If ... then ...

[MartinM]

OK, now I am following you. Instead of evaluating the truth value of the antecedent, you are evaluating the truth value of the conditional "if". That is, the "if" in the sentence is accurate

Precisely. I'm talking about the truth value of the compound statement as a whole, rather than the propositions contained within it. However, implication is truth-functional, so it's not possible to comment on one without dealing with the other.

While pendantically this is true, it is straying from the attempt to teach how to evaluate statements and claims

Well, ifriit did introduce the notion with the phrase Actually, to be pedantic

But really, it is precisely because of this that science operates by falsification. As ifriit says, no conclusion may be derived about the truth value of the antecedent if the consequent is true. The only time we learn something about the antecedent is if the consequent is false.

In our example, let us say that (as was done historically) special creation was known to be false by biogeography, comparative morphology, and embryology. Scientists already knew it was false because of this data (consequents). You are saying they can find another way to test special creation by going back and assuming it is true and derive another deduction

Ah, no. Not at all. They can derive any number of true conditionals containing the antecedent 'special creation is true', but only because it is false. So there's no way to get around the falsification by invoking these other conditionals.

However, I disagree that B can be ANY arbitrary statement. For the testing to be valid, B has to be a logical consequence of A.

In other words, to say "if special creation is true, then water is wet" doesn't work.

In terms of scientific method, you are correct. But in terms of logic, it works just fine. The seemingly strange behaviour of the implication connective is actually just a special case of two more general principles, which follow from the definition of validity. A valid argument is one where, if the premises are true, the conclusion must be true also. It's easy enough to show that any arbitrary conclusion may be derived from a contradiction. That leads to the first principle - an argument is valid if the conjunction of its premises is neccesarily false. From this it follows that A -> B is true if A is false. The second principle comes straight from the definition of a valid argument: an argument is valid if its conclusion is neccesarily true. From this it follows that A -> B is true if B is true.

Actually, neither of these is strictly neccesary - proving (¬A v B) -> (A -> B) is simple enough without invoking either principle. But it's an interesting way to look at it.

Of course, the validity of an argument is independent of the exact nature of the propositions. That is, (¬A v B) -> (A -> B) is true regardless of what A and B actually are. This leaves us in the somewhat counterintuitive position of having to state that 'if special creation is true, water is wet' is, in fact, a true statement. There are alternatives to this approach, such as the 'entailment' connective used in relevance logics. These logical frameworks attempt to take into account the nature of the propositions involved and the relations between them. However, the price of this is that truth-functionality is lost. The truth values of compound statements can no longer be deduced from the truth values of their propositions and the truth tables of their connectives.

 

[MartinM]

He never does

No, indeed. Some things never change

 

[Jet Black]

IF there were transitional fossils. Sense there are no transitional fossils, then evolution goes out the window.

what do you consider to be a transitional fossil?

 

[David Gould]

what do you consider to be a transitional fossil?

I think he considers that a traditional fossil must be: a non-existan intermediate fossil form between two species.

Thus, if you assert that such things exist, you have contradiction. Thus, evolution is proven wrong.

Bwa ha ha!