Is Craig's appeal to BGV sufficient evidence for accepting (a)? Not unless the relevant experts agree with him that BGV is correct, and that it's strong evidence for (a). Appeal to an expert's testimony that P is legitimate iff (i) the expert is reliable and credible in the given context, (ii) they're speaking within their area of expertise, (iii) their expertise is a genuine field of knowledge, and (iv) the consensus among the experts is that P. Therefore, unless the consensus of the relevant experts is that BGV shows what Craig's thinks it shows, Craig's assertion is an illegitimate appeal to expert testimony: whether Craig is right or not, I'm not justified in thinking so.[1]
But let's waive that. Suppose it shows what he thinks it shows: multiverse or not, there's an absolute beginning of spacetime. Should I then infer (b) and (c)? Not obviously. For it's far from clear that the claim that the universe (or multiverse) arose from an efficient cause without a material cause is any more plausible than the claim that it arose from neither. For both involve a strongly counterintuitive origination of something from no pre-existing materials. (To say that a log cabin popped into existence out of nothing is bizarre; it is no less bizarre to be told that a lumberjack built it without using building materials.) Therefore, pending expert consensus about the implications of BGV pointing toward Craig's assertion (viz., that it shows an absolute beginning to the universe or multiverse), it's not clear why a G.E. Moore Shift against (a) isn't an equally plausible inference.
But suppose all this is wrong. Would Craig's inference to (c) (i.e., that the cause of the absolute beginning of the universe or multiverse is a person) then be the most plausible inference? Again, this is far from clear. For there are well-known serious concerns about the coherence of a timeless agent-cause of a temporal effect.
Wes Morriston has written a number of papers that are very good with respect to points in the vicinity of those mentioned above:
http://spot.colorado.edu/~morristo/kalam-not.pdf
http://www.colorado.edu/philosophy/wes/wes2craig1.pdf
http://www.philoonline.org/library/morriston_5_1.htm
http://www.colorado.edu/philosophy/wes/wes2craig2.pdf
UPDATE: For those who may be interested, I offer a fuller exploration of Craig's appeal to the BGV here.
[1] It's true that Craig and Sinclair offer detailed arguments that BGV shows what they think it shows. But of course those arguments rely on specialized scientific knowledge that non-experts are not in a position to evaluate properly, and so, again, we're back to deference to expert consensus about the success of those arguments.
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When the universe was small and dense Quantum Gravity would have played an important role. As Sean Carrol has pointed out, this limits the applicability of the BGV theorem, which applies to purely classical space-times.
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