Chapter 1: This Chapter Has No Title

Faith Across the Multiverse by @AndyWalsh, 2018 by Hendrickson Publishers, Peabody, Massachusetts. Used by permission. All rights reserved.

The Axiom of Belief

If math can function without being able to prove everything, perhaps other domains can as well. For example, what if we take belief in the God of the Bible to be axiomatic? Trying to deduce his existence from first principles has always felt a little backwards to me, since by nature he is first principles, the cornerstone anchoring everything else (Ephesians 2:20). Even the name he gives himself, usually translated in English as “I am that I am” (Exodus 3:14), strongly suggests a self-evident quality one looks for in an axiom.

This perspective provides us with an operational definition of faith. Instead of defining it in terms of dogma or rejection of evidence, let’s say that faith is choosing a set of assumptions, or axioms, for understanding the world. And if you prefer, we can further refine this definition to state that faith is specifically choosing assumptions that either explicitly include a God or gods, or at least do not explicitly disallow the existence of such a being or beings. Many atheists and other areligious folks bristle at the idea of calling their choice of assumptions faith, and that’s understandable given the general usage of the words. I don’t see any need to insist on that broader definition of “faith,” so long as we all understand that at some point we are all making a choice of assumptions, and that no particular set of assumptions is privileged a priori nor the only option for a consistent view of the world.

Assuming God rather than proving him might seem like dodging any requirement to provide evidence. Axioms can certainly be informed by evidence, and my belief in God is definitely informed by historical corroboration of the Bible. But axioms cannot themselves be deductively proven; as with pudding, the proof is in the tasting. I am primarily interested with what conclusions follow from my belief in God and how useful they are in my real life. This is comparable to the situation in geometry, where multiple geometries are logically and mathematically valid but the ones where parallel lines intersect are useful for describing a wider range of real world experiences.

This idea that God is not a provable conclusion but an axiomatic assertion, and just one possible axiom among several alternatives, may be uncomfortable for some believers, but I think this idea is consistent with the Bible. Take the refrain of Ecclesiastes: “Futile! Futile! … Absolutely futile! Everything is futile!” The teacher who wrote the book is looking at the world around him and finding no meaning or value intrinsic in anything he finds there. Rather than descend into nihilism, he ultimately chooses to build a framework for understanding the world and living in it based on a belief in God. He does so, not out of the logical undeniability of the premise, but because he found a life so constructed to be fruitful. Usefulness is also the criterion Paul applies to the Bible, describing scripture as “useful for teaching, for reproof, for correction, and for training in righteousness” (2 Timothy 3:16).

When Jesus talks about his parables, he observes of some people, “Although they see they do not see, and although they hear they do not hear nor do they understand” (Matthew 13:13). Jesus does not expect everyone to accept his teachings; to some they will be nonsensical. Perhaps different outcomes arise because some have chosen a way of interpreting the world that renders such teachings as nonsensical. In order for his audience to come to a particular conclusion based on a deductive argument, they would have to start from the same axioms. Jesus is acknowledging that they don’t and so does not rely on deduction. Instead, Jesus describes the kingdom of God that follows from his view of the world, and invites us to be a part of that kingdom. This is an appeal to the usefulness of his assumptions, not their completeness.

We’ve already seen one example where mismatched assumptions produce nonsense. In most cases, we assume words like who, what, or no one have a single meaning. When we encounter someone assuming instead that any word can be used as a name, their statements seem nonsensical. “No he didn’t, no one did” is not a sensible response to the question “Who wrote this book?” when we adopt the usual axioms of English. But to someone crazy enough to choose the alternate foundation, well, that answer is perfectly cromulent. Fortunately, no one is that obnoxious.

Mismatched assumptions play into the plot of Raiders of the Lost Ark as well. In order to find the ark, one needs to place a bejeweled staff in a particular place on a map at a particular time, and refracted sunlight will mark the spot. Instructions for the height of the staff are written on the ornamental headpiece containing the jewel. The Germans assume their one-sided copy of the headpiece is complete, but Marion and Indy have the original with details from both sides. The Germans construct a perfectly functional staff and are able to get a location from the process, but because their assumptions don’t match reality they wind up digging in the wrong place.

Henry McCoy has a similar problem with mismatched assumptions. He assumes that natural causes which can be described with science are the opposite of anything religious or theological and that God or gods only manifest via the supernatural. Therefore, he feels compelled to reject religious concepts in spite of his own personal experience with various deities. But the dichotomy he believes in is not required by the Bible, which is comfortable associating natural causes with God. We read that “the heavens declare the glory of God” (Psalm 19:1). And elsewhere, we find the claim that “since the creation of the world [God’s] invisible attributes—his eternal power and divine nature—have been clearly seen, because they are understood through what has been made” (Romans 1:20). Drawing a sharp line between what God does and what we can understand through science isn’t strictly necessary.

At the same time, I don’t think these verses require us to conclude that creation itself indisputably proves God’s existence. If the world was such that a belief in God was the only logical conclusion, or the only logically consistent way of understanding the world, then God’s work is done from the beginning and he has no need to communicate any further. But this is not the story that the Bible tells. Instead, it indicates that God repeatedly reveals himself personally, culminating in his incarnation in Jesus. Yes, there are other purposes of the incarnation, but one of them is to enable knowledge of God. As Jesus himself says, “If you have known me, you will know my Father too. And from now on you do know him and have seen him” (John 14:7).

Don’t forget our prior discussion of this too: The Axiom of Belief.

I’ll comment as a mathematician.

I like my axioms to not be self-contradictory.

Of course, people will disagree as to whether the God of the Bible is self-contradictory. But the problem remains – as an axiom, that is far too vague. As part of an axiom system, there would need to be more specifics. And that would need to include specifics that could be made the basis for deductive inference.

I’m not at all sure it could work that way. For if God becomes the basis for system of deductive inference, then I think you finish up with an abstract God that is too aloof to have any relevance to ordinary life.

On a different point – I don’t see that an atheist could object to God as axiom. It’s just that the atheist might see that as the first step in a reductio ad absurdum.

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As someone who also take God axiomatically, I have a few questions. Note that I have not read the book or the other thread, so maybe these are already answered.

First, I agree with:

I want to know what exactly does @AndyWalsh take as axiom. What does he specifically mean by “God of the Bible”. I have some specific concerns:

  1. The properties of the “God of the Bible” depends on the interpretation of the reader. Suffice to say that for most people the “God of the Bible” is more than an O^3 God (omnipotent, omniscient, omnibenevolent). Did he take as axiom a God whose properties is based on his own reading of the Bible?
  2. It is important not to be self-justificating. The phrase “God of the Bible” seem to suggest that someone taking it as an axiom puts a lot of stock in the truth of the Bible. One could be self-justificating in the following way: assume the existence of a “God of the Bible”, then justify the Bible as obviously true - which trivially justifies our original axiom. Which is the real assumption, the existence of “God of the Bible” or that the Bible contains truth about God?

I also agree with this:

I would add that the axiom(s) of the existence of “God of the Bible” being non-self-contradictory is necessary but not sufficient. One has to also show that they are not contradictory with the rest of your axioms. Indeed, this is how we get YEC. Imagine a person with the following incompatible axioms:

a) The Bible is literally true, which implies that Genesis is literally true
b) Science works, which means that scientific dating of the Earth gives the true age of the Earth

There are at least three “outs” that one can take in this situation:

  1. Reject a)
  2. The YEC position, Reject b)
  3. Subscribe to dialetheism

The point is that the contradiction does not arise because of the religious axiom a), but because this axiom interacts with other axioms that a person can hold. One has to show that the existence of the “God of the Bible” does not interact in an unwanted way with one’s other axioms.

Finally: As exemplified by option 3), even before talking about contradictions, I have to be clear on what sorts of logical system (or systems if you are a pluralist) you adopt.

The point is this: one cannot just take any statement axiomatically. It needs to be shown that given the logical system that you adopt they do not interact in unwanted ways with the rest of your axioms. In order to do this, it is not good enough to posit the existence of “God of the Bible”. The specifics need to be laid out and at least argued that they do not interact negatively with your other axioms in your logical system(s) of choice.



I think Theism could be axiomatic… but not specifically the God of the Bible.

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I hope not the God of the OT. He was a petty jealous, God as Richard Dawkins said. The Jesus God seemed a more likable fellow, but not very God like. His miracles are not up to the super powers of most of the Gods in history like Zeus, Thor, Loki.

And don’t forget completely invisible and beyond the abilities of science to detect or measure or falsify. Your invisible O^3 God must be exactly like my non-existent God.

For me this is an extra axiom that is something like “the physical world is closed” for a suitable definition of closedness. This is more an epistemological statement about the subset of truths that is obtainable by science (more precisely physics) than anything to do with the property of God.

Yes, but then to go to mass on Sunday and accept the mysticism of transubstantiation. How do you rationalize this?

As we hashed out before, transubstantiation refers to a substantive, but metaphysical change in the host. It is beyond the physical world.

Note that what I meant by “physical world is closed” might be different than what other people meant by the same words.

I do not mean that physics is closed in the sense that God created physics and the Universe at some point and then now the film just plays out without a need for his intervention. Indeed, this is not the typical Catholic position.

Rather, I meant physics is closed in the epistemological sense - there is a subset of the world in which physics operates, and any experiments that uses physics in its axioms can only discover truths within this subset. Historically, this meaning of the world “closed” is rooted in mathematics: mathematical closure.

The end result of these two notion of “closure” is the same: physics (and any other sciences) cannot falsify or confirm God (at least rigorously), but the reasoning is different.


what is a substantive but metaphysical change in a wafer?

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Is the universe a closed system with regard to Thermodynamics?

Are you familiar with Godel’s Incompleteness theorems? How does Godel fit with the above physics?

First of, I don’t want our discussion to derail this thread, which is about @AndyWalsh’s book. Maybe it should be split off.

Here are the answers to your questions:

We hashed this out before in this thread: Several States Investigating the Catholic Church

I will repeat: The word “substance” here refers to the metaphysical substance of Substance Theory, not physical substance.

Let me preface: like I said, typical Catholics including myself do not hold that the Universe is closed with respect to God’s actions in the sense that the Universe and the laws of physics was created at some point and now it just acts without a need for God’s intervention.

Now, is the universe a closed system with regard to thermodynamics? First, a few concepts from physics:

  1. Thermodynamically closed means a system that cannot exchange matter but can exchange energy
  2. The Universe is a single bubble that had gotten out of inflation, and is a subset of the Multiverse. Our Universe is roughly FLRW.

The usual notion of energy is ill-defined for the entirety of an FLRW Universe, so unless you can supply a solid definition for energy that is compatible to 2), I cannot assess whether 1) is true for the Universe.

Yes, I am familiar with Godel’s incompleteness theorems. I don’t see how it is relevant in this case. Would you mind elaborating on what you mean?


Well, sure, self-consistency is important. I appreciate your concession that conclusions will differ here. I think a self-consistent Biblical theology is possible, while also recognizing that other thoughtful folks reach the opposite conclusion. I will also acknowledge that my particular formulation of that theology may not be self-consistent. I suppose that’s part of the point of the book – to articulate that theology as best I can and see what others make of it. So thank you and everyone for the feedback.

This is fair. My intention was to explore the sense in which God plays a role in my beliefs akin to the role axioms play in logic and mathematics. I do not consider myself enough of a philosopher or logician or mathematician to actually construct an axiomatic system around God that is suitable for rigorous deduction. And so it was never my intention to attempt that. But I can see where that would be unsatisfying to some, especially if the axiom discussion was the first thing they encountered about the book and if axiomatic systems are of particular interest to them.

I’d like to think the full chapter makes it clearer what I am trying to do, but I probably could have been clearer about what I was not trying to do.

I’m glad to hear you think there is some potential for finding common ground across faiths / philosophies. And yes, the endpoint may very well be absurd. I think I have made peace with the possibility that I might be on a path to absurdity; if my life must be absurd, this the way in which I’d prefer it to be so.

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Ah, yes; that is the $64,000 question isn’t it? In some respects, the entire book, especially the first half, is intended to unpack the answer. I chose that particular phrase to try to provide some specificity. I didn’t want to give the impression I was talking about some even more abstract notion of God, disconnected from any particular religious tradition.

So, by “God of the Bible” I mean the God of Abraham, Isaac and Jacob, the God who for a time walked among us as the man Jesus of Nazareth, who was put to death and then raised back to life to foreshadow a new creation available to us all.

Absolutely, any reading of the Bible and thus any reading of the God it describes is subject to interpretation by the reader. So yes, ultimately, the God-axiom grounding my beliefs is informed by my particular interpretation of the Bible, which I would not claim is authoritative by any stretch. I have tried and continue to try to shape that interpretation with input from other beliefs and the history of Christian tradition – something which is explored in later chapters.

Hopefully it is clear from my description of God above that I mean something more specific and personal than just a manifestation of omnipotence, omniscience, and omnibenevolence. And maybe something less as well, in the sense that I think an interpretation of God needs to adhere first to the ‘data’ of the Bible rather than abstract qualities.

Good question, and good point about self-justificating reasoning. I would say that it is the existence of God that ultimately plays an axiomatic role in my belief. I would describe the truthfulness of the Bible as an inductive conclusion based on historical evidence, and as such it reinforces the idea that my choice of grounding is reasonable.

You make some other good points about contradictions and additional axioms. I’m not sure I have anything to add on that front at the moment.

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Thank you for the clarification. Of course once you said this:

The obvious question is that why choose a God axiomatically that agrees with the God of the Bible? Why not the God(s) of other religion? Why put so much stake on one holy book instead of the others?

If you say that the Bible is probably true based on historical evidence, isn’t then your axiom really being “Techniques that unearth historical data works”? This then give you the Bible, and then give you the God of the Bible.

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So that tyrant God of the OT was that nice meek and mild Jesus of Nazareth. Wow, He really cleaned up his act in the intervening years when the OT ended and the NT began. So Jesus was God who sent Himself to be killed to make up for sins against Himself so that He could rise from the dead while never really being dead because He is eternal in the past and future so that He could rejoin Himself in heaven. Yes, it makes perfect sense. :pleading_face:

Possibly, but then why think that such techniques work? I think the answer comes back to a God who desires to be known.

And so perhaps the reality is closer to an iterative algorithm like expectation-maximization than a true deductive process.

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Perhaps any sufficiently advanced theology is indistinguishable from absurdity. :wink: