Comment author: Amanojack 05 April 2010 09:20:48PM *  3 points [-]

Not disagreeing, but fleshing out part of what it seems you're trying to say:

Numbers don't exist, that much ought to be clear. I think Eliezer says that numbers are in our minds, and our minds exist, but this is not the case: it's not numbers that are in our minds but representations of numbers.

Mathematical Platonism is, to me, religion for intellectuals. Mathematicians as esteemed at Kurt Goedel have even gone so far as to postulate that mathematics exists in an alternate universe. This is a basic error or at least wildly unparsimonious, akin to saying that modus ponens exists in an alternate universe.

To see how silly this is, it helps to realize that a sufficiently intelligent being would find all our mathematical theorems just alternative ways of stating the axioms, and all our mathematics just axioms and definitions with a bunch of obvious rephrases of the same. It would find our most advanced theorems as simple and obvious as modus ponens is to us - as just rewordings of the axioms and definitions.

From the perspective of a sufficiently intelligent being, mathematics is just a set of initial statements (axioms and definitions), along with humans' silly little demonstrations to help each other realize that a bunch rewordings of those statements (theorems) all mean the same thing.

Comment author: Roger 06 April 2010 12:56:31AM 0 points [-]

Amanojack,

Hi. I agree with you completely and like the phrase "religion for intellectuals". I just don't see the difference in saying that numbers and mathematics exist somewhere but we can never show you where and saying that other things exist somewhere but we can't show you where. But, trying to get even very intelligent people (ie, your example of Goedel) to see this or even listen to this type of reasoning seems almost impossible. Oh, well! Thanks!
Roger
Comment author: khafra 05 April 2010 02:26:48PM 1 point [-]

Hi! You seem to be asserting anti-realism and trying to arrive at a correct ontology using an Aristotelian application of deductive logic. Would you like some help with that?

Max Tegmark, the physicist who proposed the mathematical multiverse theory, was aware of the anti-realist position. However, there's good evidence that minds are made out of math, instead of the contrary position. It's a fairly mature debate, and it pays to be aware of the strongest arguments both sides.

This awareness also applies to the universe's beginnings, or lack thereof. Historically, deductive logic has had some problems locating true beliefs.

Also, welcome to Lesswrong! Feel free to post on the introduction thread; and start working your way through the sequences so you understand where other people here are coming from.

Comment author: Roger 05 April 2010 08:57:30PM 0 points [-]

Kharfa,

Thanks for your comment. In response,

o You seem to be asserting anti-realism and trying to arrive at a correct ontology using an Aristotelian application of deductive logic. Would you like some help with that?

I'm not denying the reality of anything that you can show me. Please show me where "2+2=4" is or where it exists. Using that type of argument that things like this exist is like saying Santa Claus exists. That's possible, but we can't prove it or disprove it, and you can't show him to me. There's no point in discussing it. And, by the way, I don't need any help with that. Patronizing attitudes especially when not backed up by sound reasoning are of no interest to me.

o there's good evidence that minds are made out of math, instead of the contrary position.

I believe there's good evidence that minds are in heads and are made out of matter and energy, not mathematics.
Comment author: khafra 26 March 2010 01:51:00PM 2 points [-]

Higher-level behavior can be explicitly coded into lower level rules.

Comment author: Roger 03 April 2010 03:12:11AM 1 point [-] 
Hi. After reading your posting on the mathematical universe, my coments are:

  • The only way "2+2=4" can exist is if there are first two existent objects and then a mind to come up with the construct describing their addition. "2+2=4" doesn't exist on its own.

  • My own view for why there is "something" rather than "nothing" is:

    1. There are two choices for why there is "something" rather than "nothing":

    A. "Something" has always been here. B. "Something" hasn't always been here.

    1. Choice A is possible but doesn't offer much explanatory power so it won't be
      pursued here.

    2. Going with choice B, if "something" hasn't always been here, then "nothing" must have beeen here before it. By "nothing", I mean complete non-existence which would be the lack of all volume, matter, energy, ideas/concepts, etc. However, in "nothing", there is no mechanism to change this "nothing" into "something". So, if "something" is here now, the only possible way is if "nothing" and "something" are one and the same thing. I think this is logically required if we go with choice B.

  • If it's logically required that "nothing" and "something" are the same thing, the next step is to try and figure out how this can be since they seem different. My view on how this can be is that they only seem different because we're looking at them from two different perspectives. In thinking about "nothingness", we use our mind, which exists. Next to something that exists, "nothing" just looks like nothing. But, in true "nothing", there would be no minds there, and only then would "nothing" be completely self-defining (it says exactly what is there) and therefore existent.

    An idea that's helpful in thinking about this topic is that the mind's conception of something ("nothing" in this case) and the thing itself are different. Thanks for listening!

     Roger
Powered by Reddit Powered by Reddit