Only God Could Win This Game

What the 'Why' game teaches us about knowledge, God, and Infinity

To me, how mysterious your thoughts,
the sum of them not to be numbered!
If I count them, they are more than the sand;
to finish, I must be eternal, like you
-Psalm 139:18

Toddlers and philosophers throughout history have discovered that when someone says, “because I said so!” it isn’t a promising sign that you’ll get a satisfying answer to your question. There’s something about a child’s filter free curiosity which helps them recognize when an answer doesn’t actually explain anything. And there’s something about a philosopher’s mind that keeps them from getting a real job, but I digress.

While both groups are known and mocked for questioning things we normally take for granted, toddlers are particularly infamous for driving their parents crazy by asking ‘why?’ continuously. As anyone who has been trapped in this ‘why’ game has discovered, things which once seemed obvious can quickly become less obvious, if not completely mysterious. Aside from the embarrassment and inadequacy we might feel when a toddler nails us for thinking we know more than we do, another reason the ‘why’ game is so annoying and disconcerting is that it seems like it could go on forever. Certainly with some toddlers there doesn’t seem to be any theoretical limit. And for many philosophers, it isn’t obvious that one exists. That’s because the whole point of the why game is that we think if we believe something, we need to have a good reason. After all, if a belief doesn’t have any explanation or justification, wouldn’t that make it arbitrary-literally unjustified?

Here’s the rub: what good is a good reason if that reason doesn’t have a good reason? I know some of you want to punch me now, but please bear with me, you can have my lunch money after you finish the article! Think about it: what good is “John needs to fill up the tires (belief) because they’ve gone flat (good reason)” if the person thinks the tires went flat not because they saw the flat tires, but because John poured an odd number of Cheerios into his bowl this morning (possible bad reason)? Clearly, we need to do at least some vetting of the answers we get, and sometimes we even need to vet the vetting.

But if a toddler can ask for and expect a reason for every ‘because,’ then how do you stop the why game from going on forever? And worse, how can you be sure you won’t eventually uncover a dubious link in your chain of explanations? Based on what we’ve gone over, I don’t think you can. Because whatever reason you give, it’ll either be a reason you’ve already given, or a different reason. The problem with the former is that if a belief is justified by itself, or with an explanation that was already used, then your explanation seems tainted by circular reasoning. And if you explain or justify a belief with a unique and separate explanation, then you haven’t gotten off the treadmill; you’ve made another statement which is either justified or not, and either justified by itself or a separate belief. The why game marches on.¹

This puzzle of infinite regression is as old as philosophy itself, and unless toddlers have fundamentally changed, it probably predates it. Some of the most famous and bizarre episodes in philosophy have sprung out of attempts to answer this and similar questions. Most ordinary people seem to settle on a form of what’s known as foundationalism: the idea that our knowledge has its foundation in rock bottom truths which don’t need further justification. The standard example of foundationalism is Rene Descartes’ “I think therefore I am” adventures. Descartes tried to find a sure foundation for knowledge by discovering a belief he couldn’t doubt. He eventually decided that he couldn’t doubt that he existed, and tried to base the rest of his beliefs off of this undoubtable fact.

Foundationalism seems sensible enough in general, but when you get down to specifics, all too often it turns out that one man’s foundational/self-evident truth is another man’s odd number of cheerios. To this day foundationalism is dogged by difficult questions over how to determine exactly when a belief is foundational, and how to connect those beliefs to the rest of our knowledge. I fully admit that there’s probably something I’m just not getting. All the same, I’ve never read an explanation of foundationalism that didn’t come across as special pleading to me. As a Christian, that put me in a bind. I didn’t find foundationalism convincing, but I also realized that if our knowledge has no foundation then we can’t know anything, including whether God exists.

For me the path forward came from revisiting an alternative solution we discussed when I studied philosophy at Wayne State University. This solution, which was floating around at the time of Aristotle, but nearly universally abandoned after that, is called infinitism.² What makes infinitism unique and interesting is that it doesn’t flinch at the infinite regress problem. According to infinitism, the chain of explanations goes on forever because it has to, and that’s not a problem. In fact, we can only claim to know something if we have an infinite chain of reasons. In other words, we can claim to know something as long as we think we could hang in there with the toddler who keeps asking ‘why?’ — forever.

You’ve probably already thought of some obvious and sensible objections. Here I’ll focus on two which philosophers have historically considered decisive. The most well known and straightforward of these is known as the finite minds objection. Aristotle famously wrote that “one cannot traverse an infinite series.” Because we are finite beings with finite minds, it seems like we could never fulfill the requirement of having an infinite number of reasons for our beliefs. No matter how many steps I take down an infinite path, I will have only gone a finite distance. Commenting on infinitism’s radical requirements, J.N. Williams writes:

This is psychologically, if not logically, impossible. [….] Only God could entertain an infinite number of beliefs. But surely God is not the only justified believer?³

When I first came across this objection, it was difficult for me to understand how even God could entertain an infinite number of beliefs. If traversing an infinite is impossible, why would an infinite mind succeed where a finite mind failed? If I could never finish counting all the numbers, wouldn’t it make no difference whether I counted for an hour or for a billion years? Eventually I came across what St. Thomas Aquinas had to say about the subject. He pointed out that God doesn’t know things through a step by step process of reasoning; he knows everything all at once. He writes:

The infinite defies knowledge in so far as it defies counting. To count the parts of the infinite is an intrinsic impossibility, as involving a contradiction. To know a thing by enumeration of its parts is characteristic of a mind that knows part after part successively, not of a mind that comprehends the several parts together. Since then the divine mind knows all things together without succession, it has no more difficulty in knowing things infinite than in knowing things finite.⁴

So at least God could know things if foundationalism were false. As for the rest of us, infinitists reply that we don’t need to actually have an infinite number of beliefs, we need only be confident that we have access to an infinite chain of reasons. The context of our inquiry will determine just how far down the chain we need to go.⁵

The second objection I want to look at is the ‘no starting point’ objection. According to the ‘no starting point’ objection, needing an infinite number of reasons isn’t a mere practical hurdle to knowledge, it makes knowledge a logical impossibility. Because if a series of reasons goes on forever, then there’s no source, or ultimate explanation for why beliefs are justified. Looking for justified belief is a chase after the horizon. Jonathan Dancy writes:

Suppose that all justification is inferential. When we justify belief A by appeal to belief B and C, we have not yet shown A to be justified. We have only shown that it is justified if B and C are. Justification by inference is conditional justification only; A’s justification is conditional upon the justification of B and C. But if all justification is conditional in this sense then nothing can be shown to be actually non conditionally justified.⁶

What I found intriguing about Dancy’s argument here is how closely it parallels Thomas’ arguments for God’s existence. Just as Thomas argued in various ways that a chain of conditional causes requires a necessary first cause, so Dancy is arguing here that a chain of conditionally justified statements must find its ultimate justification or cause in some unconditionally justified belief.

But I think Dancy might be mistaken in a way that many are mistaken about Thomas. Often people who are vaguely familiar with Thomas’ Five Ways assume that he tried to prove God’s existence by showing that the universe must have had a beginning. While many Christians have taken this route (most impressively, in my opinion, William Lane Craig), Thomas did not. Although he believed the universe had a beginning as a matter of faith, he did not think this could be proven logically. His arguments work perfectly fine even if we assume for the sake of argument that the universe had no beginning. His point was not that there had to be a literal chronological first cause. His point was that infinite or not, a chain of conditional causes needs a sustaining source. A professor of mine gave this illustration (my paraphrase):

Imagine you see a beam of light shining on your wall. You look outside and you see that the beam is reflected onto your wall by a mirror. At this point you haven’t yet discovered the source of the light. The mirror explains how the light got on your wall, but not where it came from. Neither could a second or a third mirror, or even an infinite chain of mirrors solve this problem. Mirrors don’t give off light. Until we find a flashlight or some other light source, there’d be no adequate explanation for where the light on your wall came from.

People make the same mistake when they assume that a beginning-less universe wouldn’t need a first cause. The chain of causes would explain how we got here but not where we came from. God is the universe’s flashlight, he’s the hook which the chain hangs from.

I think God serves the same function for our knowledge. Just as the physical universe is caused and sustained by God, I think God, as the ground of being and the source of truth makes knowledge possible. Faith in, and union with him is our best and only hope for certainty, because whether they are infinite or not, God is aware of all of the reasons behind what he tells us, and he knows they all check out.

At the end of the day, my biggest problem with foundationalism is not that I’m sure it’s unsound (I’m not), but that it can encourage us to accept some pretty lame substitutes for trusting in God. Go down the chain of reasons for any given belief you have, and I think you’ll always eventually discover a point where you simply decided to trust in someone or something. And I don’t think that point was “thank goodness! 2+2=4 and that can’t not be true!” Whatever that point was, there’s no better point to trust than God. Our knowledge has real and vast limits; God’s has none. He’s the only one who can win the why game. He is “the Spirit of truth,” and if you place prayerful trust in him, he “will guide you into all truth” (John 16:13).

1.  This problem is variously known in philosophy as the Aggripan Trilemma, the Münchhausen Trilemma, and the Fries Trilemma

2. Although abandoned for millenia, infinitism has enjoyed a lively revival of academic discussion and interest, much of this spearheaded by Peter Klein.

3. JN Williams "Justified Belief and the Infinite Regress Argument." American Philosophical Quarterly 18, no. 1 (1981) page 85.

4. Thomas Aquinas, Summa Contra Gentiles, 1.140.10, Translated by Joseph Rickaby, S.J., The Catholic Primer 2005, 113.

5. William Lane Craig makes a point here which I think illustrates this well:

“…in order to recognize an explanation as the best, one needn't have an explanation of the explanation. This is an elementary point concerning inference to the best explanation as practiced in the philosophy of science. If archaeologists digging in the earth were to discover things looking like arrowheads and hatchet heads and pottery shards, they would be justified in inferring that these artifacts are not the chance result of sedimentation and metamorphosis, but products of some unknown group of people, even though they had no explanation of who these people were or where they came from. Similarly, if astronauts were to come upon a pile of machinery on the back side of the moon, they would be justified in inferring that it was the product of intelligent, extra-terrestrial agents, even if they had no idea whatsoever who these extra-terrestrial agents were or how they got there.

Although Craig himself believes that an infinite regress of reasons would lead to skepticism, an infinitist would say that he doesn’t have to. Craig isn’t arguing that the archeologists would be justified in believing that the artifacts came from an unknown people because they had reached the end of a chain of reasons, or that their inquiry couldn’t go on any further. He is saying that the reasons given are sufficient to satisfy the demands of the inquiry. This holds even when the next stage of justification (i.e. how did the people get there) is undetermined.

6. Jonathan Dancy, 1985, Introduction to Contemporary Epistemology, Oxford, Blackwell, 55.