Ought we only form beliefs based on sufficient empirical evidence?

Question

In The Outsider Test for Faith, John Loftus often makes statements like:

Faith, as I argue, is an irrational leap over the probabilities. Probabilities about such a matter are all that matter. We should think exclusively in terms of them. (19)

If God created us as reasonable people, then the correct religious faith should have sufficient evidence for it, since that’s what reasonable people require. (22)

Because science is the only game in town. It works. It produces the goods. There isn’t a better alternative. (119)

Loftus' attitude seems representative among many atheists; while I'm aware that there are other views, it is this kind of view which leads to the title of this question: Ought we only form beliefs based on sufficient empirical evidence? Here are some sub-questions which may help guide answers:

1. How can we get an ought from an is, given that evidence only describes what is? Reformulating the title as a hypothetical imperative doesn't seem to help, because the scientific method doesn't seem to ever make a hypothetical imperative binding. And yet, surely those who would agree with the quoted text would find certain hypothetical imperatives binding?

2. Given that the scientific method includes "basic arithmetical truths and also certain truths about formal provability", Gödel's second incompleteness theorem seems to apply: a given axiomatic formulation of the scientific method will be unable to imply certain (virtually all, it turns out) truths. To say that science is complete—there are no other methods of knowing things—seems to imply that science is inconsistent. Is this 'seems' an illusion?

3. Does the scientific method require that we make observations prior to forming hypotheses? It could be argued that probabilistically, trying to come up with hypotheses before making a 'sufficient' number of observations will result in a failed hypothesis too much of the time. Is there evidence to support this which can probabilistically rule out all other kinds of hypothesis-forming?

4. Must we accept any unfalsifiable claims? The answer seems to be 'yes', given e.g. the example of crystal structure discussed by Michael Polanyi in Personal Knowledge (43-48, 1984 paperback). A set of geometries seemed to well-describe many crystals found in nature, and even if some crystals aren't well-described, that doesn't falsify the instances in which it does. This opens up the question of which unfalsifiable claims we ought to accept.

5. If we model human reasoning as Bayesain inference, we can ask what is meant by 'sufficient' by what the 'probabilities' are, prior to any observations: what universal prior ought we start with? I am tempted to say "the most effective one", but that presupposes a purpose; are we given an objective purpose?

I am left with the suspicion that one ought to only follow the scientific method to the extent that one only wants to predict one's future observations—this smells like a tautology. It seems to beg the question to say that the most important area of 'truth' is objective reality, a question which cannot be answered with the scientific method. A 'yes' answer to the main question would seem to fall prey to something like the error of Logical Positivism.

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I was tempted to phrase my question as:

Is science the only source of truth?

I believe this is a bad question, for a few reasons:

1. We care about whether a method can reliably arrive at truth/knowledge.
2. The terms 'truth' and 'knowledge' would possibly stir a debate about scientific realism vs. instrumentalism, which may not be a prerequisite for the answer to my question.
3. My question makes explicit that we are talking about what one ought to do, which is not explicit in the above formulation.

Answer 1

As you've noted, there's an open question about ought. In the absence of any really compelling unconditional oughts, you're left with conditional ones of the form you ought to do X in order for Y to obtain.

So let's turn it around: if you only form beliefs on the basis of sufficient evidence, what will the consequences be? Both at a quasi-theoretical level and at an empirical level, you will be a lot better at accurately predicting future events in the physical world. So now we ask:

(a) Is there any reason to be better at accurately predicting future events in the physical world?

(b) Is there any reason to not care about accuracy of predicting future events in the physical world?

(c) Is there any better way to accurately predict future events in the physical world?

First, on (c), the answer is unambiguously yes: you are much better off not discretizing things into belief and non-belief but allowing degrees of belief. I won't go into the mathematics of why this is true, but it falls right out of Bayesian reasoning (and allows you to adopt Sherlock Holmes' advice: "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"). So let's re-evaluate (a) and (b) with the perspective that we should be Bayesian reasoners or something equivalent.

Now, on (b) there is a difficult issue to tackle of the Pascal's Wager variety when adjudicating between belief and action. Suppose that you have a lottery where to play you pay $10, and you have 4/5 chance of not winning and a 1/5 chance of winning $100. Your expected payout is $10, so assuming you like money on a linear scale (i.e. $100 is 10x better than $10), you should play. However, as a Bayesian, you shouldn't believe that you will win; you will believe that you will probably lose (p = 0.8) but might win (p = 0.2). Now you can imagine improbable scenarios that are wildly favorable, such as that God exists and will make everything super-awesome for you personally as long as you believe in him. As with many self-referential statements, this immediately puts you in a bind: as a Bayesian, you can't believe (p ~= 1), but the weighted benefits make it look like you should. I'm not sure if there are cases where you should actually make this wager. Just as you can be wrong with the probability calculation, you can also be wrong with the calculation of how good something might be. But in theory, this would be a time to not believe what the evidence says.

Regarding (a), do you want to have enough to eat? Not get murdered? Have a working iPad? Okay. Predictions are valuable.

Answer 2

Really if you want to talk about faith being irrational you could at the very least try and respond your arguments to faith in the manner in which a religious person would hold it. If you want to talk about what faith is in a religious sense then it is really very simple.

You can believe things as they are demonstrated to you or some things which for various reason can not be demonstrated to you, you can accept some outside authorities account of the matter.

So unfortunately it cannot be demonstrated to me that the Nazi's invaded Poland in 1939 but I can still read the accounts of the witnesses and put my faith in them. If the accounts are credible (To me they are) then having faith in them is really not all that unreasonable or irrational.

Ought we only form beliefs based on sufficient empirical evidence?

That is a wholly unreasonable epistemology. Then only the things science explorers could be true.

Does the scientific method require that we make observations prior to forming hypotheses?

Well the touting of multiverses among scientist proves that you actually do not need any observations to make a scientific theory as long as the theory tries to invalidate religion.