Evidential probability

“The best the logician can do is to recommend gathering more data.”
Henry E. Kyburg Jr. & Choh Man Teng, p. 200, Cambridge University Press, 2001.

[Re-posted from The Old Site, original dd. 09-01-2010. See also my ‘common sense reasoning: Do Humans Think?’ thesis linked to elsewhere on this site. This one is surprisingly transparent ;-]

A small series on forgotton (or, let’s be optimistic: not yet discovered) pearls of this human endeavour that’s called thinking. I learned Mr. Kyburg died a couple of years ago. Given that that ís a fact, one can only hope that he turns out to be an instance of the reference class of great thinkers that have ideas requiring the environment of thought of a generation coming well after their own generation.

The series has as its common theme: three B-list philosophers, on which I based my Cognitive Science dissertation (available on-line for those inspired enough to look for the link “Do Humans Think?’).

But let’s cut to the chase:

One can sensibly ask this question: how certain is it that the probability of this coin coming up tails is about one half? Not all coins are the same; and there’s evidence of people rigging coins to come up tails more often than our experience with ‘normal’ or ‘average’ coins would have us expect. In effect: it’s the basic casino fraud to devise a game where participants expect to have this probability of outcome based on ‘everyday’ events but where the probabilities of the outcome are drastically different (& skewed toward the offerer of the casino).

Maybe, why not?, we should call it a “Humean” fraud because it consists in nothing else then the exploitation of our ‘psychological’ addiction to straightforward induction – it is the commonest fraud because common sense precisely has it that what happened some way in the past will continue to happen that way in the future.

This observation has succeeded interesting me in something that I – and not only I – thought to be not particularly interesting: probability.

As long as it is the case that philosophy has not integrated probability (and more specifically: Kyburgian probability) at the center of its body of doctrine (the way it did with logic, language, & mathematics in the XXth century) it won’t be able to make the next significant and necessary step in its evolution (and, consequently, we humans will not be able to be making the next significant step in our cultural and intellectual evolution).

I’m serious. Dead serious (somewhat aided by the music that’s in my ears now to tell you the whole truth).

Because that’s still the towering truth of Hume: we kid ourselves if we believe there’s a start for us in certainty. Take the above coin which may or may not be rigged. One perfectly defensible non-probabilistic move might be to say that  a rigged coin is not really a coin. To say that rigged coins are not a subset of the set of coins poses the type of difficulties grammar-wise that one typically will want to avoid but these are in my view not insurmountable difficulties.

This move then will keep a pristinely simple probability of one half for tails on all coins and relegate the rigged coins to a class of items that needs investigation. This investigation will turn up empty, given there is no statement at all to be made about rigged coins before inspecting a specific coin. Here comes the real problem: there is no statement we can make about any of the coins presented to us prima facie because prima facie it is not possible to make a decision whether or not the coin presented is rigged or not. This is a bummer as it is clear that whatever is presented ‘as a coin’ is typically non-rigged, and therefore is commonsensically to be attributed with near-certainty the probability of one half – in coming up tails or heads.

That was a painstakingly roundabout way of coming to the following conclusion:
in a non-idealized way of seeing the world, we never have probability as such but only evidence that is more or less corroborating the association of some certain probability to the type of a certain series of events. Naming (e.g. the naming of certain items as pertaining to the class of ‘coins’) is the most basic operation; labeling items with the same label is nothing else then saying that, at the level of what is asserted of some thing, there is enough evidence that the labeled item will be as other items with that label have been known to be in the past.

Probability comes before the label and not (just or only) after it.

And in the case of labels, or names, we can appreciate why probability is mostly sent off to the outskirts of philosophy and everyday thinking. It makes verbose what is most apparent; that rigged coins are a special subset of coins; that somebody who’s bald has between zero and some hairs. Or to try out something again for which I got blasted early on in a 10-year internet career: “Logic always holds but never applies.”

In most instances our common language has shaped itself around our common way of perceiving our common reality that we can tackle it with the purest deductive logic (with all the limitations that already poses). But when we need to be certain we have to realize the uncertainty of those ways. Not because logic is uncertain (it isn’t at all, even Kyburg’s mathematical treatment of evidential probability is certain and non-empty) but because the materials on which our logic operate are terminally uncertain. There always is some measurement error and a ‘something more’ of data that needs to be gathered.

Before going all humble and wallowing in guilty feelings of original ‘fallable’-ness of the human kind, let me add this: whatever the limitations of knowledge are – and the history of philosophy is the history of the limit of our knowledge – the knowledge of our limitations is a positive asset. Kyburg’s deductions on how to proceed with our inductive reasoning are universally true and inescapable. In all situations in which we would need to use his thought we can be certain that it is sound. The fact that, after using his methods, we wind up with conclusions that are not wholly certain is not the consequence of his fallibility, of the fallibility of his or other rational thinking – but of the systemic underdeterminedness of our conclusions by our evidence.

To resubmit to the internet another of my epiphanies of old internet-days: “Nothing is true but some things are false.” The asymmetry of knowledge isn’t something that comes on top of knowledge (as, maybe, ‘rigged’ comes on top of ‘coins’) but it is an inherent vice of knowledge. I can be conclusive in saying that racism is ‘at odds’ with knowledge but I can’t say that knowledge is conclusively pro-‘this or that kind of non-racism’.

An irritating fact is that there is a tendency to associate the negative nature of knowledge and truth to mysticism (see as an example in point: Heisenberg): this is a consequence of the psychological fact that we’re driven to take our premises for granted and hence also want to grant that conclusiveness to our conclusions. Quod non.

(I’ll want to reread this once upon a time to make sure it’s more than just poetically correct.)

[I have re-read it now and I think it is not just correct but also poetically correct specifically regarding the moral maxim to “gather more evidence” whilst “being certain of the truth of that moral maxim”.]

[Whilst writing this I was listening to: “Earth” feat. Bill Frisell, “The Bee Made Honey in the Lion’s Skull” in a genre whose existence I only recently discovered: post-rock or something with as many subgenres as one might well expect for a subgenre originating in heavy metal ;-]

One response to “Evidential probability

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