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ChristianKl comments on Rationality Quotes March 2012 - Less Wrong
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Yes, non-empirical is the wrong word. I mean to assert that mathematics is independent of empirical fact (and therefore non-social. A sufficiently intelligent Cartesian skeptic could derive all of mathematics in solitude).
Didn't Gödel show that nobody can derive all of mathematics in solitude because you can't have a complete and consistented mathamatical framework?
Goedel showed that no one can derive all of mathematics at all, whether in solitude or in a group, because any consistent system of axioms can't lead to all the true statements from their domain.
Anyone know whether it's proven that there are guaranteed to be non-self-referential truths which can't be derived from a given axiom system? (I'm not sure whether "self-referential" can be well-defined.)
It is. At least, it's possible to express Goedel statements in the form "there exist integers that satisfy this equation".
It can't.
I don't know whether this is true or not; arguments could (and have) been made that such a skeptic could not exist in a non-empirical void. But that's a bit offtopic, as I still have a problem with your previous sentence:
Are you asserting that all things which are "dependent on empirical fact" are "social" ? In this case, you must be using the word "social" in a different way than I am.
If we lived in a culture where belief in will-powered flight was the norm, and where everyone agreed that willing yourself to fly was really awesome and practically a moral imperative... then people would still plunge to their deaths upon stepping off of skyscraper roofs.
:) It is the case that the coherence of the idea of the Cartesian skeptic is basically what we are debating.
I'm specifically asserting that things that are independent of empirical facts are non-social.
I think that things that are subject to empirical fact are actually subject to social mediation, but that isn't a consequence of my previous statement.
What does rejection of the assertion "If you think you can fly, then you can" have to do with the definition of socially mediated? I don't think post-modern thinking is committed to the anti-physical realism position, even if it probably should endorse the anti-physical models position. The ability to make accurate predictions doesn't require a model that corresponds with reality.
That might be a bit orthogonal to the discussion; I'm certainly willing to grant you the Cartesian skeptic for the duration of this thread :-)
If you are talking about pure reason, don't the conclusions depend on your axioms ? If so, the results may not be social, per se, but they're certainly arbitrary. If you pick different axioms, you get different conclusions.
To me, these two sentences sound diametrically opposed to each other. If your model does not correspond to reality, how is it different from any other arbitrary social construct (such as the color of Harry Potter's favorite scarf or whatever) ? On the other hand, if your model makes specific predictions about reality, which are found to be true time and time again (f.ex., "if you step off this ledge, you'll plummet to your splattery doom"), then how can you say that your model does not correspond to reality in any meaningful way ?