"That which can be destroyed by the truth should be." -- P.C. Hodgell
Today, among logicians, Bayesian Inference seems to be the new dogma for all encompassing theory of rationality. But I have different ideas, so I'm going to present an argument suggesting an alternative form of reasoning. In essence, I going to start to try to bring down the curtain on the Bayesian dogma. This is not the end, but it *is* ‘the beginning of the end’ (as Churchill once nicely put it). I'm a fan of David Bohm, the physicist who developed the 'Pilot Wave' Interpretation of QM (which I like). So I base my argument on his ideas. The genius of David Bohm was that he showed that there’s a perfectly consistent interpretation of quantum mechanics which completely reverses the normal way that physicists think about the relationship between particles and background forces – physicists tend to think of particles as real static objects moving around in a nebulous backdrop of force fields. Bohm turned this on its head and said why not regard the *background forces* as primary and view particles as simply temporary ‘pockets of stability’ in the background forces. This idea is implied by his interpretation of quantum mechanics, where there’s a ‘pilot wave’ (the quantum potential) which is primary and particles are in effect ‘epiphenomen’ (mere aspects) of the deeper pilot wave. Now my idea as regards rationality is exactly analogous to Bohm’s idea as regards physics. In the standard theory of rationality, causal explanations (Bayesian reasoning) is primary and intuition (Analogies/ Narratives) is merely an imperfect human-invented ‘backdrop’ or scaffolding. My theory totally reverses the conevntional view. I say, why not take analogies/narratives as the primary ‘stuff’ of thought, and causal explanations (Bayes) as merely ‘crystallized’ (unusually precise) analogies? Bayesian reasoning is exactly analogous to algebra in pure math, because with Bayes you are in effect trying to find correlations between variables, where the correlations are imprecise or fuzzy. .Algebra is about *relations and functions* which in effect maps two given sets of elements (correlate them). So I suggest that algebra is simply the ‘abstract ideal’ of Bayes, where the correlations between variables are 100% precise (think of elements of sets as the ‘variables’ of statistics). Now…. Does algebra have any limitations? Yes! Algebra cannot fully reason about algebra. This is the real meaning of Godel’s theorem – he showed that any formal system (which is in effect equivalent to an algebraic system) complex enough to include both multiplication and addition, has statements that cannot be proved within that system. Since algebra is exactly analogous to Bayes, we can conclude that Bayes cannot reason about Bayes, no system of statistical inference can be used to fully reason about itself. But is there a form of math more powerful than algebra? Yes, Category/ Set Theory! Unlike algebra, Category/Set theory really *can* fully reason about itself, since Sets/categories can contain other Sets/ Categories. Greg Cantor first explored these ideas in depth with his transfinite arithmetic, and in fact it was later shown that the use of transfinite induction can in theory bypass the Godel limitations. (See Gerhard Gentzen) By analogy, there’s another form of reasoning more powerful than Bayes, the rationalist equivalent of Set/Category theory. What could it be? Well, Sets/Category theory is very analogous to categorization, a known form of inference involving grouping concepts according to their degree of similarity – this is arguably the same thing as…analogy formation! Indeed, I’ve been using analogical arguments throughout this post, showing that analogical inference is perfectly capable of reasoning about itself. My punch-line? Bayesian inference is merely a special case of analogy formation. If all this seems hard to believe at first I suggest readers go back and look at the analogy I gave with Bohm’s ideas about physics. Remember Bohm’s ‘complete reversal’ of the normal way of thinking about physics turned out to be fully consistent. All I’ve done is performed the same trick as Bohm in the field of cognitive science. Just as ‘particles’ become mere epiphenomena of a ‘pilot wave’, ‘Bayes’ becomes a mere epiphenona of analogy formation. Time for Bayesian logicians to fill their trousers? ;) --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
