Talk:Classical definition of probability

message: The last sentencve of the introduction to this article claims:
“The classical definition enjoyed a revival of sorts due to the general interest in Bayesian probability, in which the classical definition is seen as a special case of the more general Bayesian definition.” [My italics]
The italicised last clause of this sentence should be removed as logically confusing. For certainly as Bayesian probability is defined in the Wikipedia article referred to here, it is not a logically special case of the Bayesian definition, but a logically independent and mutually exclusive definition, as immediately evident from placing the two definitions side by side as follows:
Classical definition: “The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible.” 
Bayesian probability is an interpretation of the probability calculus which holds that the concept of probability can be defined as the degree to which a person (or community) believes that a proposition is true.”
If there are some people who see the first definition as a special case of the second, their logical confusion should not be reproduced in this article. However, since no source is given to demonstrate anybody who accepts these definitions of classical and of Bayesian probability believes the first is a special case of the second., I propose deletion at least until such as time as evidence of such is provided and can be discussed.
It also remains to provide sourced evidence that this classical definition as defined here did indeed enjoy a revival due to general interest in Bayesian probability as defined here.--Logicus 14:39, 14 October 2007 (UTC)
replies: text: You keep showing your misunderstanding of Bayesian probability theory. These two definitions seem different because they both deemphasize their root which is Bayes theorem. The important thing to recognize about Bayesian probability is that it is not just a degree of belief, its a degree of belief that follows Bayes theorem. Hence the name: "Bayesian". The Classical definition is a specific application of Bayes theorem where prior beliefs are defined as: "nothing leads us to expect that any one of these cases should occur more than any other" . Modern Bayesian probability theory generalizes this definition by allowing different priors according to the situation. You need to look further in Laplace's book to see that he is pioneering the Bayesian methods. Throughout the book the Bayesian optimal-degree-of-belief interpretation is clearly and consistently used. I don't know if the revival of the classical definition is due to this, but when you look at the equations it is pretty clear that Laplace was using Bayesian methods. --BenE 21:58, 14 October 2007 (UTC)

text: Logicus, the definitions in an encyclopedia doesn't have to be logically derivable from one another in the way you indicate. As you point out, the historical context is more important to have in mind. This is exactly why it's so silly to call Laplace or Bayes Bayesians. However, the current Bayesian movement often claims that Laplace really used modern Bayesian methods. In this way it's a fact that Bayesians today think that Laplace really was the first Bayesian. It's a part of their self-image and a way to justify their philosophy, I guess. It's of course not true, but it's true that they believe it's true. Anyway, for this reason some (but for sure not all) of the previously abandoned reasonings of Laplace are viewed as correct by Bayesians today. In this way Laplace's general philosophical outlook suddenly has gotten modern adherents. iNic 23:36, 17 October 2007 (UTC)

text: However, this article is far from complete. I will add a section about the paradoxes the classical definition led to as well as a short account of the major critics of the classical definition, Venn and Boole, and how they transformed the subject to become a more scientific discipline. When that is added it will be easier (I hope) to follow the history of ideas leading to frequentism and eventually Bayesianism. iNic 23:36, 17 October 2007 (UTC)

text: For sure, the Bayesian definitions (all of them) of probability differ completely from the classical definition of probability. To explain the link between the two that some Bayesians see would require some space in a section of its own. I agree with you here. However, there are other themes that are FAR more important to add to the article than to try to explain the erroneous reasonings of some contemporary Bayesians. You mention some of those things below. iNic (talk)
Logicus to iNic: Note the classical definition is notoriously essentially circular, defining probability in terms of (equal) probability. Something needs to be said about this fatal defect, breaching the classic Aristotelian requirement of adequate definition. And where are the problems of principle of indifference ? Forthcoming ? --Logicus 14:51, 20 October 2007 (UTC)
thread_title: Classical probability not a special case of Bayesian probability

message: I reverted an edit which removed the notion of equal likelihood from the Laplacian definition.  Certainly, some sources omit that presumption, but here is Laplace:  So the present text does not quote Laplace accurately, but omitting the precondition of equal uncertainty would quote him out of context. —SlamDiego←T 01:36, 9 March 2009 (UTC)
thread_title:  Misquotation and misrepresentation