leekelly

40

For anyone still following this, I have tried to restate my arguments in a new way here:

http://www.criticalrationalism.net/2011/07/20/more-on-inductive-probability/

30

Manfred,

I calculated the result for about three different sets of probabilities before making the original post. The equation was correct each time. I could have just been mistaken, of course, but even Zack (the commenter above) conceded that the equation is true.

EDIT: Oh, I see now. You have changed all my disjunctions into conjunctions. Why?

-10

Well, it wasn't actually an equation. That's why I used the =||= symbol. It was a bientailment. It asserts logical equivalence (in classical logic), and it means something slightly different than an equals symbol. The equation with the plus signs and the logical equivalence shouldn't be confused.

30

Hi,

I am the author. It wasn't a mistranslation. The logical equivalence was not translated into anything. It was merely intended to break down A according to its logical consequences shared with B. I never wrote "P(A v B) + P(A v ~B)," because that would be irrelevant.

60

DanielLC,

Hi, I am the author.

The =||= just means bientailment. It's short for,

A |= (A v B) & (A v ~B) and (A v B) & (A v ~B) |= A

Where |= means entailment or logical consequence. =||= is analogous to a biconditional.

The point is that each side of a bientailment is logically equivalent, but the breakdown allows us to see how B alters the probability of different logical consequences of A.

I linked to the previous post. That begins with something like an abstract: a statement of intent, at least.

This isn't an article or a paper: it's a blog post.