# Existence of God as Axiomatic



## Charles Johnson (Nov 16, 2019)

I'm wondering if any can help me resolve my confusion regarding an aspect of classical apologetics. It seems that treatment of the existence of God as self-evident and axiomatic is a pretty standard part of reformed scholastic prolegomena. I've seen such statements in Junius and John Brown of Haddington, for example. The Leiden Synopsis puts it this way in thesis 1.30:
"Theology is not only intellectual and semantic, but indeed discursive. For frequently, it uses many arguments for convincing naysayers, and from its principles, from its prior, _per se_ indemonstrable things, it either elicits conclusions for proving the truth or explanations for refuting the deceptive objections of the sophists. _Mt. 22:32-33; 1 Cor. 15:20-22."_
(translation my own).
So these authors believed that theology has certain indemonstrable principles. Junius, in _Mosaic Polity_, explicitly states that the existence of God is one such principle. Is it inconsistent, then, for classical apologists to attempt to use arguments like Thomas's five proofs to demonstrate the existence of God? Or does this represent two distinct schools of thought within the classical school?

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## RamistThomist (Nov 16, 2019)

Depends. Some classical arguments do a good job in showing the impossibility of traversing an infinite.


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## Charles Johnson (Nov 16, 2019)

BayouHuguenot said:


> Depends. Some classical arguments do a good job in showing the impossibility of traversing an infinite.


Which ones, and which authors?


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## RamistThomist (Nov 16, 2019)

Charles Johnson said:


> Which ones, and which authors?



Bonaventure in one his Breviloquia (sp?) was the first, I think. Bonaventure's take is interesting because it was not in the direction of Aristotelianism.

Craig and Moreland have also done a good job on possible and actual infinites. George Cantor was the mathematician that made this research possible.

The argument comes down to there can't be an infinite number of previous days. If there were, then we would have to have passed an infinite number of days before we could get to the present day, and so on.

As a general rule, I think discussing apologetic methodologies is akin to huffing pain thinner. This might be one of those exceptions. The Reformed Orthodox are interesting because they affirm a number of propositions:
a) there is a place for the proofs.
b) God is axiomatic (although what that actually means isn't quite as clear).
c) Natural theology is legitimate.
d) The nature of the covenant qualifies (a)-(c) in a way not emphasized among the medievals.

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## jwright82 (Nov 16, 2019)

BayouHuguenot said:


> Bonaventure in one his Breviloquia (sp?) was the first, I think. Bonaventure's take is interesting because it was not in the direction of Aristotelianism.
> 
> Craig and Moreland have also done a good job on possible and actual infinites. George Cantor was the mathematician that made this research possible.
> 
> ...


Didn't Cantor resolve the tortiese and hair problem by showing that some infinites are larger than others? Hence making the question irrelevant?


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## jwright82 (Nov 16, 2019)

Charles Johnson said:


> I'm wondering if any can help me resolve my confusion regarding an aspect of classical apologetics. It seems that treatment of the existence of God as self-evident and axiomatic is a pretty standard part of reformed scholastic prolegomena. I've seen such statements in Junius and John Brown of Haddington, for example. The Leiden Synopsis puts it this way in thesis 1.30:
> "Theology is not only intellectual and semantic, but indeed discursive. For frequently, it uses many arguments for convincing naysayers, and from its principles, from its prior, _per se_ indemonstrable things, it either elicits conclusions for proving the truth or explanations for refuting the deceptive objections of the sophists. _Mt. 22:32-33; 1 Cor. 15:20-22."_
> (translation my own).
> So these authors believed that theology has certain indemonstrable principles. Junius, in _Mosaic Polity_, explicitly states that the existence of God is one such principle. Is it inconsistent, then, for classical apologists to attempt to use arguments like Thomas's five proofs to demonstrate the existence of God? Or does this represent two distinct schools of thought within the classical school?


It depends on what you mean by self-evident and/Or axiomatic? Is it definitionally one and/or both of those things? Like the ontological argument?


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## RamistThomist (Nov 16, 2019)

jwright82 said:


> Didn't Cantor resolve the tortiese and hair problem by showing that some infinites are larger than others? Hence making the question irrelevant?



The question isn't irrelevant. What Cantor had to revise is that a possible infinite isn't the same concept as an actual infinite.


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## jwright82 (Nov 16, 2019)

BayouHuguenot said:


> The question isn't irrelevant. What Cantor had to revise is that a possible infinite isn't the same concept as an actual infinite.


I mean he solved it.


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## RamistThomist (Nov 16, 2019)

jwright82 said:


> I mean he solved it.



Did he solve an actual infinite or a potential one? He criticized the Aristotelian notion of a potential infinite but firmly held to an actual infinite.


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## Dachaser (Nov 16, 2019)

Charles Johnson said:


> I'm wondering if any can help me resolve my confusion regarding an aspect of classical apologetics. It seems that treatment of the existence of God as self-evident and axiomatic is a pretty standard part of reformed scholastic prolegomena. I've seen such statements in Junius and John Brown of Haddington, for example. The Leiden Synopsis puts it this way in thesis 1.30:
> "Theology is not only intellectual and semantic, but indeed discursive. For frequently, it uses many arguments for convincing naysayers, and from its principles, from its prior, _per se_ indemonstrable things, it either elicits conclusions for proving the truth or explanations for refuting the deceptive objections of the sophists. _Mt. 22:32-33; 1 Cor. 15:20-22."_
> (translation my own).
> So these authors believed that theology has certain indemonstrable principles. Junius, in _Mosaic Polity_, explicitly states that the existence of God is one such principle. Is it inconsistent, then, for classical apologists to attempt to use arguments like Thomas's five proofs to demonstrate the existence of God? Or does this represent two distinct schools of thought within the classical school?


Can one prove the existence of God though apart from His own revelation in scriptures and in Jesus Christ?


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## RamistThomist (Nov 16, 2019)

Dachaser said:


> Can one prove the existence of God though apart from His own revelation in scriptures and in Jesus Christ?



Some say yes. Some say no. It is literally the subject of every apologetics text.


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## Dachaser (Nov 16, 2019)

BayouHuguenot said:


> Some say yes. Some say no. It is literally the subject of every apologetics text.


What do you say?


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## RamistThomist (Nov 16, 2019)

Dachaser said:


> What do you say?



Generally speaking, I think God can be demonstrated. I don't think you can deduce the Trinity from looking at a tree.

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## Dachaser (Nov 16, 2019)

BayouHuguenot said:


> Generally speaking, I think God can be demonstrated. I don't think you can deduce the Trinity from looking at a tree.


So you would say that one can argue for God existing in the proper sense, but not as to Himself as triune apart from scripture and Christ?


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## Charles Johnson (Nov 16, 2019)

Dachaser said:


> So you would say that one can argue for God existing in the proper sense, but not as to Himself as triune apart from scripture and Christ?


It's a historical reality that heathens have been able to recognize that there is a single supreme deity. In Acts 17, Paul even says that the heathen Greeks had built an altar to this God. It's equally true that their ideas concerning this supreme deity tended to contain many errors, like that he is absolutely unknowable, did not create everything immediately, that there may be other, lesser deities, etc. They also never manifested an understanding of 'indemonstrable theology', ie the peculiar contents of special revelation, like the doctrine of the Trinity, of a mediator for sin, the covenant of grace, the gospel, etc.

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## Dachaser (Nov 16, 2019)

Charles Johnson said:


> It's a historical reality that heathens have been able to recognize that there is a single supreme deity. In Acts 17, Paul even says that the heathen Greeks had built an altar to this God. It's equally true that their ideas concerning this supreme deity tended to contain many errors, like that he is absolutely unknowable, did not create everything immediately, that there may be other, lesser deities, etc. They also never manifested an understanding of 'indemonstrable theology', ie the peculiar contents of special revelation, like the doctrine of the Trinity, of a mediator for sin, the covenant of grace, the gospel, etc.


So we all agree that those special items listed require divine revelation, and cannot be proven, much less known, apart from the Scriptures and Jesus?


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## RamistThomist (Nov 16, 2019)

Dachaser said:


> So you would say that one can argue for God existing in the proper sense, but not as to Himself as triune apart from scripture and Christ?



I would agree with Romans 1 that his eternal power and Godhead are manifest.


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## Charles Johnson (Nov 16, 2019)

Dachaser said:


> So we all agree that those special items listed require divine revelation, and cannot be proven, much less known, apart from the Scriptures and Jesus?


I would think all reformed folks would be able to agree on that.


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## jwright82 (Nov 16, 2019)

BayouHuguenot said:


> Did he solve an actual infinite or a potential one? He criticized the Aristotelian notion of a potential infinite but firmly held to an actual infinite.


He showed that there are greater kinds of infinity. The set of all numbers between 0 and 1 is infinite but less as a set of all natural numbers, than it's a less form of infinity.


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## RamistThomist (Nov 16, 2019)

jwright82 said:


> He showed that there are greater kinds of infinity. The set of all numbers between 0 and 1 is infinite but less as a set of all natural numbers, than it's a less form of infinity.



I don't think that is the conclusion he drew, that it was a "lesser infinity." Russell and others didn't interpret him that way. They just said "paradox."


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## jwright82 (Nov 16, 2019)

BayouHuguenot said:


> Did he solve an actual infinite or a potential one? He criticized the Aristotelian notion of a potential infinite but firmly held to an actual infinite.


That I don't know. I have a whole book on it at home, on lunch. I'll look at when I get home. I know it's universally accepted he solved that problem.


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## jwright82 (Nov 16, 2019)

BayouHuguenot said:


> I don't think that is the conclusion he drew, that it was a "lesser infinity." Russell and others didn't interpret him that way. They just said "paradox."


Maybe everything I have says that. Let me double check when I get home. Holiday hours in retail, funnnnn.


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## jwright82 (Nov 17, 2019)

BayouHuguenot said:


> I don't think that is the conclusion he drew, that it was a "lesser infinity." Russell and others didn't interpret him that way. They just said "paradox."


Couldn't find what I was looking here's a shot infinity is only a problem if we view all infinities as equal but there not. Cantor did show I believe that there are greater and lessersets of infiniti


BayouHuguenot said:


> Did he solve an actual infinite or a potential one? He criticized the Aristotelian notion of a potential infinite but firmly held to an actual infinite.


Well this might be a bit of course, I'll answer to the best of knowledge ( mediocre at best (any mathematicians can chime in ( a set within a set within a set))). Man I love math jokes. Anyway didn't find what I was looking for but I believe that the solution is that since there are greater or lesser infinities the hair is moving with greater infinities than the turtle so when added together over time will be larger, greater distance, so the hair will overtake the turtle. I can try to elaborate if need be but it seems off topic and I can't promise anything.


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## jwright82 (Nov 17, 2019)

jwright82 said:


> That I don't know. I have a whole book on it at home, on lunch. I'll look at when I get home. I know it's universally accepted he solved that problem.


Not sure it's universally accepted, my bad. Sorry.


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## jwright82 (Nov 17, 2019)

Dachaser said:


> Can one prove the existence of God though apart from His own revelation in scriptures and in Jesus Christ?


I think this gets into what we mean by truth? Can you prove God without exclusively quoting scripture? Sure, can you work with a method not influenced by your beliefs? I doubt. So that's the sort of questions I'd have for that. What's the end goal and what method are we using to get there?


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## jwright82 (Nov 17, 2019)

Dachaser said:


> So you would say that one can argue for God existing in the proper sense, but not as to Himself as triune apart from scripture and Christ?


Van Til did argue that the Trinity did solve the one and many problem.


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## Charles Johnson (Nov 17, 2019)

The tortoise and the hair problem can be resolved simply with mathematical limits, which are essential to calculus. In math, infinity cannot have a value per se, but the limit of a function as a variable approaches infinity can. The limit of the distance the hair must travel as the number of subdivisions approaches infinity is equal to the actual distance. Google is telling me that Cantor invented set theory. Set theory is not necessary to address this problem.


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## RamistThomist (Nov 17, 2019)

Charles Johnson said:


> Google is telling me that Cantor invented set theory. Set theory is not necessary to address this problem.



I think set theory sort of emerged the same time Cantor, Frege, and Russell came on the scene. In any case, strictly speaking, you are correct. Set theory isn't necessarily tied to whether we can traverse an actual infinite (which of course we can't).


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## jwright82 (Nov 19, 2019)

Charles Johnson said:


> The tortoise and the hair problem can be resolved simply with mathematical limits, which are essential to calculus. In math, infinity cannot have a value per se, but the limit of a function as a variable approaches infinity can. The limit of the distance the hair must travel as the number of subdivisions approaches infinity is equal to the actual distance. Google is telling me that Cantor invented set theory. Set theory is not necessary to address this problem.


True. He used set theory to solve it. Some sets are infinite and some infinite sets are larger than other infinite sets. The set of numbers between 0 and 1 is infinite. But it will never be larger than the set of all natural numbers (1,2,3.......). The turtle is traveling by smaller infinite sets than the hair, so the hair travels faster. You can add and subtract infinite sets.


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## Dachaser (Nov 19, 2019)

BayouHuguenot said:


> I think set theory sort of emerged the same time Cantor, Frege, and Russell came on the scene. In any case, strictly speaking, you are correct. Set theory isn't necessarily tied to whether we can traverse an actual infinite (which of course we can't).


Is math infinity though same as when we say God is infinite?


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## RamistThomist (Nov 19, 2019)

Dachaser said:


> Is math infinity though same as when we say God is infinite?



No.

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## jwright82 (Nov 24, 2019)

BayouHuguenot said:


> No.


Yeah I agree. Whatever we mean by infinite in math is not the same as infinite when apllied to God, qualitative differences. There are different infinities in math.


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## Dachaser (Nov 26, 2019)

jwright82 said:


> Yeah I agree. Whatever we mean by infinite in math is not the same as infinite when apllied to God, qualitative differences. There are different infinities in math.


Isn't God infinite in the absolute sense then, as none beyond Him?


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## RamistThomist (Nov 26, 2019)

Dachaser said:


> Isn't God infinite in the absolute sense then, as none beyond Him?



Sure. We were discussing more the idea of an infinite duration. And if you apply that to days, that means we would have had to have an infinite number of days before we get to today, which means we would have never gotten to today.


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## PuritanCovenanter (Nov 26, 2019)

God being above and outside of creation's infinite time and space is incomprehensible. I think it always will be. I think it is part of the majesty he will always have in Himself alone as we and his creation will always be tied to time and space.


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## Dachaser (Nov 26, 2019)

PuritanCovenanter said:


> God being above and outside of creation's infinite time and space is incomprehensible. I think it always will be. I think it is part of the majesty he will always have in Himself alone as we and his creation will always be tied to time and space.


He alone self existed outside of time and space proper.


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## jwright82 (Nov 27, 2019)

Dachaser said:


> Isn't God infinite in the absolute sense then, as none beyond Him?


I prefer to look at as different kinds of infinity. I brought it up because although I believe that the first cause argument is true intuitionially but I am skeptical over simplistic versions because of the work on infinities in math by Cantor show the concept is not so simple. But all the complexity of infinity that we come across on a created level is in sum total a completely different kind of "infinity" than whatever is meant by when we apply it to God.

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## jwright82 (Nov 27, 2019)

BayouHuguenot said:


> Sure. We were discussing more the idea of an infinite duration. And if you apply that to days, that means we would have had to have an infinite number of days before we get to today, which means we would have never gotten to today.


Just an example of what I'm talking about infinite duration and different kinds of infinity. Now I completely agree with your point Jacob but I noticed a paradox. The terminator paradox (which I just made up but am pretty sure there's some concept out there) John Conner sends Kyle Reese back in time to save his mother. Kyle Reese becomes John's father only for John to grow up fight the machines (don't be skeptical SIRI 2.0 might be Skynet, I don't trust those things) train Kyle and send him back to be his father. And over and over and over again on into infinity, an infinite loop but the same finite number of days of John Conner being fathered by Kyle only to live let's say 30 years to send Kyle back. That finite 30 years hasn't changed and yet there's an infinite temporal loop. You see complex.


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## Dachaser (Nov 27, 2019)

jwright82 said:


> Just an example of what I'm talking about infinite duration and different kinds of infinity. Now I completely agree with your point Jacob but I noticed a paradox. The terminator paradox (which I just made up but am pretty sure there's some concept out there) John Conner sends Kyle Reese back in time to save his mother. Kyle Reese becomes John's father only for John to grow up fight the machines (don't be skeptical SIRI 2.0 might be Skynet, I don't trust those things) train Kyle and send him back to be his father. And over and over and over again on into infinity, an infinite loop but the same finite number of days of John Conner being fathered by Kyle only to live let's say 30 years to send Kyle back. That finite 30 years hasn't changed and yet there's an infinite temporal loop. You see complex.


Isn't God being self existent Eternal Being define His infinite status?


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## RamistThomist (Nov 27, 2019)

Dachaser said:


> Isn't God being self existent Eternal Being define His infinite status?



Probably, but when we say infinity, do we mean it in terms of body, space, time, all of the above, none of the above?


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## jwright82 (Nov 27, 2019)

Dachaser said:


> Isn't God being self existent Eternal Being define His infinite status?


A different kind I guess but notice how complex infinity is in human concepts. I'd say his infinity is unique.


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## Dachaser (Nov 27, 2019)

BayouHuguenot said:


> Probably, but when we say infinity, do we mean it in terms of body, space, time, all of the above, none of the above?


Beyond and above!


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## RamistThomist (Nov 27, 2019)

Dachaser said:


> Beyond and above!



Beyond, not above. Above is spatial language and connotes that God is a body.


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