Do some inductions require a necessary first cause?
August 21, 2014 — 8:16

Author: Alexander Pruss  Category: Existence of God Uncategorized  Tags: , , , ,   Comments: 5

Suppose that we’ve observed a dozen randomly chosen ravens and they’re all black. We (cautiously) make the obvious inference that all ravens are black. But then we find out that regardless of parental color, newly conceived raven embryos have a 50% chance of being black and a 50% chance of being white, and that they have equal life expectancy in the two cases. When we find this out, we thereby also find out that it was just a fluke that our dozen ravens were all black. Thus, finding out that it’s random with probability 1/2 that a given raven will be black defeats the obvious inference that all ravens are black, and even defeats the inference that the next raven we will see will be black. The probability that the next raven we observe will be black is 1/2.

Next, suppose that instead of finding out about probabilities, we find out that there is no propensity either way of a conception resulting in a black raven or its resulting in a white raven. Perhaps an alien uniformly randomly tosses a perfectly sharp dart at a target, and makes a new raven be black whenever the dart lands in a maximally nonmeasurable subset S of the target and makes the raven be white if it lands outside S. (A subset S of a probability space Ω is maximally nonmeasurable provided that every measurable subset of S has probability zero and every measurable superset of S has probability one.) This is just as much a defeater as finding out that the event was random with probability 1/2. (The results of this paper are driving my intuitions here.) It’s still just a fluke that the dozen ravens we observed were all black. We still have a defeater for the claim that all ravens are black, or even that the next raven is black.

Finally, suppose instead that we find out that ravens come into existence with no cause, for no reason, stochastic or otherwise, and their colors are likewise brute and unexplained. This surely is just as good a defeater for inferences about the colors of ravens. It’s just a fluke that all the ones we saw so far were black.

Now suppose that the initial state of the universe is a brute fact, something with no explanation, stochastic or otherwise. We have (indirect) observations of a portion of that initial state: for instance, we find the portion of the state that has evolved into the observed parts of the universe to have had very low entropy. And science appropriately makes inferences from the portions of the initial state that have been observed by us to the portions that have not been observed, and even to the portions that are not observable. Thus, it is widely accepted that the whole of the initial state had very low entropy, not just the portion of it that has formed the basis of our observations. But if the initial state and all of its features are brute facts, then this bruteness is a defeater for inductive inferences from the observed to the unobserved portions of the initial state.

So some cosmological inductive inferences require that the initial state of the universe not be entirely brute. I don’t know just how much cosmology depends on the initial state not being entirely brute, but I suspect quite a bit.

What if there is no initial state? What if instead there is an infinite regress? Here I am more tentative, but I suspect that the same problem comes back when one considers the boundary conditions, say at time negative infinity. If these boundary conditions are brute, then we’ve got the same problem as with a brute initial state. Likewise, a contingent first cause will not help, either, since the argument can be applied to its state.

It seems that the only way out of scepticism about cosmology is if there is a necessary first cause. And I also suspect that the impact of the argument may go beyond cosmology. Presumably, we continue to come into causal contact with portions of the initial state that we have previously not been in contact with, and couldn’t that affect us in all sorts of ways that undermine more ordinary inductive inferences (e.g., a burst of radiation might kill us all tomorrow, and no probabilities can be assigned to the burst, and hence no probabilities can be assigned to any positive facts about what we will do tomorrow)? If so, then we lose quite a bit of our predictive ability about the future if we hold the initial state to be brute.

Comments:
  • I agree with the logic of your argument, but I don’t see why you think this is such a big problem for cosmology.

    It is true that cosmologists often take the “cosmological principle” – that the entire universe looks basically similar to the bit that we see near us – as the simplest starting point in building a cosmology. But of course they are aware that this is only one possibility of an infinite variety. In some models, the cosmological principle is violated rather dramatically. In eternal inflation, for example, our observable universe is a bubble of slowly expanding spacetime that has branched off from a portion of spacetime where the conditions are radically different, because the spacetime is continually inflating.

    As you say, in some cosmological models we come into causal contact with more and more of the universe as time goes on. So, in principle, the cosmological principle could eventually be disproven by direct observational evidence (in maybe a billion years or so. In other models, we see less and less of the universe as time goes on, so in that case we would never get additional evidence about the distant universe.) I don’t see a whole lot riding on this.

    In your last paragraph, you illegitimately jump from scepticism about “inductive inferences from the observed to the unobserved portions of the initial state” to scepticism about cosmology, full stop. And I don’t get the last bit at all. We could be destroyed by a blast of radiation from space whether or not the cosmological principle is true. Does that make induction impossible?

    September 21, 2014 — 6:00
    • 1. Even in eternal inflation, isn’t it assumed that the rest of *our* bubble is somewhat similar to the part of the bubble that we’ve observed?

      2. If no probabilities can be assigned to how the unobserved bits of the universe are, then no probabilities can be assigned to our being destroyed by a blast of radiation from space tomorrow. But if no probabilities can be assigned to this, then no probabilities can be assigned to other predictions about what will happen to us tomorrow. And that’s pretty thorough scepticism about the future.

      September 21, 2014 — 16:24
  • Ryan Smith

    Alexander,
    Can you say more about how a necessary first cause gets us out of your skepticism? If it is a necessary truth that all ravens are black, then that certainly gives us some predictive power about raven color. But we don’t know the necessary truths of the universe- it could be that ‘ravens are black unless their eggs were subject to some exceedingly particular set of circumstances’ or ‘ravens can be any color they wish, and thus far they all prefer black’ or some other thing is a necessary truth. So it seems to me that there being a necessary first cause is not sufficient, it must be a very particular kind of necessary first cause that lends predictability to the universe.

    September 21, 2014 — 19:50
  • I am not claiming a first cause *automatically* gets one out of scepticism. But lack of a first cause gets one into scepticism and scepticism is false. So we have the argument:
    1. If there is no first cause, scepticism is true.
    2. Scepticism is false.
    3. So, there is a first cause.

    September 21, 2014 — 20:09
  • I’ve been thinking some more about this. Roughly speaking, the problem comes when making inductive inferences solely from a set S1 of instances to a set S2 of instances where the inference goes beyond what can be predicted from any common causal influences on items in S2 and items in S1 and any common laws of nature governing the items in S2 and the items in S1.

    For instance, suppose that somehow we know that 2000 years ago, on 20 rocks in Rome suddenly inscriptions appeared causelessly ex nihilo. We now have the rocks, and have examined 19 of them. We can make some inferences from the 19 rocks to the 20th. For instance, because of the common laws of nature governing the rocks and the common climactic influences, we should expect similar degrees of weathering on the 20th rock as on the first 19. Likewise, we should expect similar amounts of dust on them.

    But inferences that go beyond common influences and common laws are going to unreasonable. Suppose that the 19 rocks each start with the inscription of an even number. If the inscriptions on them all had causes, it would be reasonable to infer that there was some common social influence that resulted in people beginning inscriptions with an even number. But if the inscriptions are known for sure to be causeless, then the inference from the 19 inscriptions starting with an even number to the 20th doing so as well is even less reasonable than the inference from 19 coin tosses being heads to the 20th being heads as well when the tosses are known for sure to be fair and independent. Even less, because in the coin case we can have at least have confidence that the 20th is heads or tails, and assign a probability of around 1/2 to heads. In the rock case, we can’t even have any confidence that the 20th inscription has any numerals on it.

    So now we see that we have a special problem when we make inferences in the absence of an ultimate common cause. Some inferences may be OK because of later common causal influences that make the cases similar. Some inferences may be OK because of common governing laws of nature that serve to ensure similarity of cases. But beyond that one cannot go.

    A quick heuristic for which inferences don’t work when dealing with items that came into existence causelessly ex nihilo is this. If the inference would allow one to say something non-trivial, positive or negative, about the initial state of such an item, on the basis of data about other items that have no been influenced by that initial state, and going beyond what laws and metaphysics necessitate, then that inference is unjustified.

    In particular, I think there will be deadly radiation burst scenarios that are unjustified by this heuristic if the universe has no cause.

    Thus, we are not in a position to have any confidence that we won’t all be annihilated by a radiation burst tomorrow. But if so, then we are not in a position to have any confidence in any of a myriad of ordinary statements we confidently make, like that we will meet a friend for lunch tomorrow, that global warming is going to harm the human community, etc. And that’s fairly widespread scepticism about the future.

    September 22, 2014 — 9:52
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