Rationality Quotes December 2011

Jayson_Virissimo

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Do not quote yourself.
Do not quote comments/posts on LW/OB.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Do not quote yourself.
Do not quote comments/posts on LW/OB.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.

The "controversy" about infinite sets is about their existence/usefulness as physical objects, not their mathematical existence (you'll note that I was careful to say that they were not physical objects in the grandparent). From that article:

"Infinite set atheism" is a tongue-in-cheek phrase used by Eliezer Yudkowsky to describe his doubt that infinite sets of things exist in the physical universe.

Thus, infinite sets are a perfect example of a mathematical object disconnected from physical reality/practical experience.

We can construct the natural numbers by starting with two symbols "0" and "1" that are naturals, and saying that if n is a natural, then n+1 is too i.e. adding 1 over and over again. Part of the definition is each time we add 1, we get a number we haven't seen before; and so we have an infinite set by construction. And we can make bigger ones by taking the power set (the power set always has a larger cardinality then the set it comes from).

So infinite sets are definitely mathematical objects because we can (and just have) construct them.

Watch Eliezers response to this question, http://www.youtube.com/watch?v=3dufqGC8X8c

scroll to 4:40 I like his one argument: if we have finite neurons and thus cannot construct an infinite set in our "map" what makes you think that you can make it correspond to a (hypothetical) infinity in the territory?

0roland14y

No. You have a rule that hypothetically would produce an infinite set if applied ad infinitum. This may seem like nitpicking but there is a difference between the concept of an infinite set and an actual infinite set, the latter can't be represented in a finite brain(I suppose). I can write down the rules of a turing machine, but this doesn't produce a working computer to spring to life if you get my point.

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Rationality Quotes December 2011

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Rationality Quotes December 2011

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