Existence of God as Axiomatic

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Charles Johnson

Puritan Board Freshman
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?
 

BayouHuguenot

Puritanboard Amanuensis
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.
 

jwright82

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

jwright82

Puritan Board Graduate
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?
 

BayouHuguenot

Puritanboard Amanuensis
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.
 

Dachaser

Puritan Board Doctor
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?
 

Dachaser

Puritan Board Doctor
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?
 

Charles Johnson

Puritan Board Freshman
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.
 

Dachaser

Puritan Board Doctor
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?
 

jwright82

Puritan Board Graduate
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.
 

BayouHuguenot

Puritanboard Amanuensis
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."
 

jwright82

Puritan Board Graduate
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.
 

jwright82

Puritan Board Graduate
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.
 

jwright82

Puritan Board Graduate
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
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.
 

jwright82

Puritan Board Graduate
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?
 

Charles Johnson

Puritan Board Freshman
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.
 

BayouHuguenot

Puritanboard Amanuensis
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).
 

jwright82

Puritan Board Graduate
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.
 

Dachaser

Puritan Board Doctor
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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