then one implication would be that you would be unable to construct proofs of that number's existence within the formal systems that you're thinking of.
This seems to me rather confused, because it is easy to construct a formal system with which we have precisely that experience. Consider this variant of the Peano Axioms:
Now clearly, in this formal system I cannot prove the existence of the number two, because its nonexistence is an axiom. Shall I conclude, then, that the number two doesn't exist, on this account? By what standard are we to judge between formal systems in which 2 is provable, those in which it is disprovable, and those in which it cannot be proved either way? Do we take a vote? Is it a question of appeal to human intuition?
it is easy to construct a formal system with which we have precisely that experience.
I included the qualification "the formal systems that you're thinking of". Were you thinking of that formal system when you wrote
There's a particular set of formal steps I can go through to convince myself that two numbers are twin primes, and a different set of steps which will convince me that some particular pair is the largest such pair, or that there isn't a largest pair.
?
...By what standard are we to judge between formal systems in which 2 is provab
I recognize the title could be more informative. At the same time I believe it says what is important.
I believe in a deity, I believe in mathematical entities in the same way.
The community of LessWrong (from whenceforth: LessWrong) is deeply interesting to me, appearing as a semi-organized atheist, reductionist community.
LessWrong seems very interested in promoting rationality, which I applaud. The effort does seem scattered, though, and this is the reason I post.
One has Eliezer's website with some interesting posts. The same of this community. The community links to some posts when you are coming for the first time into it, and you also have a filter for top posts. One has the blog. And recently, the center for modern rationality (in the same page as harrypoter fanfiction about rationality).
The point being there is no defined roadmap to go from AIC (average irrational chump to make an analogy to Game - which also seems to come up around quite a bit) to RA (again, rationality artist).
I write this post as to maybe generate a discussion on how the efforts could be concentrated and a new direction taken.
Should the creation of the Center for Modern Rationality envision this same concentration, this post may and should be disregard.
If it does not, then I leave it to your consideration.
Hang.