A Logical Examination of the Unknowability of God Hypothesis

I have thought of including a logical argument in my previous post to prove the logical failure of the unknowability hypothesis of Neo-Orthodoxy. (1) Nevertheless, due to my tight schedule, I am only able to include the arguments here.

In the current post, I will show that the "unknowability hypothesis" - which is the basic epistemological assumption of Barth - is logically vacuous, and defies the Law of Non-contradiction. We are reminded that any proposition that contravenes the Aristotelian Law cannot be true.

Suppose, for a reductio, we accept the proposition that p = "God is unknowable" is true. In fact, let us agree with the Barthians concerning the unknowability of God that p = "God is X" is true, where X is an attribute of the noumenal God which is unknowable, and therefore, not known and can never be known. We agree, for argument sake, that we are ignorant of some truth concerning God (i.e. that p) which can never be known via Scripture (or by any other means for that matter). And so we suppose that p is true but not known to be true; then (p ∧ ¬Kp) is true.

Therefore, in accordance with the "unknowability of God" hypothesis, Barthians claim that (p ∧ ¬Kp) is true. (2) Furthermore, they know that (p ∧ ¬Kp) is true, that is, ◊K(p ∧ ¬Kp). (3) Now, this is extremely difficult for any logical mind to receive. How can we know that p ∧ ¬Kp? If knowing a conjunction entails knowing the conjuncts, then K(p ∧ ¬Kp) entails Kp and K¬Kp. Now knowledge entails truth (or more accurately, justified true belief), so K¬Kp entails ¬Kp, which is a contradiction for Kp. So, by reductio ad absurdum, it is not possible that K(p ∧ ¬Kp). We have hereby refuted the "unknowability of God" hypothesis of Neo-Orthodoxy.

To further elucidate the problem of the unknowability hypothesis, we understand that the basic premise of Neo-Orthodox epistemology is K(p ∧ ¬Kp). If p = "God is X," and X represents any attribute which is unknowable of God, then the Barthian's denial of the knowledge of X would paradoxically mandate the knowledge of X. Let us say that p = "God is unknowable." We have seen that Barthians insist that p ∧ ¬Kp is true. Knowledge of p ∧ ¬Kp would entail Kp and K¬Kp i.e. knowing that "God is unknowable," and at the same time, knowing that "God is unknowable" is unknowable. This is a contradiction of the Law of Non-contradiction. In other words, if the Barthian claims that they do not know that p, they must also admit that they know that p.

The onus is therefore on those who insist that "God is unknowable" to show that their epistemological presuppositions are logically viable and coherent.

Notes

1. The "Unknowability of God" hypothesis is basically the belief that God, who belongs to the noumena, is unknowable to the mind of man. This must be distinguished from the Reformed understanding of "Finitum non Capax Infiniti," or "the finite is unable to contain the infinite." The Latin phrase should be understood within the context of the Incarnation of Christ. As Frame had aptly commented, "In the incarnation, Calvin argued, God was manifested in human flesh. However, because nothing finite can completely contain the infinite (finitum non capax infiniti), Christ is also active outside the flesh of Jesus. No less than Luther, Calvin insisted that God wills to be known only in Christ. But he did not believe this meant that God is revealed only in the incarnation; Christ, the eternal Word, also operates outside the work of Jesus. Lutheran critics of Calvin's Christology called this the extra calvinisticum." (John Frame, "Incarnation," in The Westminster Handbook of Reformed Theology, ed. Donald K. McKim (Louisville, KY: Westminster John Knox Press, 2001), 120.)

2. Where p = "God is X," including the proposition "God is unknowable."

3. For those new to modal logic, the basic unary modal operators are usually written □(or L) for Necessarily and ◊(or M) for Possibly. In modal logic, each can be expressed by the other and negation, that is:

Update:

Re: A clarification for those who are perplexed

I apologize for the use of symbolic logic which may be confusing for some, but it allows some of us to see the picture in a neat, mathematical way.

My point in this post, and the previous one as well, is this: we cannot teach that God is unknowable. Firstly, we cannot know that God is unknowable since this entails a logical contradiction. Secondly, if we do not know that God is unknowable i.e. p ∧ ¬Kp, we should abstain from teaching such a doctrine in theology classes. If you do not know that Tom is unsaved, would you teach others that Tom is unsaved with any certainty?

If God is unknowable (and Barth insists that He cannot be known even through Special Revelation), he has attributes that cannot be known i.e. p = God is X, where X is any unknowable attribute of God. Therefore, with or without the agreement of Barth, if he teaches that "God is unknowable," that proposition can be expressed as p ∧ ¬Kp. Since Barth teaches this in his Church Dogmatics, he must be fairly dogmatic (pun intended) concerning this.

But as we have seen above (in the two posts), to say that God is unknowable (and to say that you know that God is unknowable) is to say ◊K(p ∧ ¬Kp), and this entails Kp and K¬Kp. If you were to look at this expression carefully, you would notice that, to claim knowledge in the proposition that you cannot know p i.e. (K¬Kp), you must also claim Kp. To put this simply, to say that you know that you cannot know that p = God is X, you must paradoxically know that p. But this makes sense. To say, for example, that you know that you cannot know that God is X, you must know what God is X is in order to know that you cannot know that God is X! Contained within the proposition that "you know that you cannot know that God is X" is "God is X," and that logically entails knowledge of "God is X." Because without knowledge of "God is X," we cannot even claim knowledge that "we cannot know that God is X."

But the problem here is: p ∧ ¬Kp is possibly true. Then we can simply say that it is possible that God has certain attributes that we can never know, but we cannot know this for sure (i.e. it is not possible that we know this). In other words, we cannot say that God is unknowable. For surely God is knowable through Scripture, for scriptural revelation is propositional and clear. There may be attributes of God that we do not know and will never know this side of eternity, but we do not know this, and we cannot teach this as part of our theology proper.