# Logical Proof, Scientific Proof, Religious “Proof”

With yesterday’s article on “Faith” (vs Science) in the Guardian, and today’s London debate between bioligist Lewis Wolpert and the pseudorational William Lane Craig (previewed on the BBC’s Today show this morning), the UK seems to be the hotbed of tension between science and religion. I’ll leave it to the experts for a fuller exposition, but I was particularly intrigued (read: disgusted) by Craig’s claims that so little of science has been “proved”, and hence it was OK to believe in other unproven things like, say, a Christian God (alhough I prefer the Flying Spaghetti Monster).

The question is: what constitutes “proof”?

Craig claimed that such seemingly self-evident facts such as the existence of the past, or even the existence of other minds, were essentially unproven and unprovable. Here, Craig is referring to proofs of logic and mathematics, those truths which follow necessarily from the very structure of geometry and math. The problem with this standard of proof is that it applies to not a single interesting statement about the external world. All you can see with this sort of proof are statements like 1+1=2, or that Fermat’s Theorem and the Poincaré Conjecture are true, or that the sum of the angles of a triangle on a plane are 180 degrees. But you can’t prove in this way that Newton’s laws hold, or that we descended from the ancestor’s of today’s apes.

For these latter sorts of statements, we have to resort to scientific proof, which is a different but still rigorous standard. Scientific proofs are unavoidably contingent, based upon the data we have and the setting in which we interpret that data. What we can do over time is get better and better data, and minimize the restrictions of that theoretical setting. Hence, we can reduce Darwinian evolution to a simple algorithm: if there is a mechanism for passing along inherited characteristics, and if there are random mutations in those characteristics, and if there is some competition among offspring, then evolution will occur. Furthermore, if evolution does occur, then the archaeological record makes it exceedingly likely that present-day species have evolved in the accepted.

Similarly, given our observations of the movement of bodies on relatively small scales, it is exceedingly likely that a theory like Einstein’s General Relativity holds to describe gravity. Given observations on large scales, it is exceedingly likely that the Universe started out in a hot and dense state about 14 billion years ago, and has been expanding ever since.

The crucial words in the last couple of paragraphs are “exceedingly likely” — scientific proofs aren’t about absolute truth, but probability. Moreover, they are about what is known as “conditional probability” — how likely something is to be true given other pieces of knowledge. As we accumulate more and more knowledge, plausible scientific theories become more and more probable. (Regular readers will note that almost everything eventually comes back to Bayesian Statistics.)

Hence, we can be pretty sure that the Big Bang happened, that Evolution is responsible for the species present on the earth today, and that, indeed, other minds exist and that the cosmos wasn’t created in media res sometime yesterday.

This pretty high standard of proof must be contrasted with religious statements about the world which, if anything, get less likely as more and more contradictory data comes in. Of course, since the probabilities are conditional, believers are allowed to make everything contingent not upon observed data, but on their favorite religious story: the probability of evolution given the truth of the New Testament may be pretty small, but that’s a lot to, uh, take on faith, especially given all of its internal contradictions. (The smarter and/or more creative theologians just keep making the religious texts more and more metaphorical but I assume they want to draw the line somewhere before they just become wonderfully-written books).

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## 3 responses to “Logical Proof, Scientific Proof, Religious “Proof””

As we accumulate more and more knowledge, plausible scientific theories become more and more probable.

This is an interesting post, since it seems to contradict itself.
While I agree that we can put measurable probabilities on hypotheses, I’m less certain how to do that on complex theories like evolution (not the rather simple darwinian one, but the modern theory), so I tend to think of such claims as “just so stories”. (Of course we can use bayesian methods to find the best theory in simple cases, like cladistics or cosmology, they seem to be excellent for that!)
Now, if we can use conditional probabilities, we should be able to say that natural theories explaining observed data increases the conditional probability that the universe is completely natural. That would be a “religious proof” of atheism, ultimately based entirely on data.
I wouldn’t be happier than if this would be an acceptable procedure. But perhaps this instead points to the problem of making a single demarcation criteria tells us what is a good theory, including criteria based on bayesian statistics.

2. From my understanding of the radio interview (from the Today Programme website), it seems that Craig was talking about scientific evidence all along. He said, “There are many of our most basic beliefs for which we have no scientific evidence. For example, the reality of the past, the existence of the external world, the presence of other minds – all of these are what philosophers call ‘properly basic beliefs’ – they are rational beliefs to hold, but there is no way you could prove that the world was not created, say, five minutes ago with built-in memory traces and food in our stomachs…” And later: “I’m saying there’s no way that you could prove scientifically that the past is real…”
His point is that the statement that the world was not created five minutes ago is not a scientific claim. (It certainly isn’t falsifiable.) But we still believe the claim to be true.
However, all this is a bit of a distraction from Craig’s point, which is not only (1) that scientific evidence is not necessary to justify a belief, but also (2) that there is abundant evidence for the claim that God exists.
I have to say that Wolpert didn’t take the debate seriously last night, and presumably chose not to dignify the occasion by engaging with Craig’s arguments in any depth. A shame really – I was hoping to hear some powerful counter-arguments to Craig.

3. Crikey, every third blog these days seems to be about Science Versus Religion. My head is spinning. Bring back Oolon Kaloofid.
If you try to engage at a philosophical level you are on a hiding to nothing. Better to put on your Zen Master’s smile and state the obvious – that science kinda seems to work.