Existence of God as Axiomatic

Discussion in 'Apologetical Methods' started by Charles Johnson, Nov 16, 2019.

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  1. Charles Johnson

    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?
     
  2. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

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

    Charles Johnson Puritan Board Freshman

    Which ones, and which authors?
     
  4. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

    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.
     
  5. jwright82

    jwright82 Puritan Board Graduate

    Didn't Cantor resolve the tortiese and hair problem by showing that some infinites are larger than others? Hence making the question irrelevant?
     
  6. jwright82

    jwright82 Puritan Board Graduate

    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?
     
  7. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

    The question isn't irrelevant. What Cantor had to revise is that a possible infinite isn't the same concept as an actual infinite.
     
  8. jwright82

    jwright82 Puritan Board Graduate

    I mean he solved it.
     
  9. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

    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.
     
  10. Dachaser

    Dachaser Puritan Board Doctor

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

    BayouHuguenot Puritanboard Amanuensis

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

    Dachaser Puritan Board Doctor

    What do you say?
     
  13. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

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

    Dachaser Puritan Board Doctor

    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?
     
  15. Charles Johnson

    Charles Johnson Puritan Board Freshman

    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.
     
  16. Dachaser

    Dachaser Puritan Board Doctor

    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?
     
  17. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

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

    Charles Johnson Puritan Board Freshman

    I would think all reformed folks would be able to agree on that.
     
  19. jwright82

    jwright82 Puritan Board Graduate

    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.
     
  20. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

    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."
     
  21. jwright82

    jwright82 Puritan Board Graduate

    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.
     
  22. jwright82

    jwright82 Puritan Board Graduate

    Maybe everything I have says that. Let me double check when I get home. Holiday hours in retail, funnnnn.
     
  23. jwright82

    jwright82 Puritan Board Graduate

    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
    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.
     
  24. jwright82

    jwright82 Puritan Board Graduate

    Not sure it's universally accepted, my bad. Sorry.
     
  25. jwright82

    jwright82 Puritan Board Graduate

    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?
     
  26. jwright82

    jwright82 Puritan Board Graduate

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

    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.
     
  28. BayouHuguenot

    BayouHuguenot Puritanboard Amanuensis

    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).
     
  29. jwright82

    jwright82 Puritan Board Graduate

    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.
     
  30. Dachaser

    Dachaser Puritan Board Doctor

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