Quote:
Originally Posted by smrk
Consider
(a) Determinism is true and P proved the Pythagorean theorem
(b) Libertarnianism is true and P proved the Pythagorean theorem
If (a), do you maintain that P didn't really prove the theorem or that P cannot say that the proof is certainly true (and that its truth does not depend on P being incidentally determined to believe that it's true)? If you do, then you think determinism is not only incompatible with freedom, but with truth and knowledge. That's a different far harder argument to make.
edit: how would libertarian freedom (b) provide the means to certain understanding that a mathematical proof is correct or incorrect?
First, I don't really see how this analogy plays into any of the previous descriptions. But anyway...
Under (a), it's simply a matter of drawing up arbitrary boundaries. I think it makes just as much sense to say P proved the theorem as it is to say that P's parents proved the theorem, which implies that it makes as much sense to say that the big bang proved the theorem.
Furthermore, the question of "certainly true" is a bizarre one because the entire question of meaning seems nebulous to me. Consider the Conway life simulation. The system is completely deterministic. It would be fair to say that there are "complex patterns" that result from the program. It's not at all clear that it makes sense to assign meaning to those complex patterns. Even if it turned out that you could find an initial condition such that the cells spell out the words "I HAVE FREE WILL" over the course of time, it's not sensible to think that that message actually has meaning within the context of the program. In the same way, I'm not sure if it makes sense to say that anything that I type is particularly meaningful if determinism is true.
Under (b), the question of meaning has more content. It's not just a meaningless mess of symbols that we respond in a specific way because we had no choice but to respond in that way, but somewhere along the line, we have the ability to respond based on the actual content of the symbols. Indeed, the whole creation of the symbols can be seen as a willful act to create a system that communicates meanings effectively. Things like logic can be viewed as a true evaluation process in which people decide the value of a system of statements.