Vorkosigan

I do not see how materialism throws into doubt one's ability to confirm truth. Can you elaborate?

Michael

Francois Tremblay

Actually, if I did not accept logic, you could not say anything to me, since I couldn't interpret your words the same way than you do. In fact, I couldn't do much of anything at all. Since we seem to communicate just fine, it must be the case that I accept the laws of logic (^_^)


That question, I suppose, was supposed to reflect the principle of validation, therefore it is probably a straw man. No one is asking you to "accept rationality before you accept it", but rather to base all reasoning on proper axioms and to validate any subsequent proposition or concept.


But that presumes acceptance of logic, and therefore the axiom of identity. Therefore your system falls flat on its face because of circularity.

[ February 04, 2002: Message edited by: Franc28 ]</p>

NialScorva

Though I'm not sure I agree with your premise that logic is required for communication, that's not really important at the moment (just registering an objection if I need it in the future). However, am I to interpret this as you saying that you accept logic because you find it useful? That's not really a logical reason, you know. Utility does not imply truth, afterall religion does have quite a bit of utility in primitive cultures.

Actually, it was refering to my position that metaphysical positions (rationality included) are founded upon non-rational decisions. The choice of rationality is inherently irrational.

Sort of, kind of, but not really. It only falls flat on it's face if you presume that rationality is required in axiomatic choice, which is what I'm arguing against. I irrationally choose which axioms I wish to accept, but from within those axioms, I can rationally prove things. When I find that my axioms produce P and ~P, then I make the similarly irrational choice that I don't like this system, and I want to change it so that it's consistent. I am not producing a system, rather I'm systematically showing that it must be non-systematic to preserve infinite regress.

Consider the advent of relativity. Newtonian mechanics produced inconsistency with empirical observations, but were internally inconsistent and useful. What reason was there to replace it?

Draygomb

Valid methods can't invalidate themselves. Therefore, Unlike circular reasoning a valid method should validate its self. But that can't be the only criteria. A method should also validate all of the other methods that are valid, or at least not invalidate them.

NialScorva

Ideal, but undoable except in trivial instances. No computational system strong enough to represent itself can prove it's own consistency. First order logic can be proven consistent, but no second order formal system can be, according to Godel's 2nd Incompleteness Theorem.

Draygomb

So that's a definate Yes for for methods being able to invalidate themselves.

And a we'll never know for sure because you have to assume a method is true before you can use it to validate its self.

Basically the question is, how do you construct a non-method for determining valid methods.

Francois Tremblay

I do not accept usefulness as a standard of validity. On the other hand, axiomicity can be confused for utility, since indeed not being able to discuss meaningfully could be said to be useful.


I am not sure where you got that idea, but since I do not believe this, I guess our disagreement wasn't really a disagreement (^_^)

[ February 05, 2002: Message edited by: Franc28 ]</p>

NialScorva

Hrm, rereading your original comment, I completely misunderstood your position. I'm not sure what I was thinking in my first response to you. Many apologies for that, most of my argument has been out of line due to that misunderstanding.

However, I still strongly disagree with you on whether metaphysical systems can be validated rationally. Rationality is at least a component of a metaphysical system, and is thus arbitrary. Without access to a transcendental validation of knowledge, all we have is internal validation techniques. A validation schema is nothing more than a priveledged metaphysical position for proving "validity", and the choice of such validation system is just as arbitrary as the system that you're validating. You say that a metaphysical system must "obey the laws of logic" aka "be rational", but that is not an inherently priviledged position, however pragmatic it is.

Francois Tremblay

I'm not sure if we are using the same terms, because it seems obvious to me that rationality is not a metaphysical issue. Maybe you could expand on that.

CardinalMan

What do you mean when you say that First-order logic can be proven consistent? Under what set of axioms in what first-order language are you referring to? If you axiomatize set theory in first-order logic in the usual way using the Zermelo-Frankel axioms, then by Godel's Second Incompleteness Theorem, this system can not prove its own consistency (assuming, of course, that it is consistent).

I always wonder what people think when a mathematician talks about a proof that some mathematical system is consistent. Where, in everyone's mind, does this proof take place? Is it a mathematical proof? If so, does it simply follow from the axioms of set theory? And if you answer yes to this, then why should we trust it, since we know that set theory can not prove its own consistency? Is it a nonmathematical proof? If so, then why should we trust it all?

CardinalMan