The other day in class in our introduction to Metaphysics the teacher had said something about how numbers didn’t pre-exist human minds. One student shot up his hand and said “well, even before man was here, the universe was operating mathematically or intelligibly, numbers still existed…” and the teacher seemed serious and adamant when he replied that “well, numbers are thoughts, and thoughts have to exist in minds, so that would require something like God.. [laughs] and since we’re disqualifying that… etc”
I think the point was brushed by a little too quickly, but I agree with the intuition of the professor, it is hard to see how numbers could be anything other than thoughts, and how the universe could work prior to contingent minds in an intelligible way, which contingent minds could come to reflect on and understand as intelligible. I would like to follow this meditation for a little while.
On Atheism, (I think on just about any form of it), it is the case that we can speak about the universe following intelligible patterns prior to those patterns of intelligibility existing, as yet, as part of any model of the world, only in an extended or extrapolated sense. However, let us take inventory of one’s options on this assumption: either something like metaphysical Naturalism (meaning approximately physicalism) is true and thoughts are fundamentally physical things which only semantically cannot be spoken of as physical things because they supervene on physical things (in the same way software cannot be spoken of as physical, even though ultimately it is physical), or else something like idealism is true. This means that things like numbers, or even laws of logic, are essentially ‘natural kinds’. Idealism would allow us to adopt models like Naturalism (meaning approximately physicalism) as the best models or language games in which to speak about our world. Ultimately the conviction is, however, that experience is all that, at bottom, exists. As I’ve said before, Idealism is fundamentally the conviction that Relations are ontologically prior to relata. Our models, then, arise from experience, which is all that exists. The alternative on Atheism being something like Metaphysical Naturalism (meaning approximately physicalism), these alternatives are quite different.
Naturalism has, as its problem, that it isn’t possibly ‘rational’ and that it tries to retain a semantic distinction between material and immaterial things (like rocks and laws of logic) while maintaining that this semantic distinction is only provisional and not ‘metaphysical’. Idealism has the problem of being in fundamental denial of the Principle of Sufficient Reason, which many, most or all typical ‘rationalists’ or even analytic philosophers accept as a constraint on Rational propositions and thoughts. Of course, an idealist might be able to speak about a weaker principle of sufficient reason provisionally (in, say, a scientific language game) while denying the PSR or even the WPSR as a constraint on Metaphysics.
Of course, the Naturalist may also disagree with the PSR (let’s say, because they are committed via the rubrics of Naturalized Epistemology to an indeterminite interpretation of Quantum mechanics on which the Principle of Sufficient Reason is undermined).
So, if somebody is convinced that the Principle of Sufficient Reason is necessarily true (true about the way we construct and understand propositions and the relations between propositions – thus a law of logic) then both Idealism and Naturalism may be undermined (I take it that Naturalism entails naturalized epistemology). Their option, it seems, is likely to be something relevantly similar to the Medieval Exemplarism which is maintained in the Augustinian tradition by philosophers such as by Bonaventure. According to this model thoughts exist independent of man entertaining them (if at some time the proposition “Montreal is a Canadian city” is not being reflected on or entertained by any living person, the proposition still actually exists as a thought, precisely because it remains in the mind of God who, being omniscient, ‘knows all true propositions’). Assuming that objections, like Grim’s Cantorian argument against omniscience, can be dissolved, this view seems attractive.
The Student’s question brought to my mind these options, and made it clearer to me recently that these seem to be the three fundamentally live options in analytic philosophy today. Perhaps there are some other options on Theism, but I doubt that there are any options other than Metaphysical Naturalism (meaning something like Physicalism) or Idealism on Atheism. Therefore, if ever I want to go on and do a thesis in Modal logic, or Epistemology, I will have to find good arguments to disqualify not only Naturalism, but also Idealism, and to promote something like Theistic Exemplarism.