This is a very rough argument, and I do not know if it can be given much precision.
Thesis: We should expect that there be either none or infinitely many causeless universes.
For either it's impossible for there to be a causeless universe or it's not. If it's impossible, there will be no causeless universe. But if it's not impossible, then there is an infinity beyond cardinality (e.g., maybe for every cardinal, there is a possible world with that many photons) of possible causeless universes. But given just how many universes there are—beyond cardinality—if any of them has a real chance of coming into existence, we would expect infinitely many to come into existence.
8 comments:
I think this is a great point.
Supposing we replace "causeless universes" with something else, say "giraffes," "tables," "roughly cubical objects." Do you think there are reasons to accept the thesis you've given that would not translate into reasons to accept these substitution instances? It seems that the number of possible giraffes is beyond cardinality, or at least has a very high cardinality. (Perhaps for every cardinal, there is a possible world with that many giraffes?)
I think the logic is a kind of PSR stepchild. It would be cleanest (most sufficiently reasonable) if every event had a cause. If would be a little less clean if there were uncaused events, but if we have to live with that, let it be a regular occurrence. (Quantum fluctuations maybe.) It would be super unreasonable if there were only one (or finite N) uncaused event(s). Then we’d not only have no explanation for why there was that event, but also no explanation for why there was only one (or N).
A somewhat different version could be more epistemological. It would be not be too surprising if every event had a cause. It would be a little more surprising if there were uncaused events. It would be *really* surprising if there were only one uncaused event. In general, it is easier and more rational to believe the less surprising hypothesis.
Brian: Giraffes and the like may require a background spacetime that has enough space in it for them, which complicates things a little.
Heath: Yes, that sounds right. Unless perhaps the probabilities of an uncaused event are in a very narrow sweet spot that makes one expect exactly one event. There are mathematical problems with supposing such a sweet spot, plus it's unlikely that that the probabilities would be so well calibrated.
Dear dr. Pruss,
What do you think of the following argument presented by atheist philosopher Richard Carrier:
"The formalization of the argument proceeds as follows:
P1: In the beginning, there was absolutely nothing.

P2: If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.

C1: Therefore, in the beginning, nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.

P3: Of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing, one universe popping into existence is another thing, two universes popping into existence is yet another thing, and so on all the way to infinitely many universes popping into existence, and likewise for every cardinality of infinity, and every configuration of universes.

C2: Therefore [given logical necessity], continuing to be nothing was no more likely than one universe popping into existence, which was no more likely than two universes popping into existence, which was no more likely than infinitely many universes popping into existence, which was no more likely than any other particular number or cardinality of universes popping into existence.

P4: If each outcome (0 universes, 1 universe, 2 universes, etc. all the way to aleph0 universes, aleph1 universes, etc. [note that there is more than one infinity in this sequence]) is no more likely than the next, then the probability of any finite number of universes (including zero universes) or less having popped into existence is infinitely close to zero, and the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.

C3: Therefore, the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.

P5: If there are infinitely many universes, and our universe has a nonzero probability of existing (as by existing it proves it does, via cogito ergo sum), then the probability that our universe would exist is infinitely close to one hundred percent (because any nonzero probability approaches one hundred percent as the number of selections approaches infinity, via the infinite monkey theorem, similar to the law of large numbers).

C4: Therefore, if in the beginning there was absolutely nothing, then the probability that our universe would exist is infinitely close to one hundred percent. "
For more elaboration and defenses of the premises see his entire post at:
http://freethoughtblogs.com/carrier/archives/468
Any thoughts would be welcome.
GGDFan777
Probability theory completely breaks down with infinite fair lotteries.
But if we allow such reasoning, scepticism follows. For there are way more universes that are just like ours up to the present but where the laws of nature break down tomorrow (there are beyond cardinality many ways for induction to break down tomorrow) than universes which are just like ours but where they don't so break down.
I commented on Carrier's blog and mentioned the two things Pruss just said, as well as one more extremely important point: The production of things requires causal capacity (or, at least, causal potentiality). The total absence of limits in "nothing" is accompanied by a total lack of potentiality or causal power. Therefore, while it is the case that no production is any more likely than any other, it is also the case that production is impossible.
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