The Axiom of Belief


#1

Originally published at: http://peacefulscience.org/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 biologist become intellectual omnivores and polyglots. To be successful, we must weave between several fields. This comes through in…


The @Swamidass Model. What is "seeking peace"?
#2

@AndyWalsh congrats on your book. This book is a great read. I’m hoping you will let me post more excerpts in the future, and I hope you pass a link to the main article around networks.

I think this an important article too. I’m curious what everyone thinks of this. The distinction between an axiomatic and a contingent fact is important.


#3

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).


#4

I too congratulate him on his book. While I can’t say it “indisputably” proves God’s existence because humans dispute all kinds of things which are manifestly so and humans are not logical, I would say a belief in God is the only logical conclusion and yet knowledge from the universe does not finish God’s work in our hearts but only begins it.

It would be like me looking at the works of Picasso and saying that was all their was to him. God wants the relationship, not just the knowledge their was an Artist who made this art.


#5

Thanks so much. I’ve shared the link and encouraged folks to check out your other offerings.

I’m happy to have other excerpts posted here. I think it’s helpful for folks to know what they are getting themselves into.

I enjoyed your observation that the recommended comics suggestion was the longest. I suppose there are a couple of reasons for that. One is that I hope to engage my fellow comic book fans with these ideas, and so I need to establish my bona fides. Reading comics and talking to comics fans, it’s apparent many of them take for granted that scientists are not believers. Comic fans recognize the mythological qualities of superheroes and the potential for comic book stories to provide guiding moral principles (e.g. “With great power must come great responsibility.”). Following those parallels past the data, some conclude that religious stories are pure fiction just like comics.

And another reason is that actually reading comics is a fairly niche activity, and so I figured that body of work would need more of an introduction to non-comics fans.

Plus comics are a deeply collaborative medium, which I really appreciate, and so it just takes up more room to properly credit all the folks who contributed.


#6

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.


#7

@Philosurfer and @JustAnotherLutheran, what is your thoughts on this?

It reminds me of things I’ve learned from Lutherans: “we trust the Bible because of Jesus, not the other way around.” The epistemological ordering is important here. in the language of mathematics (Vis-a-vis @AndyWalsh), Jesus becomes the axiom, not a contingent fact. This analogizes well with @AndyWalsh’s point, that we do science because believe God exists, not to prove that He exists. God is the axiom, not a contingent fact. The way I would put it is that “the world makes sense in light of Jesus.”

(Note to atheists, of course, one does not need to believe in God to do science. That is not what we are saying. Rather, we are talking about how we as Christians do science.)


#8

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.


#9

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.


#10

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!


#11

You did great. So good to see you here Dr. @Philosurfer, I see you philosophical training coming out. What if you do not take him saying that God literally is an axiom, but saying that God is like an axiom. Does that ease your objections?

I’ll have to think about this. What do you think @jongarvey and @AndyWalsh ?


#12

Thanks!

This is good point, and at least alluded to elsewhere in the book, in a discussion of how axioms in mathematics were/are regarded as self-evidently true. I think that is not far removed from “incapable of being untrue”. But over time, experience has revealed that self-evident is not always as straightforward a category as we might have hoped. And so in using the language of choice, I wanted to create space for readers who do not regard God as self-evident.

However, I did not intend choice to imply neutrality. One’s prior or innate disposition needn’t be a precisely 50/50 proposition to allow for a choice. We frequently make choices where the outcome is influenced by external or internal factors biasing us in one direction or the other, but the fact that we can and sometimes do still opt for the less likely option is evidence that we had a choice.

And I would say that evidence suggests at least some of us are biased towards belief in God. As a believer, I would explain that as a consequence of being created by God for a relationship with him. Others explain it in terms of cultural context or cognitive bias towards explanations involving agency. Thus I’m not certain the existence of such bias tells us much.


#13

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.


#14

Actually, it tells “us” clearly that God exists, and “others” that “we” are clearly suffering cultural bias. So the only way in which it doesn’t tell us much is when we seek to adopt a “view from nowhere” that accommodates both what “we” know and “they” know in a synthesis.

That seems to me to be achievable only by stripping away the certainty on each side, and replacing it with a third, uncertain term, ie the choice of an axiom, even though neither side actually chose, but acted on ore-existing conviction.

But that attempt at value-free objectivity is itself a chosen axiom, and one that is a lot more difficult to argue as “properly basic”.


#15

@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!


#16

Well, I would agree with this. My discomfort with “God as the axiom” stems from this as too. I know God by Jesus. I would think more accurate would be to say that the person of Jesus (rathe than the concept of God) is like an axiom. It is by Him that we ground everything else.


#17

Perhaps for you it does, and if so, great. For me, the reasoning runs in the other direction. I believe God exists and created humans for other reasons. Because I believe those things, any bias towards belief in God that I observe in humans I include as part of what God included in his creation process. Thus I can’t also count it as evidence for God’s existence, since the only reason I associate it with God’s work is because I already believe in God. And thus I am not surprised when others do not see it as evidence for God’s existence.

So as I see it, am not so much attempting a view from nowhere as trying to be clear about which of my beliefs depend on which other ones. At the same time, I recognize that other believers construct their belief differently and so may have a different chain of dependency.


#18

Great! I’m looking forward to a group discussion as well.

OK, thank you for this follow-up. I now understand more of what you were trying to get at.

And this is exactly the direction the book moves in, using the language of physics to transition from abstract pure mathematics to concrete reality in order to discuss God’s incarnation as Jesus of Nazareth. Because I agree that any Biblical theology which leaves God as a metaphysical abstraction is incomplete. Incidentally, that’s also why I don’t find many attempts at proofs for God to be personally compelling, because they only point to an abstract supreme being. I find the historical particulars of the Biblical narrative more interesting; the life and teachings of Jesus are much more counterintuitive and therefore engaging.

As a non-Lutheran, I am happy to hear more about that particular perspective in the course of our upcoming discussion.


#19

Hi Jon. In any axiomatic system, with a certain strength, expressed in first order language with assumptions (basically modern math is first-order logic with assumptions - usually ZF set theory with the axiom of choice) we have to assume, without prove (due to Godel and refined by others), that the system is consistent. If with can prove consistently of said system then it is inconsistent. Truth and provability in mathematics are not the same thing (again due to a result of Gödel). For example I can prove that ‘n DOES not equal n’ if say Peano Athematic is inconsistent although it true that n=n. As for axioms cannot be deductively proven (see Joshua’s post above) is nonsense - just go to a richer or different system. For example the axioms and theorems of most mathematics can be proven from set theory. Also Axioms can be disproved, for example they produce inconsistently (example Frege’ s Basic Law V (5)) or probably untrue (Godels V=L axiom in set theory).


#20

Welcome to the forums @theman8469. Can you tell a bit about your training and background? Thanks.