Deducing the four sources of knowledge

My defense of the second premise of my modal-epistemic argument relies amongst others on the claim that (on the specific conception of knowledge used for the argument) there are no more than four sources of knowledge: logical proof, self-evident intuition, experience and testimony. Here is an interesting suggestion from L. Newton to deduce that these four sources of knowledge are indeed exhaustive. Knowledge is either from oneself or another. If it is from another, then it is from 1) testimony. If it is from oneself, it is either from 2) experience or from the intellect. If it is from the intellect, it is either 3) self-evident or 4) logically proven.

A metaphysical principle entailing theism? (II)

Recently I proposed a new argument for theism based upon a metaphysical principle connecting logic, knowledge and truth. Against this argument two specific objections can be proposed. In what follows I shall present and respond to both objections.

(A) It is also logically impossible to know that God exists (for someone could, even encountering God, believe that she is dreaming, or hallucinating, or being deceived). But then, by parallel reasoning, it also follows that, necessarily, God does not exist. And hence my argument fails. My response would be that it is not logically impossible to know that God exists. Take a possible world in which God exists. In this possible world there is a subject that knows that God exists, namely God. In that world God knows that God exists. So, it is not logically impossible to know that God exists.

(B) There might be some true mathematical Gödel sentence G that cannot be proven by any proper mathematical system. Hence, G is unknowable. But then not all truths are knowable, and therefore my principle (which entails that all truths are knowable) fails. My response would be that G is in fact knowable. For, there is a possible world in which G is known. Take again a possible world in which God exists. In that world God can be taken to know at least all mathematical truths by immediate intuition, and therefore God knows G as well.

A metaphysical principle entailing theism?

Take the following metaphysical principle, connecting logic, knowledge and truth: 'If it is logically impossible to know that p, then p is necessarily false'. This principle seems to be cogent. For, if a given proposition p could be true, then, plausibly, there is a possible world in which some subject knows that p is true. In other words, if in all possible worlds all subjects do not know that some proposition is true, then, plausibly, that is because that very proposition cannot in fact be true.

Well, on a cartesian view of knowledge, that is, to know p is to be certain that p is true, the above principle has an interesting consequence. For, take for p the proposition 'God does not exist'. It seems reasonable to hold that it is impossible to know that God does not exist. For, whatever the arguments against God, there will always be some (perhaps an extremely remote) possibility that God does exist after all, so that we can never truly say, on the cartesian view, that we know that God does not exist. But then it follows that it is necessarily false that God does not exist. Hence, it is necessarily true that God exists.

One might object that it is also impossible to know that God exists. And thus, by similar reasoning, it would follow as well that it is necessarily true that God does not exist. However, I would argue that there is a possible world in which some subject can truly say that he or she knows that God exists. Take a possible word in which God exists and in which there is an afterlife, such that all who enter the afterlife in that world will encounter the divine. In that case, those subjects who enter the afterlife will in fact know that God exists. So, it is not impossible to know that God exists.

Note that a similar move to reject the argument for theism is not open to the atheist. For, if God does not exist, then, plausibly, there is no afterlife. And besides, even if there would be an afterlife, then entering it would not bring a subject in the epistemic condition of knowing that God does not exist.