*An unfocused post today; just some notes on a paper. Busy day for me.*

Andrew Curtis wrote, “The science of subjectivity” in the January 2012 issue of the journal *Geology* (sent to me by our pal Willie Soon). It’s the kind of paper that shows up in journals from time to time when nothing pressing needs publishing. But since it has some philosophy of science in it that is curious, I thought we’d look at it.

[T]he scientific method comprises at least two components: forming hypotheses, and collecting data to substantiate or refute each hypothesis (Descartes’ 1637 discourse [Olscamp, 1965]). A hypothesis is a conjecture of a new theory that derives from, but by definition is unproven by, known laws, rules, or existing observations.

Part of this is true. A hypothesis is unproved given the evidence in support of it. If it were proved, i.e. we could *deduce* the hypothesis from the prior evidence, then the hypothesis would not be a hypothesis: it would be a theorem.

And part of this is false, in a sense. I mean that bit about “laws”, a ubiquitous word in science but with no fixed meaning. If a law is a deduced theorem—which is a true statement validly derived from prior knowledge which itself is known to be true—then a law is something which cannot be broken. Plenty of laws exist in mathematics, then. But most “laws” are merely theories-on-steroids: i.e., statements which are very probably true but are not deduced to be true. Most scientific “laws” are only probably true and not known to be true absolutely.

Incidentally, “practically true” is not logically equivalent to “true”; neither is “almost certainly false” logically equivalent to “false.” Just as “impossible” means “false” and “certain” means “true.”

Hypotheses are always made by one individual or by a limited group of scientists, and are therefore subjective-based on the prior experience and processes of reason employed by those individuals, rather than solely on objective external process. Such subjectivity and concomitant uncertainty lead to competing theories that are subsequently pared down as some are proved to be incompatible with new observations.

If by this Curtis means that it is humans who create hypotheses, then he is right and trivially so. And this includes those hypotheses generated from some computer program—because that program itself was created by humans. But if he means that a hypothesis cannot be objectively induced from prior evidence then he wrong: many hypotheses are created in just this way.

The use of the word “incompatible” is too loose. If a hypothesis says, “Event Q cannot happen”, which is equivalent to “It is impossible that Q can happen”, then if Q is observed the hypothesis is falsified. The observation of Q is “incompatible” with the hypothesis, which is now known to be *false*. Not *improbable*, but false. If the hypothesis merely said “Event Q is very, very unlikely (but not impossible)”, then if Q happens the hypothesis might still be true. Q is then not “incompatible” in any strict sense.

The bulk of the remainder of Curtis’s paper is given over to some management-theory-of-the-week about how scientists comes to consensus about particular geological questions. I pass over it without (additional) comment.

Curtis does put a good word in for Bayes, particularly “subjective” Bayes. Have you heard of this? It’s a branch of Bayesian theory which claims that a fixed quantification can be reached on any event’s probability. If I say, “What is the probability of Q?” a subjective Bayesian is supposed to say “Exactly 0.4566.” Or some other precise number. Even if he doesn’t know Q. Even if other evidence points in a different direction.

I think subjective Bayes is hooey. But only in theory. In practice, subjective Bayesians (as near as I can tell) do the same things as objective Bayesians, so our disagreement is only academic.

But since I’m an academic, I might as well bore you by saying that a subjective Bayesian can, if he likes, answer the question, “Given there are three balls in this opaque bag, only one of which is blue, if you pull just one out what is the chance it is blue?” with 0.8 or 0.2 or any other number he “feels” is right. I don’t know of any subjective Bayesian who, even under torture, would say anything but 1/3, but because the theory tolerates the possibility of different answers, I cannot abide it.

More on this another date.

Categories: Philosophy, Statistics

Mr. Briggs,

Based on your recent posts, I would expect you to make a fuss over the subjective/objective distinction. For example, subjective and objective are not logical opposites.

I’m looking forward to hearing more of your thoughts on subjective Bayesians.

I’m still trying to get my head around some things you said a long time ago, regarding reasonable assumptions, such as it being unnecessary to claim that coins or dice are fair.

It made me think about something else…

Suppose I throw a die, what is the chance of getting a 5?

Suppose I do get a 5, what is the chance of getting another 5 on a second throw?

What if the second throw gives an 8 – now what is the chance of getting a 5?

If the first 1000 throws are all in the range [4,9], what’s the chance of getting a 2? Can you really quantify the probability of an event occuring which you have never previously observed? Is it OK to guess zero?

I’m interested in whether you can quantify this because it feels like the kind of heurestic decision we humans need to make in order to be able to state, “this die has six sides”. It also seems very relevant for real world statistics where we observe more complicated systems. We often say our research shows that there’s a 95% chance of a result being “true”, but that’s always conditional on some other model which we never seem to bother quantifying – and you’re lucky if it’s mentioned at all.

George,

Good questions. You must remember that you can never ask, “What is the probability of Q?”, where Q might be “Getting a 5” (or any of your other events), without also adding the evidence by which you will derive your answer.

If your evidence E = “I have a six-sided object with just three sides labeled ‘5’, which will be tossed once” the probability of Q = “Getting a 5” with respect to E is 3/6. And so on for your other problems.

This answers JH’s comment, too.

No Q comes equipped with an E. The E must be supplied. In that sense, probability is subjective. But once E is in place, the probability of Q follows. That is, you and I must come to the same probability given the same E and Q.

This warrants a separate post.

Where do hypotheses come from?

Famously, Kekule’s dream, for one. Are dreams subjective or objective?