Posted: Jan 25, 2012 11:46 am
proudfootz wrote:
Bayes’ Theorem has been proven formally valid. Any argument that violates a valid
form of argument is itself invalid. Therefore any argument that violates Bayes’ Theorem
is invalid. All valid historical arguments are described by Bayes’ Theorem. Therefore any
historical argument that cannot be described by a correct application of Bayes’ Theorem
is invalid. Therefore Bayes’ Theorem is a good method of testing any historical argument
for validity.

... so nerny-ner-ner-ner-ner.

A more lucid refutation of an argument was never typed. But really - have you got any rational reasons to not like what is written here?

Alright then, if you really want to go through it...

Bayes’ Theorem has been proven formally valid. Any argument that violates a valid
form of argument is itself invalid. Therefore any argument that violates Bayes’ Theorem
is invalid.

Arguments are valid. A valid argument is one in which the conclusions follow from the premises. Bayes' Theorem is not an argument or a form of argument, it's a theorem. As such it doesn't make much sense to say it's valid. I suspect that what Carrier means is that it's proven. The proof is simple, it follows from the definition of conditional probability in about 3 lines, meaning that Bayes' Theorem is in effect a tautology, like all theorems.

Bayes' Theorem is not a form of argument, but it can be used in a valid argument. It can serve as the justification for inferring one statement about probabilities from another.

All valid historical arguments are described by Bayes’ Theorem.

Two points here. Firstly, Bayes' Theorem can be used in a valid argument. It absolutely does not follow that all valid arguments use Bayes' Theorem. That's equivalent to saying that because a mop can be used to effectively clean a floor, all floor cleaning that doesn't use a mop is ineffective. Basic logical error.

Secondly, we've moved smoothly from talking about a theorem having a proof to the validity of a logical argument, to the validity of a form of logical argument, to the validity of historical arguments as if they were all one and the same. They clearly aren't the same. Bayes' Theorem is a theorem because it's a tautology based on definitions. Does Carrier really want to say that all valid historical arguments are tautologies based on definitions?

Therefore any historical argument that cannot be described by a correct application of Bayes’ Theorem
is invalid. Therefore Bayes’ Theorem is a good method of testing any historical argument
for validity.

This paragraph as a whole is a jumble of misapplied terminology and logical error, written in the tone of a petulant teenager who thinks he's scored a point. It sinks any credibility Carrier might have had.