argumzio comments on two puzzles on rationality of defeat - Less Wrong

4 Post author: fsopho 12 December 2011 02:17PM

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Comment author: argumzio 14 December 2011 03:41:39AM 2 points [-]

...I don't see how you can talk about "defeat" if you're not talking about justified believing

"Defeat" would solely consist in the recognition of admitting to ~T instead of T. Not a matter of belief per se.

You agree with what I said in the first bullet or not?

No, I don't.

The problem I see here is: it seems like you are assuming that the proof of ~T shows clearly the problem (i.e. the invalid reasoning step) with the proof of T I previously reasoned. If it doesn't, all the information I have is that both T and ~T are derived apparently validly from the axioms F, P1, P2, and P3.

T cannot be derived from [P1, P2, and P3], but ~T can on account of F serving as a corrective that invalidates T. The only assumptions I've made are 1) Ms. Math is not an ivory tower authoritarian and 2) that she wouldn't be so illogical as to assert a circular argument where F would merely be a premiss, instead of being equivalent to the proper (valid) conclusion ~T.

Anyway, I suppose there's no more to be said about this, but you can ask for further clarification if you want.

Comment author: Gust 14 December 2011 04:35:54AM 1 point [-]

2) that she wouldn't be so illogical as to assert a circular argument where F would merely be a premiss, instead of being equivalent to the proper (valid) conclusion ~T.

Oh, now I see what you mean. I interpreted F as a new promiss, a new axiom, not a whole argument about the (mistaken) reasoning that proved T. For example, (wikipedia tells me that) the axiom of determinacy is inconsistent with the axiom of choice. If I had proved T in ZFC, and Ms. Math asserted the Axiom of Determinacy and proved ~T in ZFC+AD, and I didn't know beforehand that AD is inconsistent with AC, I would still need to find out what was the problem.

I still think this is more consistent with the text of the original post, but now I understand what you meant by " I was being charitable with the puzzles".

Thank you for you attention.

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