When was that exactly?

“But faced with massive data, this approach to science ? hypothesize, model, test ? is becoming obsolete.”

This terrifying sentence is becoming true in the sense that published articles often don’t include reproducible results when developed with huge data sets. And by this don’t mean that the results are dishonest. I mean the results simply cannot be reproduced by anyone with out the big data set required to develop those results. I am increasingly alarmed at how the convenient conventions and short cuts that arise in science are mistaken for the proper practice.

Thanks for the heads up. I had no idea I had any length limit set up. I’ll check into it.

I wish the rest of my comment hadn’t fallen off. Anyway, the short answer is that this doesn’t model the concept wel. Consider a sorites: is this man bald? We don’t evaluate the phrase “is he bald” to mean “balder than average”. Similarly, when we compare titanium white with ecru, we don’t make a statement about any probability. Now, if what you mean is tht “fuzzy logic” and “probability logic” are both examples of infinite-valued logics where the characteristic function has the closed interval [0,1] as the range, instead of the set {0,1}, I’d have to agree that they’re (probably, I don’t have a proof to hand) reducible one to the other. But they’re different models. (Which wraps us right around.)

Mostly I agree with you, but where I disagree is over the meaning of words again.

First, I do not hold with the frequency interpretation of probability, but the logical view. And in the view, I can see no difference at all between “fuzzy” logic and probability.

Martin Gardner has an excellent review article on the supposed differences between the two theories.

In that paper he says “Michael Arbib suggests that the cult would never have arisen if Zadeh had named his logic ’set theory with degrees of membership.’” Incidentally, I have often thought the same about the mysticism associated with “quantum mechanics”—if it had instead been called “discrete movement physics”, nobody would have ever thought it had magical powers. Nobody, for instance, would have thought of writing a book called “Discrete movement physics healing.”

Gardner also says, “he line between fuzzy logic and probabiliy logics is blurry. To assign ‘very tall’ a fuzzy value of n is the same as saying that, in a given culture, a person over six feet will be called tall with a probability of n. Is fuzzy, detractors ask, merely probability theory in disguise?” Good question.

You’re off track on fuzzy logic, though — as an old fuzzy logic guy I’ve had this argument a fair number of times — because while both probability logic and fuzzy logic can be viewed as infinite-valued logics on the [0..1] interval, the interpretation is different: in a probability logic, you interpret that characteristic function in terms of membership in some set; in fuzzy logic, you interpret the characteristic function in terms of the match between some statement of a property and the real property involved. So, for example, you might make the statement “houses on Staten Island are white” and assign it some probability p based on a population and a frequency; on the other hand, you can’t state based on that “the house at such and such an address is white” — you can only say what you’d be willing to bet.

On the other hand, in the fuzzy world, you can look at a titanium-white house with titanium-white trim and say that the value of the characteristic function “This house is white” has a value of 1, but that a titanium white house with blue trim is white with a value x

Say it aloud a few times. Stochastic. It’s like “fantastic” but inductively better.

Mmmmmm….Stochastic.

For instance, performing a Kaplan-Meier survival analysis sounds a lot sexier than calculating a conditional probability. Probably pays better too.