just like old times

russell poldrack just published a paper in trends in cognitive sciences on reverse inference (a.k.a "abductive reasoning") in neuroimaging work, the chain of logic for this being:

a) in the experiment, we observe that brain region x is active
b) from previous work, we know that cognitive process z engages brain region x
c) therefore, in this experiment, cognitve process z (unobservable) is being engaged

(this in contrast with the typical inductive chain:

a) cogntive process z (observable) is being engaged
b) during this time, brain region x is active
c) therefore, cognitive process z engages brain region x)

because i had to do a presentation on the paper, i called cp to check on my general understanding of inductive/abductive reasoning, only to find that he was not familiar with abductive reasoning, and that he thought the example i gave him was logically flawed (this bit came up later over profiteroles in bakerzin).

the simplified examples:

inductive:
a) this is a cow
b) it is black
c) all cows are black

abductive
a) all cows are black
b) this is black
c) it is a cow

this last argument seems, on the surface, to be quite wrong -- but only (as i pointed out) because the set of cows is only a small subset of the set of all animals -- if you started exterminating all animal life forms other than cows, the strength of the argument would increase, and approach the soundness of deduction as the difference between the set of animals and the subset of cows approached zero. nonsense! say cp and su-lin in unison, there are no infinitesimals involved here, statement (c) is either true or untrue, depending on whether or not there is at least one non-cow animal on earth.

(note: i'm still not satisfied on the point that induction (see example above) does not work in quite the same way. (c) is either true or untrue, depending on whether or not there is one non-black cow -- yet there is a scale of strength for how strong an inductive inference is anyway.)

so i counterargue that the argument doesn't hold only because cows are discrete and countable, and that if you replaced (a) with a set that has a subset that can meaningfully have an infinitesimal difference from it, then the whole house of cards may stand up. to which cp says "what about 'all jello is red'?" and su-lin points out that just because jello is wobbly doesn't mean that it's different from a cow and we crack up.

(and cp says that instead of him teaching gp we should all of us just troop into his class and sit down and converse with each other in front of his students, which i think is a splendid idea.)

(you can check out the real story of abductive reasoning here. technically, the cow thing is right; it just sounds really strange because it's not a real world causal relationship. it is not fallacious however, merely dependent on two things: how likely it is that a object is a cow given that it is black, and our prior belief that any given object is a cow. but to prove that you need bayes' theorem and math, which will make most of you break out in a rash. scroll down the wikipedia page to the "grass is wet" example for something a bit more sensible)

Currently reading:
A Skin Diary - John Fuller
And all the Pratchetts. Again and again and again.