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Friday, August 18, 2000

Belief

A letter to a small mailing list I'm on:

There is this assumption floating about in many of these postings that any scientific theory is just a convenient claim or guess or leap of faith which may prove useful today but tomorrow it could be just as wrong as any other belief--mystical, religious, fantasy or otherwise. Common example is, say, that relativity "disproves" Newtonian physics.

Also there is this question of what constitutes a "simple" explanation, or what does Occam's Razor really say?

Thirdly, there's the question of n'th-hand knowledge, which we did not personally observe, and isn't that just faith?

The value, or validity, of any belief, from a scientific perspective, lies entirely in its *ability to predict observations*. Really there's no other basis nor use for truth besides that. After all, what does it matter if you "know" something which has no bearing on your future observations? It doesn't matter at all, and hence it's not really knowledge. (Note that knowledge of the past *can* have bearing on the future, even if it's just in predicting that someone else may remember the same things, but let's not digress into distinctions between instance memory and conceptual knowledge -- I'm primarily addressing the latter here.)

From there it's very easy to address all three of the above issues:

Occam's Razor is really just a rephrasing of exactly the same thing: Take any belief and break it down into the predictive portions and the non-predictive portions, and throw the latter away because they're arbitrary. E.g., "god makes the sun rise and fall every day" can easily be broken down into "the sun rises and falls every day" and "god makes that so", which Occam's Razor prunes simply to: "the sun rises and falls every day". That's useful, predictive knowledge. "god makes that so", on the other hand, doesn't help us predict anything. You could infer from it that god will also make the wind blow, but then you could infer from it that god will turn off gravity every night too! In order to make it real knowledge, you need to expand the definition of god to include other observations, at which point we once again can simply prune off the god part and just leave the observations.

Next, since we're predicting *observations*, a belief only need hold within the same scope as the observations it refers to. E.g., Newtonian physics remains perfectly true, within the domain (time and space scale) in which it was derived. To posit, prior to the discovery of relativistic observations, that Newtonian physics applies at all scales would be but a hypothesis--one to which we could assign some notable confidence via the meta-belief of inference, but which we could equally accept as false since inference is only a statistical indicator. Note that inference itself is a belief about beliefs based on observations of relationships between beliefs, which allows us to predict the probability of validity of untested beliefs.

Lastly, as Jack* pointed out we can observe the correlations between other people's (or other information sources', as of mathematics) claims and our own observations, and from this with inference place odds on the truth of beliefs we have not validated through personal direct observation. Hence, we are effectively able to predict future observations through quite an elaborate chain of inference and reasoning, such as upon hearing of a physicist in Germany who is running a certain experiment, we might infer what we will read soon in one news article or another about what he claims to have observed, based on what a physicist friend of ours here in San Diego told us the other day about the results of his own secret experiment. I.e., ultimately we are pasting together predictions about and by our own direct observations, through a chain of meta-belief derived abstraction and concretization, and it is the success of this chain that boosts or adjusts our confidence in our system of inferences and thus indirectly in our system of nth-hand beliefs.

So there. :)

-Simon

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