A conceptualist argument for the existence of God.
This argument is flawed. I’ll leave the entry up anyways. See comments.
[[[As some of you may have read, as recently as my last blog I held to a constructivism view of mathematical objects. I’d been aware of this argument for the existence of God before, but thought it was flawed because (1) was false. Recently, however, I’ve been exposed to anti-nominalist arguments. Because of this, I’ve reconsidered this argument, and decided to post it here:
1) Numbers or propositions are abstract objects.
2) Abstract objects are either independently existing realities or concepts in some mind.
3) Abstract objects are not independently existing realities.
4) Therefore, abstract objects exist as concepts in some mind.
5) Abstract objects are not grounded in finite or contingent minds.
6) Therefore, if abstract objects are concepts in some mind, then they are grounded in an omniscient, metaphysically necessary being’s mind.
7) Abstract objects exist, and they are grounded in some mind (1, 4).
C) Therefore, an omniscient, metaphysically necessary being exists.
Justification for (1): I feel that this is the crucial premise (probably because I was a nominalist until recently). What swayed my stance is that we live in a world with a mathematical order. If mathematics were purely a human invention, then these inventions constructed from axioms produced in the 5th century B.C. would almost certainly fail to predict the accuracies seen in quantum mechanics, quantum electrodynamics, quantum chromodynamics, special relativity, general relativity, etc. Additionally, world-renowned mathematical physicist Roger Penrose makes a compelling case for mathematical objects being discovered, not invented, and thus abstract.
Justification for (2): This premise follows directly from (1). If these things are abstract, they are either independently existing realities or concepts in a mind–this is an exhaustive list, given the truth of (1).
Justification for (3): The main justification I have for this argument is the epistemological argument against Platonism. I think that this argument holds. David Liggins is a prominent proponent of this argument. He develops the above argument further in this article, but in it he invokes a false dilemma between Platonism and Nominalism. His argument against Platonism holds, but Conceptualism (both human and divine) provides an alternative to Nominalism. One can freely accept Conceptualism and avoid the problems of both Nominalism (referenced in premise (1)) and Platonism. Additionally, Platonism faces a few additional mathematical problems. To quote William Lane Craig, “Platonism is peculiarly burdened with the antinomies of naive set theory, specifically Burali-Forti’s antinomy, Cantor’s antinomy, and Russell’s antinomy. Further, I explained [in his book, The Kalam Cosmological Argument] that the customary means of avoiding these paradoxes, such as logicism or axiomatization, sit ill with a metaphysic of Platonism” (Craig 1999, Religious Studies 35). All this put together should suffice to demonstrate that Platonism does not suffice to ground abstract objects.
Justification for (4): This premise follows directly from (3).
Justification for (5): This premise is easily justified, as numbers and propositions cannot be grounded in some human mind(s), for there are too many such objects to be grounded in anything less than infinite intelligence. Additionally, since many of these objects exist necessarily–mathematical objects either exist necessarily or not at all–, they cannot be in any case grounded in the mind of a contingent being.
Justification for (6): This premise follows from the truth of (5). If a mind is not finite in intelligence, it is omniscient; if something is not contingent, it is metaphysically necessary. If abstract objects exist in some mind, since (5) holds, they exist in an omniscient, metaphysically necessary mind.
Justification for (7): This follows from the truth of the previous premises.
Now, some might state that the truth of this argument implies that an actual infinite exists in the divine mind, and thus, the kalam is false (which I have defended at length in a previous post). This isn’t actually the case, however. When presented with this question, William Lane Craig responds as follows:
Not at all! In the first place, one need not be conceptualizing consciously all that one knows. I know, for example, the multiplication table up to 10 although I am not consciously entertaining any of its individual equations, so that my knowledge of the multiplication table does not imply that I have 10^2 ideas. Secondly, and more importantly, the Conceptualist may avail himself of the theological tradition that in God there are not, in fact, a plurality of divine ideas; rather God’s knowledge is simple and is merely represented by us finite knowers as broken up into knowledge of discrete propositions and a plurality of divine ideas. William Alston points out that such a doctrine of divine knowledge does not commit one to a full-blown doctrine of divine simplicity. Such a full-blown doctrine faces well-known difficulties; but with respect to divine intellection such a simplicity doctrine has considerable advantages independent of the concerns of the kalam cosmological argument. For example, it allows one to circumvent wholly Patrick Grimm’s paradoxes of omniscience based on God’s knowledge of individual truths. (Craig 1999, Religious Studies 35)
So this argument would not entail the existence of an actual infinity if the abstract objects are indeed in a divine mind. It seems to me that this argument holds, and thus, an omniscient, necessary being exists.]]]