The Axiom of Belief

Dr. Andy Walsh, a Ph.D trained computational biologist, and he is publishing his first book, Faith Across the Multiverse: Parables from Modern Science

Dr. Walsh is computational biologist, just like me. Early in our training, computational biologists become intellectual omnivores and polyglots. To be successful, we must weave between several fields. This comes through in his book, which is divided into four languages, that of (1) math, (2) physics, (3) biology, and (4) computer science. There are two other languages that seamlessly weave through the rest, the language of (5) theology and of (6) comic books. The appendix includes suggested readings in all these areas. Tellingly, the longest suggested reading list of all is of comic books.

This book is playful, smart, grounded, mathematical, and a must read for those of who care about the public square. Dr. Walsh presents a public theology of science. This is not a defense of the faith, but something far more coherent. Unlike nearly all books in the theology-science dialogue, Andy can’t help but mention Jesus almost everywhere. Walking a challenging theological line, he correctly uses parables to explain and expound in the language of science what is know already about Jesus, rather than using science to define Jesus. The parables of the scientific world expose a deeper reality we find in HIm. 

In this excerpt, Dr. Walsh asks whether God is the axiom or a contingent fact. In my view, this explains what it means to make Jesus the cornerstone, the axiom of belief. I hope there will be more to come. 


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).

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  1. Regarding Romans 1:20, I think he has it right:

    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).

  2. Thanks!

    Agreed! One of the motivations of the book is to show how natural theology can be about more than just knowing that God exists; it can also help us know who God is so we can deepen that relationship.

  3. 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.

  4. Good article, Andy, and thanks for bringing it to us, Josh.

    Just one thing to add, and that is that axioms are often not a choice simpliciter, but assumptions founded on things basic to human existence.

    In maths, for example, n=n seems incapable of being untrue, though I suppose (as a non mathematician) it would be difficult to prove. Similarly the sequence of integers. Likewise, “the world of the senses is real” is so fundamental that solipcism, whilst a possible alternative, is a philosophical by-water in practice.

    I say this because it is possible that human beings are not created neutral with regard to the assumption of God. Specifically, being created according to the image and likeness of Christ might be one strong bias towards recognising God in his work as the outworking of our given nature; whilst the ancestral experience of Adam’s spiritual relationship with God in the garden might be even more compelling.

    Ecclesiastes says “God has put eternity in their hearts,” and it would actually be odd if he hadn’t also put some knowledge of himself into the human heart, too. After all, nothing in the biblical record suggests that man was created in order to persuade himself of God’s existence before ruling the earth on God’s behalf.

    Alvin Plantinga’s concept of belief in God as “properly basic knowledge” seems somewhat akin to Andy’s approach, but if I understand Plantinga aright, then such knowledge is not so much the free choice of an axiom, so much a part of human makeup as basic as the existence of numbers.

    That would shift the argument significantly, for instead of Romans 1:20 being, in effect, targeted at those who have chosen the "God " axiom and willfully ignored it, it would make non-belief akin to choosing solipcism as your axiom of perceived reality - ie there is a need to investigate the individual’s reasons for a perverse choice of axiom, rather than concluding that such a choice is a matter of indifference.

  5. Thanks for the invite Josh! Also, I’m new to this whole internet forum platform, so if I don’t get my quotes right or use those fancy @_____ correctly, mea culpa.

    @swamidass

    I must admit that the axiom of God language makes me a bit nervous. Ironically, for the very reasons related to Plantinga’s ‘properly basic beliefs’ that @jongarvey makes reference to positively. Perhaps I can revisit Jon’s thoughts at a later time…

    Theologically, Lutherans, or perhaps it is just me(!), tend to view God nakedly in a moral sense, not as the classical Greeks understood God as a metaphysical anchor securing a universe in turbulent waters. When I hear God as axiom, I do not think of a theoretical principle which makes possible and sense of thought itself, as in a transcendental category. I immediately think about the God of Job, where Job AND his three counselors where questioned by God in a terrifying manner, “Where were you when the x and the y came to be?” We might even take this to imply something like, “Where were you when I posited the mathematical and logical categories in place?” This universal sledgehammer that God used in Job to silence Job and his “friends” relates to what the whirlwind (how God appears in Job) might say regarding the thought of God as an axiom, “Where were you when I created axioms!” Job replies, “But wait, You are the axiom.” God, “That is not how I reveal myself.”

    Lutherans will speak of Jesus as the center of faith with all doctrines radiating outwards like waves. This may sound axiomatic, and it is in terms of salvation. However, it is unclear how the redemption granted through Christ relates to God as axiom of my intellectual world or as Josh pointed out,

    Thus, I’m still nervous about God as axiom language. Moreover, while Josh’s Lutheran thought about Jesus and the Scripture is true, I’m not sure it is so similar to the God as axiom motif. Seeing as God was IN the world reconciling the world to Himself in Christ (2 Cor. 5:19). This puts a certain epistemological ordering in place for us humans as one bound by contingent history. I may know that God is an axiom through the work of Christ, but my vision of what God even means by axiom is limited to an incomplete human set, even as I participate in the divine through Christ. Wouldn’t we say that even mathematical axioms are part of the incomplete human set of historically bound contingent knowledge?

    Now I don’t want to imply that God is absent in holding the universe together or as Josh and Andy suggest, Christians view the world differently. In that sense, I would read Andy’s book as something more like an intellectual meditation along the lines of Anselm’s Ontological Argument. Not an argument for God’s existence, but reflections on what it MIGHT mean to live life in a God-given universe. It is good, right, and salutary for believers to meditate on the book of nature where God is assumed to be true. However, and this is the sticking point for me, at some point, the question must be raised, even in meditation, as to why one axiom and not another…

    Cheers!

  6. I appreciate the honesty of this assessment. I’m not entirely certain I can relieve those nerves. I think Josh made a good point that the axiom language, and indeed all the parables in the book should be treated formally as “is like a” statements or “has properties similar to” statements. It is not my intention to attempt an exhaustive definition of God.

    It is also not my intention to portray God purely as abstract. I think a full picture of God includes a personal dimension as well, which I hope comes across from the book as a whole.

    I’m not sure I really follow the point you are making with respect to Job. If you are saying that mathematical language would be incompatible with that dialogue, I’m inclined to agree, if only because such language would have been meaningless to Job and to the original audience of the text.

    This seems appropriate to me.

    My answer, such as it is, to this question (beyond the mention of historical validation of the Bible’s narratives) has to do with what flows from one’s particular axioms. I have found that belief in the God of the Bible, and subsequently following the teachings of Jesus, to be a fruitful way to lead one’s life. And so that is my justification for choosing that axiom.

  7. @AndyWalsh

    Thanks for replying. I think we are on much the same page and I hesitate to dive too deeply without reading your actual book! I’m looking forward to reading it with other Peaceful Science participants.

    I do think that treating God “like” an axiom might be helpful. It raises further questions of realism versus anti-realism as well as an old philosophy of science distinction between context of discovery versus context of justification, a distinction that hasn’t received much attention since Thomas Kuhn famously argued its collapse in his Structures of Scientific Revolutions. But, again, I will wait until I spend more time with your actual text!

    Lastly, the Job point was more of an observation of what a Lutheran might “hear” when the language of ‘axiom’ is used in relation to God. Your sense of God as a starting place for thought brought to my mind that medieval view of God as the completion/perfection of the gods of Plato and Aristotle. God is necessary in that his logical and mathematical perfection allows all of our extrapolations of knowledge about the universe to be metaphysically valid as you either touch the Forms (Plato) or properly deduce the causal syllogism (Aristotle). When Luther searched the scriptures for a metaphysical God, he found a terrifying being that sat in condemnation of him, e.g., Job. Which is why Luther’s rediscovery of Christ as God IN the world reconciling it to Himself was such a big deal to him. It gave him a way to understand the concreteness of God, not as an axiom, but through discourse with the person Jesus of Nazareth revealed in the Scriptures. God was physically present, not axiomatically assumed for reconciliation. In that sort of vein, I was more thinking through whether or not I could follow Josh in comparing your notion of an axiom with

    I’m still not sure Luther, the Lutheran’s or scripture imply the epistemological ordering Josh is suggesting. However, that is for us all to discuss, and I really am looking forward to reading your book for more context!

    Peace!

  8. Will Walsh’s book be available in audio format (e.g., Audible books)? I rarely have time to read books recreationally these days, but I love to consume them in 30-minute chunks while I commute.

    Thanks!

    Chris Falter

    P.S. I love the site and the forum, @swamidass !

  9. Great question! That would be really cool, but usually first printings don’t have such things. Very unfortunate. Maybe there are some new technology solutions to this that @AndyWalsh can pursue with his publisher:

    Also, just FYI, we are probably going to do a book club on this book. I hope you can join: Considering a Peaceful Science Book Club.

    Thanks! It is really great having you here. I’ve always enjoyed interacting with you elsewhere. I hope we see more of you here in the future.

  10. Argon says:

    It has to be a good review. It doesn’t use the word ‘paradigm’ in the entire piece.

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