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rkr1410 comments on How to Convince Me That 2 + 2 = 3 - Less Wrong

53 Post author: Eliezer_Yudkowsky 27 September 2007 11:00PM

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Comment author: rkr1410 05 January 2011 11:14:32PM 0 points [-]

I guess when one reasons inside a fully axiomatized formal system, this something the rules for symbol manipulation depend on is the set of axioms.

Now I'm putting on my uneducated hat, so excuse me if this is heresy: Starting with the axioms you apply logic to formulate more specific rules (in this case the abstract is empirically falsifiable, since we're working on natural numbers).

So, to arrive at SS0+SS0=SSS0, you'd have to venture outside the realm of reason I'm afraid.Tthat would maybe manifest itself as magic - getting 4 apples on the table during night, but 3 during day when you put 2 and 2 apples side by side. And could mean ability to produce something from nothing by clever arrangement of apples. and waste disposal would become easy :)

In other words my opinion is it's not possible even as thought experiment unless you introduce some random factor from beyond the scope of axioms.

Comment author: Will_Sawin 06 January 2011 02:10:29AM *  3 points [-]

well there's the special other thing, the reason you can't explain Peano Arithmetic to a rock, which is that axioms are static sequences of signals, but in addition you have these dynamics.

Best source on this is Lewis Carroll http://www.ditext.com/carroll/tortoise.html

These dynamics are contained within the structure of our thoughts, which is why they're preserved in a thought experiment. But we still have to actually check our thoughts, which are part of reality.

Sorry if this wasn't very coherent.