An interview on God and mathematics

_{Denyse O'Leary

January 17, 2021

Intelligent Design, Mathematics, theism}

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Some of us think mathematics is the best argument for God available. Anyway, here’s Jerry Bowyer’s interview with philosopher Vern Poythress:

The standard modern culture-war revolves around God vs. the mathematical sciences. Take your choice: Faith or physics. Then there are the voices of mutual toleration, which attempt to leave room for science among the faithful and for faith among the scientific. Poythress, though, taps into a different tradition entirely, one which is seldom heard in modern debate: That God and science are neither enemies, nor partners, but rather that God is the necessary foundation for mathematics and therefore of every science which uses it.
The argument is that mathematical laws, in order to be properly relied upon, must have attributes which indicate an origin in God. They are true everywhere (omnipresent), true always (eternal), cannot be defied or defeated (omnipotent), and are rational and have language characteristics (which makes them personal). Omnipresent, omnipotent, eternal, personal… Sounds like God. Math is an expression of the mind of God. Sound strange? It isn’t. Modern natural science was created by people who said that they were trying to “think God’s thoughts after Him.”
Jerry Bowyer, “God In Mathematics” at Forbes

See also: Things exist that are unknowable: A tutorial on Chaitin’s number

Hat tip: Philip Cunningham

Comments

Viola Lee: I like the expression I offered best because it is what follows from the formula, but some like the other way because of the way it includes both 1 and 0. I like your way best. I disagree with the first part of that. There is nothing paradoxical about it, we do understand it and know what it means in the sense that we know how it relates to various other mathematical understandings, including all the concepts upon which it is built. Yes, perhaps Mr Peirce was trying to take the side of someone who had less knowledge of the underlying structures and wanted to sympathise that it all looks a bit fantastical. Or maybe, being a philosopher, he didn't understand it either. I think the real puzzle is how e^(ix) = cosx + isinx . . . unless you know power series. :-)JVL_{January 21, 2021
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KF said:
Where, given that God is a serious candidate, worlds-framework necessary being, he is either impossible of being (just as a square circle cannot be instantiated in any possible world) or else he is actual.
That argument applies to anything that is possible. If it is possible, it exists.William J Murray_{January 21, 2021
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More philosophically, Wikipedia also says "And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler's identity during a lecture, stated that the identity "is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth" I disagree with the first part of that. There is nothing paradoxical about it, we do understand it and know what it means in the sense that we know how it relates to various other mathematical understandings, including all the concepts upon which it is built.Viola Lee_{January 21, 2021
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I see that Wikipedia does say e^(i*pi) = -1 can also be called Euler's equation, which as I explained I think is wrong. It also calls e^(ix) = cos (x) + i sin (x) Euler's formula, which is maybe better than calling it Euler's equation because it is used to find the value for a particular x as opposed to solving for x. It also points out that it can be written as e^(i*pi) + 1 = 0. I like the expression I offered best because it is what follows from the formula, but some like the other way because of the way it includes both 1 and 0. Obviously they say the same thing.Viola Lee_{January 21, 2021
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Viola Lee said:
Not believing in God does not necessarily mean that one believes in a materialistic explanation for math: those are not the only two possibilities.
True. One of the problems in debates here is that materialists (or semi-materialists) and Christians are very comfortable arguing with each other. Not so much with anyone representing other perspectives. As BA and KF point out, mathematics represents a mental reality we all share. 2+2=4 is an undeniable truth that lies in the mind of any sentient being in any universe. Nobody can even imagine it not being true. This means we are all accessing the same something that actually exists in a nonmaterial state, something that is directly accessed and not subject even to personal interpretation. When you or I look at a physical object, or experience some event, we can come away with widely varied interpretations. Not so when we access 2+2=4. There are other thoughts that have the same quality, such as "I exist." Now try to imagine "not existing." It's literally impossible. IMO, this represents another mental, universal fact as profound and as essential as "I exist." There's no such thing as "not existing." As far as "did mathematics come into being with the advent of intelligent agents," this is IMO a bad question. Nothing "comes into existence." That would imply that at some point it "did not exist." Everything that exists is eternal and can't "not exist" or "be created" or "end." Such things, IMO, are rooted in a materialist perspective that experiences sequences of things coming into and out of their view, so to speak, like walking along a road thinking that the landscape that changes around them as they walk coming into existence and the going out of existence as they amble along.William J Murray_{January 21, 2021
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Viola Lee: Small point: e^(i*pi) = -1 is an identity, not an equation. Viola Lee: Two points. Interestingly: Wikipedia says . . . oh, wait, never mind. I was being dumb. It happens.JVL_{January 21, 2021
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Small point: e^(i*pi) = -1 is an identity, not an equation. It is a fact about numbers, like 2 + 2 = 4, but it has no variable in it and is not an equation. e^(ix) = cos (x) + i sin (x) is the equation, and Euler's identity is the expression of the equation for x = pi.Viola Lee_{January 21, 2021
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Viola Lee: I appreciate KF’s arguments about the necessary role of mathematics in the structure of the world (even if I don’t entirely subscribe to them), but I don’t agree at all about the jump he makes to the necessary existence of a “maximally great and highly intelligent being”. I think Kairosfocus sees 'the hand of God' in all of reality so, for him, the wondrous and beautiful mathematics we all enjoy has a source, a creator. It's like the Rainbow and Eclipse arguments for the existence of God. They're all fine-tuning arguments. One of Kairosfocus's favourite mathematical results is Euler's equation which I admit is pretty cool. But for him it's like the system has been fine tuned to create that kind of beauty. Clearly he's never taken a higher-level statistics course; that stuff is so messy and bleh.JVL_{January 21, 2021
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ET: Mathematics is an abstract concept. Abstract is something formed in the mind. Therefore mathematics could not have existed prior to intelligent agencies. Hmm . . . So, you're on the side that says mathematics is invented as opposed to those that think mathematics is discovered. I lean to the discovered side and I think that means that mathematics is universal and invariant which means that it exists independent of any beings which means it was true before any beings came along to discover it. Let's say, for the purpose of discussion, that you're correct that mathematics is invented and you think by some supernatural being . . . are humans continuing the invention or are they discovered that which was already invented by your being who is not subject to the laws of physics and chemistry? If some being created mathematics and humans are just slowly uncovering and discovering that which was already laid down would not the supernatural originator be able to answer mathematical questions which we can't? Like the Goldbach Conjecture? Or the Continuum Hypothesis?JVL_{January 21, 2021
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I appreciate KF's arguments about the necessary role of mathematics in the structure of the world (even if I don't entirely subscribe to them), but I don't agree at all about the jump he makes to the necessary existence of a "maximally great and highly intelligent being". I agree with JVL that math is about "is" but not about "ought", and that there is no logical reason why is and ought are fused at the root of reality.Viola Lee_{January 21, 2021
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Mathematics is an abstract concept. Abstract is something formed in the mind. Therefore mathematics could not have existed prior to intelligent agencies.ET_{January 21, 2021
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JVL:
Why should mathematics not apply to a supernatural designer which you don’t even know exists?
The definition of supernatural, duh.
What does math being abstract have to do with whether or not the rules apply to all beings?
Oh my. You are too stupid to even follow along. Good luck with that.ET_{January 21, 2021
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Kairosfocus: The implicit moral government behind your arguments implies that in the root of reality there is a unity of is and ought, which points to the only being capable of fulfilling that bill. Mathematics has nothing to do with morals. And there is much beside, but evidence and reason can always be rejected, that is the nature of freedom. The no evidence gambit is a fallacy. No good hard empirical evidence. A lot of supposition and wishful thinking, yes. PS: We must notice the pervasive presence of selective hyperskepticism as an embedded facet of radical secularist ideologies, and that this stance is inherently self referentially incoherent and agenda serving, a civilisation-destructive fallacy. Again, nothing to do with mathematics which is NOT incoherent or an ideology. And it has nothing to say about morals or theology.JVL_{January 21, 2021
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JVL, there is none so blind as s/he who refuses to see. The implicit moral government behind your arguments implies that in the root of reality there is a unity of is and ought, which points to the only being capable of fulfilling that bill. And there is much beside, but evidence and reason can always be rejected, that is the nature of freedom. The no evidence gambit is a fallacy. KF PS: We must notice the pervasive presence of selective hyperskepticism as an embedded facet of radical secularist ideologies, and that this stance is inherently self referentially incoherent and agenda serving, a civilisation-destructive fallacy.kairosfocus_{January 21, 2021
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Kairosfocus: On what grounds is anyone sure that reality’s root is not a necessary, maximally great and highly intelligent being? Because of the lack of evidence for such a being. Where, given that God is a serious candidate, worlds-framework necessary being, he is either impossible of being (just as a square circle cannot be instantiated in any possible world) or else he is actual. I don't think you can argue for a necessary being based on mathematics. Regardless, that doesn't answer the query: is mathematics universal and invariant? If it is then all beings are subject to its rules. Which means all beings are limited to the rules of mathematics. If mathematics is NOT universal and invariant then it doesn't apply in all situations or to all beings. Which means it can't be used as the basis for any theological argument.JVL_{January 21, 2021
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JVL vs ET: >>That math existed before any intelligent agents>> On what grounds is anyone sure that reality's root is not a necessary, maximally great and highly intelligent being? Where, given that God is a serious candidate, worlds-framework necessary being, he is either impossible of being (just as a square circle cannot be instantiated in any possible world) or else he is actual. Any takers on God is impossible of being, post the collapse of the deductive form of the problem of evil under impact of Plantinga's free will defence? KFkairosfocus_{January 21, 2021
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ET: I made it clear that I was talking about a supernatural designer when I said that math doesn’t apply. YOU changed that so it is a strawman. Why should mathematics not apply to a supernatural designer which you don't even know exists? Mathematics is an abstract concept. THAT is how it applies. I thought you understand mathematics? How did you not know this? What does math being abstract have to do with whether or not the rules apply to all beings? If being abstract means they don't apply to some beings then why do they apply to you since you think you have a soul which exists outside of space and time? It seems to me you do not think mathematics is universal and invariant as it seems to not apply to some hypothesised beings. If mathematics is not universal and invariant then isn't it just a story, a metaphor, that applies sometimes but not others?JVL_{January 21, 2021
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LoL! @ JVL- I made it clear that I was talking about a supernatural designer when I said that math doesn't apply. YOU changed that so it is a strawman. Mathematics is an abstract concept. THAT is how it applies. I thought you understand mathematics? How did you not know this?ET_{January 20, 2021
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ET: That is a strawman as I never said anything about that. You said something which was not an accurate reflection of what I said and I clarified things. How is that a straw man? Are you even paying attention? And there aren’t any other meanings of the word abstract in the context of this discussion. Or do you think nature can write openings to articles? I don't understand why you can't specify how 'abstract' is pertinent to the above discussion. You're the one who brought it up; try and state clearly and concisely how it applies.JVL_{January 20, 2021
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JVL:
I said they could change if they didn’t apply to all beings.
That is a strawman as I never said anything about that. And there aren't any other meanings of the word abstract in the context of this discussion. Or do you think nature can write openings to articles?ET_{January 20, 2021
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ET: YOU said they would change from situation to situation. That doesn’t follow. I said they could change if they didn't apply to all beings. Pay attention. Abstract is something formed in the mind. As I said, get a dictionary and learn how to read and use it. There are other meanings. How does it pertain to the conversation?JVL_{January 20, 2021
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JVL:
That math existed before any intelligent agents
There isn't any evidence for it so it can be dismissed.
‘2’ stands for two things of some kind, how else can you define it?
It can be defined as anyone wants. Definitions are arbitrary constructs.
I thought you liked asking questions and drilling down on accepted truths.
Can't drill down on something we cannot study, duh. As I said, you are ignorant of science and apparently proud of it.
IF the laws of mathematics are universal and invariant then they apply always to everyone, all life forms.
YOU said they would change from situation to situation. That doesn't follow. Abstract is something formed in the mind. As I said, get a dictionary and learn how to read and use it.ET_{January 20, 2021
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ET: References for something that didn’t happen? Thank you for continuing to prove that you are ignorant of science. How do you know it didn't happen? That math existed before any intelligent agents. That depends on how 2 and 4 are defined, duh. And definitions require a mind. '2' stands for two things of some kind, how else can you define it? If there are no other ways to define it then does it require a mind to be true? It has NO meaning to my life. Okay. I thought you liked asking questions and drilling down on accepted truths. My mistake. That doesn’t follow. IF the laws of mathematics are universal and invariant then they apply always to everyone, all life forms. IF the designer is not constrained by the laws of mathematics then the laws are not universal and invariant because it's possible to by-pass them. It's really simple. It is clear that you don’t know what abstract means. Why don't you explain how it pertains to the conversation instead of just dancing around as fast as you can and not answering some questions?JVL_{January 19, 2021
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JVL:
References?
References for something that didn't happen? Thank you for continuing to prove that you are ignorant of science.
If it’s universal and invariant then yes. Why should 2 + 2 not equal 4 just because there is no one around to see it?
That depends on how 2 and 4 are defined, duh. And definitions require a mind.
Why not? Aren’t you curious?
It has NO meaning to my life.
So, if the designer(s) is not constrains by mathematical laws then the laws of mathematics are not universal and invariant, i.e. they change from situation to situation.
That doesn't follow.
I know what abstract means, what’s your point?
It is clear that you don't know what abstract means.ET_{January 19, 2021
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ET: It didn’t happen. References? It could be possible. We would just have to figure it out one way or the other. Could mathematics exist absent a mind? If it's universal and invariant then yes. Why should 2 + 2 not equal 4 just because there is no one around to see it? I don’t think about that. Why not? Aren't you curious? Probably not. That’s pretty much what supernatural means, JVL So, if the designer(s) is not constrains by mathematical laws then the laws of mathematics are not universal and invariant, i.e. they change from situation to situation. So, maybe, for some beings 2 + 2 does not equal 4? Or we just don’t fully understand them- we just haven’t figured them out. So, it is okay to say 'we don't know'. Look up the word “abstract”. I know what abstract means, what's your point?JVL_{January 19, 2021
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I have no idea. First of all, I'm not a Platonist, but the idea has been around since Plato. Second, the same kind of "why" question can be asked, I think, about the nature of the interaction between the metaphysical and the physical of all sorts: positing a personal divine deity doesn't remove the mystery.Viola Lee_{January 18, 2021
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Viola Lee @ 3, > They do believe a world of Platonic mathematical forms imprints themselves on the physical world without a personal divine diety being involved. How? What is the method or the sequence of cause/effect relationships that goes from a mathematical form to a physical result? (A variation on the question _we_ always get from ID skeptics.)EDTA_{January 18, 2021
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JVL:
No, it just means we haven’t figure it out yet.
It didn't happen.
I’m asking: could intelligent agents have existed before mathematics?
It could be possible. We would just have to figure it out one way or the other. Could mathematics exist absent a mind?
What do you think?
I don't think about that.
Does math have a beginning?
Again, can math exist absent a mind?
s that ultimate designer constrained by the laws of mathematics?
Probably not. That's pretty much what supernatural means, JVL
If no then the laws of mathematics are not universal and invariant.
Or we just don't fully understand them- we just haven't figured them out.
If yes, the designer is constrained by the laws of mathematics, then wouldn’t it have had to come into existence AFTER the laws of mathematics were already in existence?
Look up the word "abstract".ET_{January 18, 2021
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AaronS1978: ALL but one of my math teachers were horrible! I had one good math teacher Sadly a very common experience. People thought it was bizarre that I could do advanced math in chemistry Higher level chemistry in particular is full of mathematics.JVL_{January 18, 2021
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@16 LOL ALL but one of my math teachers were horrible! I had one good math teacher People thought it was bizarre that I could do advanced math in chemistry But if you put a geometrical proof in front of me I would just die I know how you feel like quite literally every one of my teachers was just some Murphy’s Law joke except for oneAaronS1978_{January 18, 2021
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