing the quantifiers and replacing the variables with constants in the sentence ‘∃x∃y(x knows that y)’.
Now, (vi), (vii), and (ii)–(v″) jointly lead to a contradiction, which can be shown as follows:
(1′) <S knows that K> is an instance of K [by (vi) and (vii)]
(2′) K ↤ <S knows that K> [by ∃∃ GROUNDING and (1′)]
(3′) <S knows that K> ↤ K [by (vi) and TRUTH GROUNDS KNOWLEDGE]
(4′) K ↤ K [by (2′), (3′), and TRANSITIVITY]
(5′) ¬ (K ↤ K) [by IRREFLEXIVITY]
(6′) ¬ (1′) [RAA; by (1′)–(5′)]
As I said, (vii) follows from Whitcomb's definition of ‘being an instance of’. (ii)–(v″) are principles that Whitcomb needs for his grounding objection to omniscience or that he is committed to in virtue of his argument against omniscience. This means that Whitcomb has to deny (vi), that is, that there is someone who knows that someone has knowledge. In other words, it follows that none of us knows that he or she or any one else has knowledge. This would be quite a bullet to bite for Whitcomb.
It is not the only bullet he would have to bite, though. Consider the three following principles, where ‘B’ stands for the fact: <Someone holds one or more true beliefs > .
(viii) Some person S truly believes that B.
(ix) If some person S truly believes that B, then S's truly believing that B is an instance of B.
(x) For every fact F of the form S truly believes that F*, F ↤ F*. [TRUTH GROUNDS TRUE BELIEF]
I assume (viii) for the sake of argument. (ix) is true in virtue of Whitcomb's definition's of some fact's being an instance of some other fact. And if principle (iv), that is, the principle that truth grounds knowledge, is plausible, then so is (x), that is, the principle that truth grounds true belief. Whitcomb even explicitly acknowledges that true belief is partly grounded by truth (p. 183). However, (viii)–(x) in conjunction with (ii), (iii), and (v″) lead to a contradiction, which can be shown as follows:
(1″) <S truly believes that B> is an instance of B [by (viii) and (ix)]
(2″) B ↤ <S truly believes that B> [by ∃∃ GROUNDING and (1″)]
(3″) <S truly believes that B> ↤ B [by (viii) and TRUTH GROUNDS TRUE BELIEF]
(4″) B ↤ B [by (2″), (3″), and TRANSITIVITY]
(5″) ¬ (B ↤ B) [by IRREFLEXIVITY]
(6″) ¬ (1″) [RAA; by (1″)–(5″)]
(ix) is true by definition, (x) is true if (iv) is true, and Whitcomb accepts (ii), (iii), and seems committed to (v″). Hence, there is only one way out for Whitcomb, namely to deny (viii). Thus, Whitcomb has to embrace the claim that no one truly believes that someone holds true beliefs. But many of us do believe that we hold true beliefs (I, for one, do). If, as many philosophers hold, all propositions that we believe are either true or false, it would follow that anyone who believes that he or she holds true beliefs thereby believes something false. And that means that most of us (all of us who believe that we hold true beliefs) do not hold any true beliefs. But, again, we hold beliefs and it is widely thought that beliefs are either true or false. It would, thus, follow that most of us hold only false beliefs. Again, that is a dire consequence, to say the least.
The problems with Whitcomb's argument, however, are not confined to the cognitive realm, that is, the domain of knowledge and beliefs. Let me close this section by arguing that a third unacceptable consequence of Whitcomb's argument is that there are no truths. Consider the following principles, where ‘T’ stands for the fact: <there are truths > .
(xi) It is true that T.
(xii) If it is true that T, then its being true that T is an instance of T.
(xiii) For every fact F of the form It is true that F*, F ↤ F*. [REALITY GROUNDS TRUTH]
I will assume (xi) for the sake of argument. (xii) is true by (Whitcomb's) definition of what it is for a fact to be an instance of some other fact. As to (xiii), it seems correct to say that if it is true that something is a fact, then that fact grounds that truth. If it is true that p, then it is true that p in virtue of p; it is not the case that p in virtue of its being true that p. However, (xi)–(xiii) in conjunction with (ii), (iii), and (v') lead to a contradiction, which can be shown as follows:
(1‴) <It is true that T> is an instance of T [by (xi) and (xii)]
(2‴) T ↤ <It is true that T> [by (1‴) and ∃ GROUNDING]
(3‴) <It is true that T> ↤ T [by (xi) and REALITY GROUNDS TRUTH]
(4‴) T ↤ T [by (2‴), (3‴), and TRANSITIVITY]
(5‴) ¬ (T ↤ T) [by IRREFLEXIVITY]
(6‴) ¬ (1‴) [RAA; by (1‴)–(5‴)]
(xiii) is highly plausible and accords well with Whitcomb's understanding of grounding, (xii) is true by definition, and Whitcomb accepts (ii), (ii), and (v′). Hence, the only way to escape this reductio which is available to Whitcomb is to deny (xi). Thus, he would have to say that it is not true that there are truths. But if it is not true that there are truths, then, presumably, it is false that there are truths. Hence, there are no truths. Of all dire consequences that Whitcomb's argument has, this one is perhaps the most devastating.Footnote 4
I take it that these are three consequences that Whitcomb should want to avoid at all costs. However, the only way he could do so is by denying one or several of his premises (ii)–(v). (I say ‘(v)’ because, as I argued, if he should deny (v′) or (v″), then, it seems, he should deny (v) as well.) But whichever of premises (ii)–(v) he denies, his argument against omniscience will not survive, for we are led to a contradiction only if each of them is correct. I conclude that the grounding objection to omniscience – and, thereby, to theism – fails.Footnote 5
What went wrong?
However, if the grounding objection to omniscience and theism fails, can we explain why it is wanting? After all, each of (ii)–(v) seems at least prima facie plausible. Where did the argument go wrong?
I would like to suggest that the argument went wrong because Whitcomb's notion of grounding actually covers two distinct kinds of relations. More precisely, the clause ‘X obtains in virtue of or because of Y’ that we also use in ordinary language is ambiguous between at least two kinds of grounding relations G1 and G2:Footnote 6
G1: Y is a particular instance of X.
G2: Y is ontologically more basic than X, and X comprises Y.
As to G1, remember that, according to Whitcomb, Y is an instance of X if and only if Y is a particular fact that can be expressed by removing the quantifiers and replacing the variables with constants in statements that express the more general fact X. Thus, that it is true that there are truths is an instance of there being truths, for we can replace ‘∃x(x is a truth)’ with ‘the proposition p is a truth’, where p is the proposition that there are truths. And my truly believing that I have true beliefs is an instance of my having true beliefs, for we can replace ‘∃x(I truly believe x)’ with ‘I truly believe the proposition q’, where q is the proposition that I hold true beliefs.Footnote 7
As to G2, Whitcomb gives several examples of facts that stand in this relation to each other. If God approves of certain acts because they are right, then the fact that these acts are right stands in the relationship described in G2 to the fact that God approves of them. Their being right is ontologically more basic than God's approving of them and God's approving of them comprises their being right. If knowledge entails truth, then the fact that a proposition that is known is true stands in the relationship described in G2 to the fact that that proposition is known: its being true is ontologically more basic than its being known and its being known comprises its being true. Other examples of facts displaying the relationship described in G2 to each other are me truly believing that I have hands partly because I believe that I have hands and there being even prime numbers partly because 2 is an even prime number.
When relation G2 holds between X and Y (X ↤2 Y, for short), it does not follow that G1 also holds between X and Y (X ↤1 Y, for short). For instance, the fact that I know that p is grounded by the fact that it is true that p. But its being true that p is not an instance of my knowing that p, for its being true that p is not a particular fact that can be derived from the more general fact that I know that p by removing certain quantifiers and replacing the variables with constants. Nor does the fact that G1 holds between X and Y imply that G2 holds between X and Y. The fact that it is true that there are truths is, on Whitcomb's definition, an instance of the fact that there are truths, but there is no reason to think that the fact that it is true that there are truths is ontologically more basic than the fact that there are truths. In fact, the fact that it is true that there are truths seems ontologically less basic than the fact that there are truths – the fact that <It is true that p > seems necessarily less basic than the fact that <p > .
Now, let us consider the TRANSITIVITY principle with this distinction in mind. If the distinction is correct, then TRANSITIVITY can be understood in at least two different ways:
(ii′) For all facts X, Y, and Z: if X ↤1 Y and Y ↤1 Z, then X ↤1 Z. [TRANSITIVITY′]
(ii″) For all facts X, Y, and Z: if X ↤2 Y and Y ↤2 Z, then X ↤2 Z. [TRANSITIVITY″]
Are these principles correct? It seems to me that the second principle, (ii″), is highly plausible. For if Y is ontologically more basic than X and Z is ontologically more basic than Y, then it is clear that Z is ontologically more basic than X. The first principle, (ii′), also seems convincing to me, although Whitcomb's definition of ‘being an instance of’ has the somewhat weird implication that the antecedent of (ii′) is never met. According to Whitcomb, Y is a particular instance of X just in case we can get to the statement that Y obtains by removing all quantifiers from the statement that X obtains and by replacing the variables in that statement with constants. But if that is correct, then there cannot be a further particular instance Z of the more general fact Y, for there will not remain any quantifiers to be removed or variables to be replaced. I think that Whitcomb can meet this worry by saying instead that Z is an instance of Y just in case we can get to the statement that Z obtains by removing some quantifiers or replacing some variables with constants in the statement that Y obtains.Footnote 8 Thus, the fact that God knows that I exist is an instance of the fact that God is omniscient and the fact that God is omniscient is an instance of the fact that there are omniscient beings.
However, with merely (ii′) and (ii″), Whitcomb's objection to omniscience does not go through, since he uses (and needs to use) the grounding relation equivocally in his argument. Thus, he is committed to something like:
(ii‴) For all facts X, Y, and Z: if X ↤1 Y and Y ↤2 Z, then X ↤1 v 2 Z. [TRANSITIVITY‴]
Premise (2) of his argument corresponds to the first conjunct of (ii‴)'s antecedent, premise (3) corresponds to the second conjunct of (ii‴)'s antecedent, and premise (4) corresponds to (ii‴)'s consequent. The problem with (ii‴), however, is that it is not at all clear why we should think that it is true. If Y is a particular instance of X and Z is ontologically more basic than Y, it is not at all clear how it is supposed to follow that Z is a particular instance of X or that Z is ontologically more basic than X. Take the example about truth that I gave. Its being true that there are certain truths is a particular instance of there being truths and there being truths is ontologically more basic than its being true that there are certain truths. It follows neither that there being truths is a particular instance of there being truths nor that there being truths is ontologically more basic than there being truths. In fact, it is clear that there being truths is not an instance of there being truths (a thing cannot be an instance of itself, at least not on Whitcomb's definition of ‘instance’), and it is clear that there being truths is not ontologically more basic than there being truths (a thing cannot be more basic than itself).
Hence, when we disentangle the ambiguity in Whitcomb's notion of grounding, then it turns out that the version of the TRANSITIVITY principle that he needs for his grounding objection to omniscience to go through is untenable. The fact that the ordinary language expressions ‘because of’ and ‘in virtue of’ nicely capture both kinds of grounding relations that underlie this ambiguity explains why the argument will seem to many prima facie convincing.
Conclusion
Whitcomb's objection to omniscience fails. First, it faces a reductio, for if his argument is sound, then it follows that we do not know that we have knowledge, that most of us hold only false beliefs, and that there are no truths. Second and closely related to this, the argument fails because of an ambiguity in Whitcomb's notion of grounding. If we distinguish between two different kinds of relations that underlie the grounding relation, namely something's being a particular instance of something else and something's being ontologically more basic than something else, then the transitivity principle that Whitcomb needs for his objection to go through is untenable.Footnote 9
