Wednesday, December 2, 2009

Science and theism

Suppose I am a theistic scientist, and I come up with a simple and elegant theory that fits the data. You ask me:

  1. But what reason do you have to believe that the theory is true?
I am likely to answer:
  1. There is a good God who created a world exemplifying genuine values like simplicity and beauty.
Indeed, if there is a good God, it is more likely that a simple and elegant theory that fits the data is true than if there is no God at all. Whatever one thinks about induction and inference to best explanation, it seems exactly right to say that:
  1. If (2) is true, its truth significantly raises the probability that a simple and elegant theory that fits the data is true.
But now imagine two scientists, one a theist and one an atheist, and they have together come with a simple and elegant theory that fits the data. It may very well be the case that the theist should assign a probability of 0.6 to the theory—after all, there may be other simple and elegant theories that fit the data that they have failed to discover, and which fit well with the world being the sort that is created by a God who loves lawlike simplicity. But if (3) is true, the atheist scientist's credence in the theory should be significantly lower. It seems likely, then, that if the theist assigns 0.6, the atheist scientist may very well need to assign something below 0.5.

If this is right, then you will have cases where a theist and atheist scientist agree on the scientific evidence, but the theist weakly assents to the theory but the atheist is more skeptical of the scientific theory.

In general, assuming rationality on both sides, we would expect atheists to be significantly more sceptical of scientific claims than theists who, in turn, should be bolder theorizers. But I think we do not observe this. Hence, on one or both sides, there is some irrationality—or else I am wrong about (3).

10 comments:

Heath White said...

Just anecdotally/atmospherically, it seems to me that theists and atheists are about equally sensitive to the values of simplicity and elegance as marks of the truth of a theory. The point you raise is that theists have an explanation for this, while atheists do not (roughly). But this just means that theists have a more comprehensive explanatory framework, with more ontological commitments, while atheists have more loose ends but fewer ontological commitments. It's not obvious to me that either is irrational as such, although one view might have more explanatory virtues (and this might differ in individual cases).

Jonathan D. Jacobs said...

Of course it may also be that scientists feel pressure to show more confidence in their theory than they in fact have.

PFS said...

Alex,

Having read your paper, "How to reconcile evolution and creation" (which I thought was very good), I have a question that relates to this post; specifically regarding claim 3): "If (2) is true, its truth significantly raises the probability that a simple and elegant theory that fits the data is true."

In your paper, you very nicely identify a conflict between evolution as a complete theory and Divine creation as a complete theory. You propose the following weakening of evolutionary theory to avoid the conflict: "drop the neo-Darwinian’s claim that the statistical facts are explanatory of the notable features of the human species." As you point out, in evolution probabilities are (in part) assigned to "'ambitious' explanatory claims" (i.e., they are assigned to natural causes for "notable phenotypical features."). You show, I think rightly, that there is an incompatibility regarding the statistical claims in evolutionary theory and the causal reality of God bringing about (in a broad sense of agence) some phenotypical features of human beings. In the conclusion, you support the claim that given that Divine creation is true these statistical claims are not explanatory of the features, although they appear to be.

I wonder if your conclusion in the paper does not conflict with your claim in this post. Here, you say that "a simple and elegant theory that fits the data is true." This is grounded in the fact that given God's existence (and creative agency?) "it is more likely that a simple and elegant theory that fits the data is true than if there is no God at all." However, it seems true that the probabilities pertaining to evolution of notable phenotypical features of human beings fit the data and is a more elegant account for said features.

Thoughts?

BTW, I really liked your articulation of the Thomistic "way out" of the conflict. I think that there is more work that can be done with it to address the conflict, but at this point the burden is on articulating it in a coherent way.

TP said...

Alex,

I don't share the intuition that "if there is a good God, it is more likely that a simple and elegant theory that fits the data is true than if there is no God at all"

Consider this analogy. Suppose you are a very good piano player, and you are writing a song. You want the song to show off your abilities, and so you write a very complex and intricate song. But you don't want it to be so complex that no one in the world could tell its complexity from sheer randomness (for some musical examples of great complexity being almost (or not so almost) indistinguishable from sheer randomness, watch some videos of the Japanese band "Ruins" or the American band "Behold the Arctopus" on youtube). Rather, you might write the song with just enough complexity that only someone really in the know about music could tell what's going on ("oh my gosh, he just added an additional 64th note to the of every measure for 64 measures straight." Then those people in the know can explain just how awesome it is to the rest of us, and we can be wowed at your abilities. Or, even better, you might include much more complexity at higher levels, so that no matter how far the music theoriest dug in, there would always be something more complex just beneath the surface ("and...wow...there is a perfect correlation between the decibel of the low C notes and this function involving the decimal expansion of PI..."). I submit that such a song would be really amazing, and would show off your musical genius to all the world. But it wouldn't be simple.

So, why think that "if there is a good God, it is more likely that a simple and elegant theory that fits the data is true than if there is no God at all" Why isn't it possible, for all we know, that God would want to make a really complex song (so to speak)?

Tim

Alexander R Pruss said...

Heath:

Let p be the claim that simplicity and elegance are evidence of strength s for the truth of a theory. (Here s is some constant.) Let's suppose, as I think is the case, that theists and atheists roughly speaking agree in believing p. Nonetheless, there is the question of their credence in p itself.

And here there seems to be a difference, and not just a difference in explanation but in reasons for belief. The atheist and the theist both have the evidence of their intuitions in favor of p, as well as the circular, but perhaps not entirely so, evidence from the successes of science. However, the theist has an additional reason to believe p, namely that p is likely given the existence of God.

Moreover, the atheist should be more suspicious of high level philosophical intuitions, like the intuition that p is true, because these intuitions come from processes that are survival and not truth directed.

Nonetheless, I now see that my reasoning behind (3) is fallacious. For while the theist has significantly more reason to believe p than the atheist does, (3) does not follow. For suppose that the atheist assigns probability 0.95 to p, while the theist assigns probability 0.98 to p. Then, indeed, the theist has a significantly higher credence in p (2% uncertainty is less than half of 5% uncertainty). However, this does not translate to a significantly higher credence in particular theories.

My argument for (3) works iff the probability that the atheist assigns to p is smaller, say 0.7. But if both the theist and atheist assign a very high probability to p, then even if the theist's probability is significantly higher, than doesn't affect scientific practice much.

PFS:

Nice point. I'd say, however, that we don't yet know that the complete evolutionary theory fits all the relevant empirical data, or even much of it. For, as far as I know, we do not yet have sufficiently rigorous mathematical estimates of how long something like a primate brain would likely take to evolve, if only because we don't understand primate brains all that well yet so we don't know what features of them are essential and what are not, and until we have such mathematical estimates, we do not know whether a complete evolutionary explanation in fact fits the data.

TP:

Yes, there are different things God could do. So initially, given theism, we might assign equal probabilities to the first of three hypotheses, and a smaller probability to the third: (a) largely discoverable order; (b) bits of order embedded in disorder; (c) no order. Consequently, initially, the theist might assign probability 1/3 to (a). However, after seeing some of the more spectacular successes of science, she might reasonably raise that probability.

On the other hand, I think the atheist should initially assign a much smaller probability to (a) than to (b) and (c). The reason for that is that intuitively that there are so many more ways of arranging matter in accordance with (c) than with (b), and so many more ways of arranging matter in accordance with (b) than with (a). The value facts that the theist relies on, that (a) is comparable in value to (b), and that both (a) and (b) are significantly more valuable than (c), are irrelevant to the atheist.

Alexander R Pruss said...

Here's an objection to my argument to Heath:

1. All the theist's reasons for believing in God depend on p.
2. So the belief in God does not give the theist a reason to believe p.

I am not completely sure that 2 follows from 1. I suspect there is controversial epistemology there. But I also think that 1 is false. Testimony is not inference to best explanation, for instance. Still, if a lot of a theist's reasons for believing in God depend on p, then my argument for a significant difference may not work--it may only yield a small difference.

PFS said...

Alex,

Thanks for the helpful response. I have a quick follow-up: does your account ultimately rely on a God-of-the-gaps (Dawkinsism) understanding of God as creative agent and science? That what science can't presently account for leaves us room for having God fill in the cracks, at least concerning assigned probabilities in evolutionary science and the reality of God as actual causal agent for bringing about a certain notable human feature.

Douglas said...

Hi Alex,

Suppose I am a nontheist scientist, and I come up with a simple and elegant theory that fits the data. You ask me:

(1) What reason do you have to believe that the theory is true?

I answer:

(2') Natural phenomena and their laws exemplify genuine values like simplicity and beauty.

Indeed, if genuine values are exemplified by the laws of nature and natural phenomena, then it is more likely that a simple and elegant theory that fits the data is true than if nothing exemplifies any genuine values. Moreover:

(3) If (2') is true, its truth significantly raises the probability that a simple and elegant theory that fits the data is true.

Does this reasoning show that a nontheist can put as much confidence in a partly confirmed theory as a theist can do? If not, why not?

Alexander R Pruss said...

PFS:

No, I don't think so. It relies on the possibility of divine intervention, but that's all.

Another part of my argument in that paper is that we have, at this point, discovered some of the naturalistic mechanisms behind evolution: various sorts of selection (individual, group, etc.; at the genetic and at the mimetic level), and well as other mechanisms (e.g., exaptive ones). The number of phenomena to be explained, and the variety of mechanisms available, gives us significant reason to think that not all the mechanisms have yet been discovered. But if not all the mechanisms have yet been discovered, then if we're going to give a complete-but-sketchy explanation of how humans arose in terms of evolution, all we can really do is say: We evolved by means of natural selection, kin selection, ..., and other natural mechanisms. But the "and other natural mechanisms" clause is metascientific rather than scientific. One is not entitled, qua scientist, to posit "other natural mechanisms" without saying what they are, since absent scientific evidence as to what these mechanisms actually are, one has no scientific evidence that they are natural.

Douglas:

What non-circular reason does she have for believing (2'), though?

PFS said...

Alex,

Ah, I see. Would you say that your duct-tape analogy is apt here? It is unlikely that all of the mechanisms will be able to be sufficiently accounted for naturally?

I'm catching on. I suppose that you can teach an old Thomist (me) new tricks.