Rationality Quotes March 2012

Thomas

Here's the new thread for posting quotes, with the usual rules:

Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself
Do not quote comments/posts on LW/OB
No more than 5 quotes per person per monthly thread, please.

Here's the new thread for posting quotes, with the usual rules:

Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself
Do not quote comments/posts on LW/OB
No more than 5 quotes per person per monthly thread, please.

I'm not sure that's how it was motivated historically. Note that Euclid's proof (Edit: not Euler) doesn't require measuring anything at all.

To use a different example, how would one go about measuring whether there are more real numbers than integers? The proof is pretty easier, but it doesn't require any empirical facts as far as I can tell.

To use a different example, how would one go about measuring whether there are more real numbers than integers? The proof is pretty easier, but it doesn't require any empirical facts as far as I can tell.

There are all kinds of quantitative ways in which there are more real numbers than integers. On the other hand a tiny minority of us regard Cantor's argument (that I think you're alluding to) as misleading and maybe false.

0Vaniver14y

I think you mean Euclid's proof, and he was working centuries after Pythagoras, who was himself working over a thousand years after the Babylonians, who discovered Pythogorean Triples (the ones you notice by measuring). To restate, I'm fine with saying that a proof for the Pythogorean Theorem exists that does not require measuring physical triangles, but I'm not comfortable with the statement that it cannot be proved by measuring physical triangles, which is what your original comment implied to me. As discussed in the other subthread, I think that Deutsch's intention was to argue that any instance of a proof, as an object, has to exist in reality somewhere, which is a very different claim.

5

Rationality Quotes March 2012

5

5

5

Rationality Quotes March 2012

5

5