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In order for religious ideas to deserve serious consideration, should those ideas be "real" or "true" or "provable"?
"Real" and "true" and "provable" seem not to be synonyms.
Scientific culture emphasizes material reality as its topic and, although not entirely hostile to supposed logical demonstrations, is skeptical of alleged proofs which remain untested by experiment. The scientific attitude towards long complicated arguments seems to be that these arguments are merely interesting jabber unless, at regular intervals throughout the argument, the alleged facts can be shown to match measurable features of the real world.
Much of modern mathematics, on the other hand, is devoted to establishing truth by rigorous argument, without regard for the material reality of the subject matter: here one finds various "true" assertions of the form "such and such a thing exists," even when there is no possibility of actually exhibiting to the unindoctrinated nonexpert any example of the sort of thing alleged to exist. Here, the distinction between "true" and "provable" was made quite forcibly by Godel in the 1930's, when he showed how, if given a theory for arithmetic, one could find a statement which not only was unprovable in the theory but also which was necessarily true because it was unprovable.
There is also a common, subjective notion of truth -- illustrated by the quote "It's the truth even if it never happened" in One Flew Over the Cuckoo's Nest -- which raises the question whether, for example, one might learn "truths" from admitted fictions. The Zohar -- a Jewish cabalistic text first known in the Middle Ages and (rightly, I think) often regarded as profound and beautiful -- was attributed to a much earlier period by its medieval transcriber, although according to some traditions, the transcriber's wife asserted he had invented the text himself.
One might ask whether religious notions are "real" in a scientific sense, whether they are "provable" in a mathematical or logical sense, or whether they are "true" in some other sense.
Utterances commonly associated with the word G-d suggest that the scientific method might be useless for the purposes of investigating the notion, since it is unclear how devices such as rulers and clocks could be applied to investigate "something" which presumably transcends space and time. As Chuangtzu said, "That which gives things their thusness cannot be limited by things: so when we speak of limits, we remain confined to limited things."
Nor is it clear that G-d, as a notion, can be subjected to any reasonable logical analysis, since for meaningful logic one needs axioms and deduction rules and (just as importantly) a subject which is limited enough to reason about, since otherwise the sophomoric paradoxes -- such as, "Supposing X can do anything, can X create a rock too heavy for X to lift" -- can be endlessly recast in ever more-sophisticated forms.
Religions often involve assertions that something Divine can come into the world. Sometimes these assertions are associated with miraculous or Supernatural claims, which are necessarily unscientific, since they do not involve phenomena governed by natural laws; sometimes these are assertions are of the form that we cannot understand by logic some hidden and transcendent Purpose.
Here's a specific theological question: could The Divine actually come into the world through myth or fiction?
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