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This whole Shroud business raises a general question about how we should treat such things.
In general, if God exists, and if God did something, why should it be necessary that we be able to understand how God did it? Wouldn't we kinda have to be God in order to understand precisely how God acts?
How is electromagnetic radiation capable of transmitting messages across the Internet? Well, it propagates at the speed of light through the electromagnetic field. But how does it manage to do that? Etc.
One can continue this scientific story, but in the end we will end up saying "It just does. That's just how it is. Things are just like that."
We get to the basic processes and laws of nature, and we stop.
But would it be in place to say, "But the basic processes and laws of nature (call it Nature for short) don't really explain anything anything, do they? I mean, essentially all you're saying is 'Nature diddit'"?
Ah, but at least we understand how Nature operates, using our mathematical reasoning powers. Leaving to one side where mathematical reason comes from, or why there should be such a thing, couldn't it be the case that the way God operates vastly transcends the abilities of finite mathematical reasoners to comprehend, using their finite mathematical powers of reasoning?
It seems to me that it would be begging the question to insist that if God operates in some way, or does some particular thing (like raise Jesus from the dead and supernaturally produce his image on the relic known as the Shroud of Turin), then it must be the case that God did it in a way that our finite powers of mathematical reasoning (and other finite cognitive powers) must be able to comprehend.
And in fact, it might be that Nature is like this too. It might be the case that there are some aspects of Nature the explanations for which are such that they are beyond our abilities to understand. (Some philosophers take this view with respect to consciousness itself, most prominently Colin McGinn and the New Mysterians).
So essentially, we come down to the following: there are a bunch of phenomena that our conscious minds are more or less aware of. These include, a mathematically intelligible physical world; consciousness; rationality; moral experience; religious experience; aesthetic experience; the experience of meaning, love, goodness, etc. And we ask the general question, How Come? And some people answer, 'Nature Diddit', by which they mean that blind, impersonal material processes obeying inexorable purposeless regularities did it, and that these processes just happen to exist and have the properties they do. That's just the way it is. Their abductive hypothesis is that the best explanation is 'matter in motion', or something like that. They take material process as basic.
Others say that mind/consciousness/reason/goodness is basic and transcends all material processes, and their abductive hypothesis is that all the existence of all these phenomena can best be explained by the existence and creative action of a transcendent Mind.
Both hypotheses are examples of the 'inference to the best explanation' type of reasoning. One posits material process as the best explanation. The other posits transcendent creative Mind as the best explanation. In neither case is there an attempt to take the explanatory process further. They are simply competing explanatory end-points.
Now, it's not obvious to me that the materialist abductive hypothesis is clearly more reasonable than the theistic abductive hypothesis. But that's not my point. My point is that it's a poor argument to say that the theistic hypothesis doesn't explain anything. After all, one might as well say that the materialist hypothesis doesn't explain anything, because within each hypothesis something is taken as explanatorily and causally and ontologically *basic*.
The materialist may reply that only the materialist hypothesis allows for quantitative, mathematical explanations and sensory perceptual forms of evidence. But insisting that quantitative mathematics and sensory perception is the be-all and end-all of explanation and evidence is precisely what's at issue as between the two competing hypotheses. Hence that insistence is a systematic example of the logical fallacy of begging the question. The issue at stake, in other words, is precisely whether quantitative sciences and sensory perception disclose in principle the full nature of reality.
Obviously, if theism is true, then they don't. But then one can't non-circularly show that theism is not true simply because theism is not verified by quantitative sciences and sensory perception. That would be an egregious logical error. It would be like saying there is no number greater than 100 simply because your calculator only goes up to 100.
In other words, if theism (or indeed any form of supernaturalism) is true, then it's ridiculous to question it because it doesn't conform itself to the methods and criteria of natural science. This is the kind of mind-boggling stupidity that led the Soviets to declare that atheism is true because Yuri Gargarin had been up in space and found no God there.
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