Proving God's Existence and Geometric Theorems; Evidentialism within Presuppositionalism

Here I would make some personal observations about apologetics with my own experience in apologetics and doing mathematics, and then make some tangential notes about the presuppositionalist-evidentialist debate. I would like to, at the outset, make a distinction between believing in God versus the truth claims of Christian revelation, and be focused mainly on the former in the context of discussing reason and natural revelation.

I remember when I was in junior college, as an unbeliever, I had a classmate who is a Christian. When I first engaged him, I was extremely belligerent about it, and then he said one thing which changed the course of the entire conversation, and probably my whole life: "Believe whatever you want." That phrase, doubtless meant to end the conversation, made me reconsider my approach and whether I was being deliberately wilful about my objections and rejection of whatever my friend had to say. When I changed my attitude, that fundamental re-orientation, from wilfulness against belief to willingness to believe, led me to explore the reasons for God's existence, then Christiainity, at greater depth and eventually led me to where I am today.

However, I think there is an argument to be made that most of us may need such a "presuppositional" attitude, a willingness and desire to believe, maybe even through our whole lives. I think there are two considerations for this:

(1) The noetic effects of sin, the fundamental unwillingness to believe, is so deeply rooted that we will be fighting every attempt to believe at every step in the argument, at every premise of the proof. If we don't have the fundamental "presupposition" to believe, we will never overcome it. Take as an analogy the objective difference between man and woman, or the wickedness of even allowing adults to undergo sex change operations. Most people in the West are so viscerally and morally conditioned to reject both these propositions that they will fight every argument against these at every step of the way, otherwise they will be consider wicked and evil by others. If we don't demand that they suspend their visceral wilfulness for moral respectability for a moment, we will never get anywhere.

(2) For a proposition as simple and basic as God's existence, the proofs can be very complex. As I've argued in a previous post, there are many mathematical propositions which seems obvious to us, e.g. 1+1=2, the shortest distance between two points is a straight line, which can only be proven by very complex deductions based on even more abstract and elementary concepts. Who is going to master a battery of axiomatic set theoretic concepts just to prove that 1+1=2, or a battery of calculus or vectorial concepts just to prove that the shortest distance between two points is a straight line? The reality is that most of us go about our lives, "presupposing" these truths without bothering our heads to learn deductively and rigorously the proofs to these. Some of us who are not mathematically inclined will never be able to grasp such proofs, but it does not follow that they are not entitled to belief in those claims.

Thus, even if, in theory, you can prove propositions like 1+1=2 or the shortest distance between two points is a straight line, in practice, most of us are simply going to be presuppositionalists about those anyway.

In this light, does it follow that evidences, reasons, or arguments are useless? I don't think it does, but it will re-orient and delimit the role and place of evidence and reasons. I think the "proof" will look something more like this.

I remember when I was in university I had a tutorial assignment where one of the question was to find the volume of a doughnut (or torus), given the radius of the each segment of the doughnut and the ring itself as a whole.

We were supposed to use some integration method to find the volume, but it seemed to me that that wasn't necessary. All you had to do was to cut the doughnut and straighten it out into a cylinder, and it's a piece of cake to find the volume of a cylinder. It was obvious and self-evident to me that this cylinder would have the same volume as the doughnut. You can find the height of the cylinder by calculating the circumference of the doughnut and then the top and bottom area of the cylinder by calculating the cross-sectional area of the doughnut. So I completed this question in like literally three steps with basic algebra.

I was told to present my solution during class and after just jotting down the three step solution my professor was like, okay, your answer is right, but how does it work. When I explained that I simply cut the doughnut and straightened it out as a cylinder and calculated the volume, he got it but said that technically I assumed certain topological properties, e.g. that the volume is preserved under deformation which itself is a provable theorem. Later on, many many years later when I started reading calculus on my own, I came across the Theorem of Pappus which precisely proved that you can treat it like a cylinder by using the notion of moments and center of mass. (If you can't follow the screenshots, skip!)

I suggest this as an analogy to how we can understand knowledge of divine existence. There are three ways knowledge that the torus is equivalent in volume to a cynlinder can be acquired:

(a) It is just obvious and self-evident that they have the same volume. Many, or even most of us, will be able to simply imagine cutting the doughnut, straightening it out, and that it has the same volume. Likewise, to most people it should just be obvious and self-evident that there is a God.

(b) Rigorous proof and deductions. A few of us, who are more mathematically inclined, can learn calculus, moments, etc, etc, and then rigorously prove Pappus's Theorem for volumes and satisfy ourselves with such a deduction. Likewise, the divine existence and be demonstrated by very rigorous arguments and deductions from exquistely rarefied and defined philosophical concepts.

But what if you're a midwit, who is neither willing to grasp the "obvious" fact that a doughnut has the same volume as a cylinder, nor have the mental bandwidth or capacity for a rigorous calculus proof? Then we have the last option:

(c) Rhetorical illustrations which evidences or points to the truth. Here is a way to persuade someone that they have the same volume: Take a non-absorbent but flexible cylinder, then immerse it in a bucket of water. Measure the difference in volume, then take it out and bend the cylinder into a doughnut, then immerse it again into a bucket of water. Measure the difference in volume again. Compare and they should be the same. Is this a "proof"? Obviously not, physical experiments are never mathematical proofs, nor is this a completely rigorous proof (the results may vary depending on the material, water, temperature, etc, etc). But as an illustration, it suffices to be a token of the truth of the proposition, a promissory note as it were, that there is a proof to be had even if one lacks the conceptual toolbox to grasp it. Thus, we can have a lot of lay level apologetics or easy illustrations for God's presence in this world, which should satisfy the curious or the doubtful.

In the end, I suggest that there is something to be said for the Westminster Confession of Faith understanding of how "assurance of salvation" works, but as applied to knowledge and certainty of the divine existence:

Thus, the "infallible assurance" or knowledge by rigorous proof, does not "belong to the essence of faith", and true believers may have to wait long, very long, (or even ever in this life!) before they can partake or acquire such rigorous proof. Yet, such rigorous infallible proofs are not required nor demanded by faith, and that is the essence of presuppositionalism: rigorous proofs come after presupposing or being willing to belief, and they are the gifts to some of the faithful after long and hard pursuit, but does not constitute the essence of faith. In the mean time, there are many (c) kind "evidences" and rhetorically helpful illustrations which can be given to point the way to the knowledge of faith.