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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.


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.
  • What is this 'error' of logical positivism that you speak of? Interesting question, by the way. – Hunan Rostomyan Oct 23 '13 at 22:00
  • @HunanRostomyan: roughly, LP was grounded in the claim that only empirical statements have meaning, but this core axiom was self refuting. From the WP entry: "Interviewed in the late 1970s, A J Ayer supposed that 'the most important' defect 'was that nearly all of it was false'." Arguably, Gödel's second incompleteness theorem presaged the downfall of LP and any other attempt to say, "Starting from here, all truth can be known." – labreuer Oct 23 '13 at 23:26
  • (1) How is it self-refuting? (2) I'm not sure what Ayer is talking about; what is the 'it' picking out? If I say that nearly all of analytic philosophy is false, will anyone understand what I'm talking about? (3) No logical positivist/empiricist I know (including Carnap, Reichenbach, Menger, Hahn, Neurath, Schlick) has claimed that "starting from here, all truth can be known". So, the third question is: which logical positivist said such a thing? – Hunan Rostomyan Oct 24 '13 at 1:57
  • @HunanRostomyan: (1) The claim that "only empirical statements have meaning" is not an empirical statement. I suggest that any more than this be taken to Q: What are/were the main criticisms of logical positivism?, or a new Q. (2) See Logical Positivism#Retrospect. (3) I did not attribute the quoted text to anyone; it was merely shorthand. Perhaps this should also be taken to the aforementioned Q? – labreuer Oct 24 '13 at 3:19
  • Labreuer that is the same argument I made for Positivism being a self defeating epistemology. – Neil Meyer Oct 25 '13 at 15:07
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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.

  • Under a 'yes' answer to my question, would Democritus have been allowed to develop his philosophy (not 'hypothesis') of Atomism? – labreuer Oct 26 '13 at 3:05
  • @labreuer - Why not? If he was insisting that everyone should believe Atomism without evidence, he should be politely ignored, but there's no reason to discourage intellectual inquiry. It's really hard to gather evidence for or against various ideas if you don't even explore the ideas. – Rex Kerr Oct 28 '13 at 19:48
  • This begs the definition of 'belief'. Democritus spend a lot of time doing things that he would not have done had he not believed in the possibility that Atomism was true. Perhaps it is the case that as long as he didn't force other people to believe in his then-unfalsifiable idea, what he did was ok? Perhaps this is the crucial difference? – labreuer Oct 28 '13 at 19:55
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    @labreuer - There is a vast difference between believing in the possibility that something is true and believing that it is true. If he needed to believe that it was true in order to work on an interesting idea, then that falls under the Pascal's Wager category: as a Bayesian you think you're probably wrong, but the expected payoff suggests that on average you're better off being wrong most of the time so that you increase the chance of a big payout if you're right. – Rex Kerr Oct 28 '13 at 19:57
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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.

  • Hmm, I wonder if a different Q on faith would be a better idea. I'd rather not muddy this one up too much with the word 'faith'. I hesitated on using the quotations, but they seemed more 'real' than anything else I could muster. How much would it damage your answer to remove the word 'faith' and replace it with other stuff? Think about it. :-) – labreuer Oct 25 '13 at 19:36
  • "Then only the things science explorers could be true." — I'm not sure this is quite correct. My question doesn't claim that only the things science can demonstrate could be true; instead, it talks about which truth-claims we can be justified in holding. There are many unfalsifiable truth-claims which we should arguably remain agnostic on. We clearly ought not go about believing whatever we want when there's no evidence, so it seems like there exists a rule for what ought not be believed. – labreuer Oct 25 '13 at 19:40
  • Until the Higgs Boson was found Scientists around the world were prepared to throw out the entire model we use to understand the universe. The key to the Scientific Method is falsifiability: There are no truths, only supported hypotheses; At any time the things we believe are true can be turned on their head, thrown out in favor of something new and (hopefully) more informative. – Jason_c_o Oct 25 '13 at 19:46
  • @Jason_c_o: (1) Are you saying that we ought only believe falsifiable claims? This threatens to deconstruct the word 'believe', but perhaps 'belief' can be defined as "premises upon which thoughts and/or actions are predicated". (2) Would you say Democritus was wrong to believe in Atomism? That philosophy seems to have turned useful, and arguably it was helpful to have it before the requisite science was done. (3) Polanyi's discussion of crystal structure makes the whole idea of 'falsifiability' fuzzy. Have you thoughts on this? – labreuer Oct 25 '13 at 20:07
  • @labreuer: (1)Aren't all claims falsifiable? Something is only true until proven false, and it is simply that some things prove resilient to falsification. (2)It was a 'belief' that was eventually falsified and replaced, but was he "wrong" to hold it? Instruments at the time did not offer the information required to falsify the position and, until they did, it was the best position to hold. Though, this is tough to argue as "Science" at the time usually meant logical reasoning without much empirical testing or evidence. (3)To be honest I'd have to read it before I fathom a response. – Jason_c_o Oct 25 '13 at 20:25

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