With Mermin, I also hold this truth to be self-evident (though it took me some time to get there), that probabilities are intrinsically subjective. ...I agree with this, but do not deny the importance of probability.Mermin invokes the celebrated probabilist Bruno de Finetti, who wrote: “The abandonment of superstitious beliefs about the existence of Phlogiston, the cosmic ether, absolute space and time. . . , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our actual probabilistic beliefs.”
Taking the mind-independent existence of the external world for granted, de Finetti holds that there is no place for probability in such a world, any- more than there is for Phlogiston and the rest.
All scientific theories are inherently probabilistic. Even classical celestial mechanics, the textbook example of the clockwork deterministic universe, was always probabilistic in practice. Observations in the sky always had errors, and predictions had uncertainty. Linear regression was invented to make probabilistic predictions about celestial orbits.
Probability is a mathematical means to quantify an observed *regularity*, as in contrast to an observed *causality*.
ReplyDeleteProbability is a concept of method which is used in order to quantify the relative frequencies of every possible outcome, in the limit that the number of events approaches infinitely many.
As such, the concept arises when
(a) enough phenomenological evidence has been gathered that all kinds of outcomes which are at all objectively possible (within the current phenomenological context) have been well isolated and listed (i.e., the classes of outcomes have been objectively identified), together with an objective identification of the quantities to be measured in the [statistical] "experiments",
BUT
(b) a fully satisfactory theory has not yet been developed, primarily because cause-and-effect relationships among the so defined variables have not yet been identified,
and yet,
(c) enough observational evidence has been gathered that it is possible to attach theoretical notions such as quantities defined via limiting processes to the experimentally gathered data.
This is the primary context, motivation, scope, and the most basic use-case regarding this term.
Then, the same concept can also be put to the use even when the causal law is known but the system is too complex, and so, there is a case to attach the above-mentioned limiting processes and thereby define probabilities for different outcomes. For example, pseudo-random number generators, or any other example of a sufficiently complex system involving the deterministic chaos.
Pray, where do you find the subjective in any part of this all? or the intrinsic? And if people fail to provide to show either, why should I buy the double whammy viz. the intrinsically subjective?
Au contraire, it is the objective which rules each and every part of it. Go ahead, check it for yourself!
Best,
--Ajit
[PS: This is an *informal* take, written on the side while chatting with visitors who dropped by. ... And come to think of it, people write all those *journal* papers which evade so basic considerations as those casually mentioned above! Viz., that the objective rules! Retards...]