Conditional Probabilities & Bayes’ Theorem

Is a Society equivalent to the sum of its members and will the actions of the members of that society serve to fashion and to shape it, and that the social consequences of intentional actions will most often be unintentional? So, what is a Society to do to ease itself into an obvious oblivion?

Scientific Theories are predictive, however, societies’ songs prohibit most predictions…WOW!

For the Programmer:

Bayes’ Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes’ Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position.

Indeed, the Theorem’s central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology.

Bayes’ Theorem. PE(H) = [P(H)/P(E)] PH(E)

The probability of a hypothesis H conditional on a given body of data E is the ratio of the unconditional probability of the conjunction of the hypothesis with the data to the unconditional probability of the data alone.

Definition:  
The probability of H conditional on E is defined as PE(H) = P(H & E)/P(E), provided that both terms of this ratio exist and P(E) > 0

Here are some straightforward consequences…
Probability. PE is a probability function.
Logical Consequence. If E entails H, then PE(H) =

Preservation of Certainties. If P(H) = 1, then PE(H) =

Mixing. P(H) = P(E)PE(H) + P(~E)P~E(H)

So too, there are no reasons for a Society to forever Survive…Societies cannot forever last because they cannot be predicted into a certain oblivion…No Way and No How and Oh My!