A test case for explanationism

Here is a test case for explanationist stories about initial priors, on which a more explanatory theory has a higher initial prior. Consider these hypotheses:

1. The universe is not created or governed by reason, has a finite lifetime, and has low initial entropy.

2. The universe is not created or governed by reason, has a finite lifetime, and has low final entropy.

Causation goes from past to future, so absent some kind of foresight involved in the initial conditions, initial conditions are more explanatory than final conditions. Now, presumably there is a nice one-to-one correspondence between worlds where (1) and (2) hold, so absent an explanationist bias in the priors, we shouldn’t have a preference between (1) and (2).

This is just a test case, but I have to confess I don’t have any direct intuition comparing the probabilities of (1) and (2). I like explanationism, so I have a theory-laden reason to assign a higher probability to (1) than to (2).

Samuel Clarke on our ignorance of the essence of God

At times I am made uncomfortable by this objection to arguments for the existence of God: there feels like there is something fishy about inferring the existence of a being about which we know so very little. It may be that theism is the only reasonable explanation of the universe’s existence, but if we know so very little about that explanation, can the inference to the truth of that explanation be a genuine version of inference to best explanation?

Newton's disciple Samuel Clarke has a nice answer to this objection:

There is not so mean and contemptible a plant or animal, that does not confound the most enlarged understanding upon earth; nay, even the simplest and plainest of all inanimate beings have their essence or substance hidden from us in the deepest and most impenetrable obscurity.

In other words, all our ordinary day-to-day inferences are to things whose essence is hidden.

It may be thought that now that we know about DNA, we do know the essences of plants and animals. But even if that is true, which I am sceptical of, it doesn’t matter: for belief in plants and animals was quite reasonable even before our superior science. And even this day, our knowledge of the essences of the fundamental entities of physics (e.g., particles, fields, wavefunctions) is basically nil. All we know is some facts about the effects of these entities.

Explanation and understanding

In the 1960s, it dawned on philosophers of science that:

1. Other things being equal, low-probability explanation confers equally good understanding as high-probability explanation.

If I have a quantum coin that has a probability 0.4 of heads and 0.6 of tails, and it yields heads, I understand why it yielded heads no less well than I would have had it yielded tails—the number is simply different.

On the other hand, the following thesis (which for years I’ve conceded to opponents to low-probability explanations):

2. Other things being equal, low-probability explanations are less good than high-probability ones.

Finally, add this plausible comparative thesis:

3. What makes an explanation good is how much understanding it confers (or at least would confer were it true)

which plausibly fits with the maxim that I’ve often been happy to concede that the job of an explanation is to provide understanding.

But (1)–(3) cannot all be true. Something must go. If (2) goes, then Inference to Best Explanation goes as well (I learned this from Yunus Prasetya’s very recent work on IBE and scientific explanation). I don’t want that (unlike Prasetya). And (1) seems right to me, and it also seems important to defending the Principle of Sufficient Reason in stochastic contexts.

Reluctantly, I conclude that (3) needs to go. And this means that I’ve overestimated the connection between explanation and understanding.

Best explanation and sexual ethics

Consider three ethical claims about sexuality:

1. Rape is always wrong.

2. Incest is always wrong.

3. Bestiality is always wrong.

Take these claims in the strong sense: they hold genuinely always, no matter what the circumstances. Rape is wrong even if the victim is in a coma, is unharmed physically, permission is given by a proxy, and nobody (including the victim) ever finds out. Incest is wrong even between consenting adult relatives raised apart, with no chance of conception. Bestiality is wrong no matter whether the animal is aware of the event, and no matter how low on the evolutionary scale the animal falls or how much the animal wants the act. All these things are wrong even if much rides on them: they are wrong even to save multiple lives, including the life of the victim in case (1).

Now, although it is easy to find ethical views of sexuality that explain why rape, incest and bestiality are almost always wrong, it is hard to find coherent and well-developed views that explain why these are always wrong. But such views do exist. I know of two families of them: there are traditional natural law views and there are views like those of Karol Wojtyla which meld natural law with personalism (my One Body is in this category). However, these two families of views also entail highly controversial further prohibitions on unmarried sexuality, artificial contraception and same-sex sexual activity.

This yields an indirect inference to best explanation argument for the controversial further prohibitions: the best views we have that explain (1)–(3) also entail these further prohibitions.

Of course, one can try to turn the argument around. But I think generally speaking we have better epistemic access to what is forbidden than what is permissible, and so arguing from commonly accepted prohibitions to controversial prohibitions is better than arguing from commonly accepted permissions to controversial permissions.

I am not saying that those who deny the controversial prohibitions need to deny that (1)–(3) are exceptionlessly true to be consistent. I am just saying that they probably aren't going to have a good explanation for why (1)–(3) are exceptionlessly true.

Aesthetics is epistemically central

Inference to best explanation is central to our epistemic lives. Aesthetic judgments about theories are central to inference to best explanation. Hence, aesthetic judgments are central to our epistemic lives. Thus we should be objectivists about at least a part of aesthetics.

Inference to Best Explanation, crummy explanations, and the Principle of Sufficient Reason

Suppose that we ruled out all but one possible explanations for a phenomenon. The remaining explanation H is the poorest and most contrived explanation you can imagine. But a poor and contrived explanation is still an explanation. And in this case it is the best explanation by a mile: none
other comes close, as all others have been ruled out. Thus by Inference to Best Explanation:

1. We should accept H.

But:

2. If there was any chance that there simply was no explanation, the hypothesis that there is no explanation would be preferable to H, given how poor and contrived H is.
3. So, there is no chance that there is simply is no explanation.

But this argument would work for any phenomenon. And so it pushes us to conclude that the Principle of Sufficient Reason (PSR) must be true. If all we had was a presumption of explanation rather than the guarantee that the PSR gives, then we couldn't say that there is no chance of there being no explanation, and we couldn't conclude to the really poor explanation H.

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:

2. 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:

3. 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).