God, Mathematics, and the Trinity

(Hunter Vallejos) #1

I want to preface this by saying that this is hardly a question about the the application of faith, but more about something that I’ve thought about for a while with regards to the fundamental nature of God.

My thought process can be outlined by the following.

Assumption 1: God is Trinity
Assumption 2: The only thing which pre-exists creation is God.
Assertion 1: Because God is Trinity, the number 3 must pre-exist creation.
Assertion 2: Because 3 pre-exists creation, so does 1 and addition.
Assertion 3: Because 1 and addition generate all numbers and essentially all mathematics, all mathematics must pre-exist creation.
Assertion 4: Because God is the only thing that pre-exists creation, mathematics must be fundamentally part of God.

With regards to Assertion 1, I believe it is currently fashionable in modern philosophy of mathematics to think of mathematics as synthetic a priori, meaning that

  1. The things in mathematics are the same regardless of the state of the universe (since 1+1=2 regardless of whether or not it will be 70 degrees Fahrenheit tomorrow).
  2. Mathematics exists regardless of our ability to conceptualize or think it, because the universe obeys mathematical laws. Hence, 1+1 must be 2 regardless of whether or not we think it, since the very 2-ness of something is a fact in our universe.

So, this assertion takes a similar stance with regards to God’s nature: in order for a Trinity to exist, there must a priori exist the number 3.

Assertion 2 expounds upon this, for, “what is 3 but 1+1+1?” The very existence of 3 implies that there are three things, three 1’s, which make up the very 3-ness of 3. Hence, the “making up of the 3-ness of 3 with 1’s” is addition. So the existence of 3 implies the existence of 1 and addition.

Assertion 3 takes this a little bit further: If 1 and + exist, then every whole number exists a priori, since any number is sufficiently defined and captured in the objects “1” and “+”. Nearly all of mathematics can be constructed from these two operations, and so it becomes difficult to see how the inclusion of “1” and “+” is anything less than the inclusion of all of mathematics.

Assertion 4 ties up the claim I am making. Essentially, because God’s existence is contingent on his Trinitarian nature, God’s existence must coincide with the existence of “3”, “1”, and “+” and hence all of mathematics. Because the only uncreated thing is God, we are forced to conclude that math is part of God.

Now, the nuance here is that we’re are not saying that God is mathematical, or that God uses math to describe the universe, but we are claiming something much more seemingly preposterous: that is, that math is fundamentally part of Him. Mathematics here becomes theology, and one does not point to mathematics as a reason for God to exist, but the very essence of God littered throughout the physical universe.

There are many places to go after going down this rabbit hole. I’m curious if you think that this line of reasoning is correct?

The weakest assertion is probably Assertion 1. However, if we say that Assertion 1 is wrong, then we say that “3” is not fundamental to the nature of the Trinity, essentially saying that the Trinity is not the Trinity – that our understanding of the Trinity does not even approximately reflect what the Trinity actually is. I get the odd sense that this is dangerous territory, and Assertion 4 seems much safer than to contend Assertion 1.

Anyways, thank you for reading this. I would really appreciate your input. As someone studying to become a mathematician, I connect with God through mathematics the same way someone might connect with God walking through a beautiful forest. This ultimately not-so-discretely biases me towards these assertions.

Best wishes!

(Frederick Meekins) #2

One of the great mysteries that confounds the unbeliever is how something as rationally abstract as mathematics has direct correspondence and addresses so exactly how the externalized world functions.

(Jennifer Judson) #3

I’m fascinated. I’m no mathematician, not how my brain is wired–but I’m still fascinated by seeing how math and science work and function in the world.

I think what struck me when I was reading was in Assertion 4 – “because God’s existence is contingent on his Trinitarian nature” – is this an assumption we can make? We know that God is Trinitarian in nature, but can we say his existence is contingent on this?

I guess what I’m asking is does the reality of God as he is, limit him in any way. We can assume God had the capacity to create what is, should we not also assume he had the capacity to create what is not, or what is not yet?

Boy howdy, this had my mind blowing gaskets! Mathematics and philosophy are way out of my league, but you have really fascinated me.

Anyway, this made me think of the wonderful mathematics built into the universe in the Golden Ratio. And that mathematicians recently help medical research and found a new shape in nature – the scutoid.

Seems science is discovering God’s perfect math everyday!

(Hunter Vallejos) #4

Hi Jennifer,

I think you’re probably right – or at least contingent probably isn’t the right word.

It depends on what philosophical frame we’re working in. If we think that essence is more fundamental than existence, then: if the Trinity is part of God’s essence, but the Trinity does not exist, it cannot be that God (at least in Trinity) exists.

However, I’d like to rephrase Assertion 4 informed by some of St. Thomas Aquinas’s Summa Theologica:

"P1. Whatever a thing has besides its essence must be caused by the constituent principles of that essence or by some exterior agent.

P2. Consider a created thing. It is impossible for a created thing’s existence to be caused by its essential constituent principles because nothing can be the sufficient cause of its own existence if its existence is caused.

C1. Therefore, a created thing has its existence different from its essence.

P3. God is the first efficient cause.

C2. As the first efficient cause, anything God has cannot be due to an exterior agent. C3. God’s essence is identical to his existence."

Aquinas argues that essence and existence are the same thing for God, since He is uncaused. Hence, because God exists and his essence is Trinitarian, so must the number 3 and all of mathematics. Not because His existence is contingent on the existence of 3, but rather:

Because God’s essence includes mathematics, it must be that mathematics is part of God, for God’s existence cannot be separated from His essence.

(Anthony Costello ) #6


Awesome, awesome question. So, one book I will recommend right off the bat that I think will help you sort through some of these questions is William Lane Craig’s book on God & Abstract Objects:

In this book Craig argues that mathematical objects, often construed of as platonic Abstracts, are not real, i.e. they are just useful fictions, or instrumental concepts), that do not have actual existence. Numbers are not substantival in that sense; or, one might argue, that when using the existential quantifier ∃, one would not say “numbers exist” in the same way one would say “that dolphins exist” or “that angels exist.” If numbers exist, they exist in a non-ontological sense; the same way “Sherlock Holmes” might be said to exist, yet we do not believe that Sherlock Holmes has existence.

Basically, Craig is arguing in this book that since God exists a se, as the only uncreated being, that, in fact, numbers cannot exist as coterminal abstract entities (uncreated abstract objects), nor are they created by God as such. If numbers aren’t real, i.e. they have no ontological reality, then your Assertions 1 & 2 would be undercut, because “3” simply does not exist.

That said, Craig’s anti-realist view on things like numbers has turned some heads in Christian philosophical circles. For example, J.P. Moreland is firmly a realist on things like numbers (or other universals, like “redness”) and he wrote this book together with Craig!

Which, I would highly recommend reading, if you haven’t already; although the nature of your question tells me you are at least familiar with it.

Theologically speaking, however, and speaking now as a realist about things like numbers, the most prevalent, classical view on such “universals”, has been a view usually called “Divine Conceptualism.” And, I think you’ve sort of outlined something like this in your conclusion; that mathematics exits “in God.” Whereby, we might say that mathematics exists as thoughts in God’s mind. This view is not without its problems, however, as Craig also shows in his book. Here, however, is a short defense of Divine Conceptualism:

Another option is Absolute Creationism. This would argue that God creates everything, to include numbers, mathematics, logical relations, etc. The problem here, as you pretty much have discerned, is that God would have to create properties that are already essential to Him. So it is not just his “threeness” that God would have to create, but also His omni-potency, His omniscience, His omni-benevolence, and so on; but these are properties that He would already possess! This is called the “bootstrapping” problem.

Here is another article by Craig that clears up some of these views:

Also, you say this:

Essentially, because God’s existence is contingent on his Trinitarian nature, God’s existence must coincide with the existence of “3”, “1”, and “+” and hence all of mathematics.

But, I am not convinced that God’s existence is contingent upon his Trinitarian nature. That strikes me as false. It seems to me that if God is a necessary being, then God is necessarily Triune. But I don’t think that God’s existence is therefore contingent upon “Triunity” or “being Triune”. But, perhaps this goes back to what I said above about Absolute Creationism, for God would have to create His own essential property.

Personally, I think you are certainly well within an orthodox tradition, if you argue that mathematics, logical relations, numbers, etc. are something like thoughts in God’s mind. However, there are Christian Platonists who would argue that there are simply such things as abstract objects (numbers, shapes, etc.) that exist co-eternally with God, since they are also uncreated. However, obviously these things do not have causal powers, they are impersonal, they are not worthy or worship, etc.

Probably the most prominent Christian Platonist is Peter van Ingwagen. Here is a very good debate between Craig, van Inwagen, and J.T. Bridges on exactly this topic:

So, I have no idea if any of this helps, but I at least hope the resources I’ve linked might lead you further in your research on this issue. Unfortunately, I haven’t studied it as much as I would like, nor have I had any formal class on metaphysics yet, so my explanations are most definitely amateurish.

in Christ,

(Hunter Vallejos) #7

Hi Anthony,

Thanks so much for all of these resources! I am skimming the last article by Craig. He seems to identify Divine Conceptualism with anti-Platonism.

I’m not quite sure how he reaches such a conclusion. At least, it seems that he derives his argument from the idea that abstract objects in Divine Conceptualism are “God’s thoughts” which, according to Craig, aren’t real objects. He states,

Our thoughts are certainly not abstract objects. It seems bizarre to think that one of God’s thoughts, on the other hand, could be an abstract object. Their causal efficacy alone will preclude their being thus classified. So according to absolute creationism, in contrast to divine conceptualism, things like propositions and properties are not God’s thoughts but are abstract objects which are the causal products of, and not identical with, God’s intellective activity.”

But I suppose perhaps I am espousing something a little more nuanced: that these abstract objects are God, the same way that we would say God is love, or God is justice, etc. etc. Not that they completely contain who God is, but rather that its existence is God’s existence. That they are not merely “God’s thoughts” but rather that they are part of God, and hence they exist because God exists.

I don’t see how such a view necessarily contradicts Platonism, because abstract objects as we understand them exist extrinsically, and that extrinsic existence is hence found in God.

I also don’t understand this tendency to think of the abstract ideas as “God’s thoughts” when we commonly say, at least as Christians, that God is love – that love does not exist apart from Him.

Additionally, I don’t see how his statement “Their causal efficacy [that is, God’s thoughts] alone will preclude their being thus classified [as abstract objects]” makes sense. We do see these abstract principles in creation, such as mathematics, directing how matter behaves and how the physical universe is structured.

(Anthony Costello ) #8


Hunter, great thoughts! I like that you are getting deep into this; the Lord knows we need serious thinkers like yourself in the Church today. I hope that you continue to do research in this area, and that it will edify your faith in Christ, and also bring additional light to His church.

So, I think, and again let me preface my “thinking” by saying this really isn’t my main area of focus; but, I “think” that what Craig is saying is that because God’s thoughts would have causal powers (or efficacy), therefore, they cannot be properly construed as abstract objects, because abstract objects are by definition (and maybe by nature) causally effete. Of course, maybe you could argue that they are not, I haven’t thought about that.

Initially, therefore, I would disagree with your statement that mathematics “direct[s]” anything in the physical universe. I, at least, cannot see how a mathematical formula or logical relationship can actually direct anything; if we construe “directing” as an actual generative action. For a truly causal action, it seems it would have to be God doing the directing of the physical constituents of the universe, perhaps through the axioms of math; and those we can then discover and put into our own symbolic language.

Further, although I don’t accept Craig’s view in toto, (I, at least, do not want to be an anti-Realist about universals), I don’t think you would want to say

that these abstract objects are God…"

I don’t think you want to put it that way, because obviously you don’t want to say that God doesn’t have causal powers. However, I do think you can say, as you do here:

rather that they are part of God, and hence they exist because God exists."

That seems better to me, because then you could say that these abstract objects (numbers, logical relations, etc.) are not really abstract objects, in the sense that they exist outside of God in some co-eternal Platonic realm, but that these things are dependent upon God’s existence, because they are part of Him. Of course, behind the talk of “parts” lurks the problem of Divine Simplicity. But, I’ll leave that for now, and wait to hear more from you on this.

in Christ,

(Gert Pieter Wensveen+++++++++++++++) #9

God, by definition is omniscient. He is the eternal, omniscient originator of the whole of reality, including, therefore, His own–self existent–reality. Thus, all potential mathematical and semantic ideation finds its eternal origin in Him.

Time, space and matter/energy can all be expressed mathematically in finite mathematical concepts. Thus, “in the beginning”–of time, space and matter/energy–God created the universe of time, space and matter/energy. Thus, the finite came out of the Infinite. It is logically impossible for the finite to have come out of the finite, for then its creation of itself would have predated its creation of itself.

So, yes, I agree with that argument totally.