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Warrigal comments on Logical Pinpointing - Less Wrong
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It's almost a tautology. What we have is an iterated identification. There are two objects that are named "apple," they are identical in identification, but separate and distinct. This appears in time. I'm counting my identifications. The universality of 1+1 = 2 is a product of a single brain design. For an elephant, the same "problem" might be "food plus food equals food."
Would you argue, then, that aliens or AIs might not discover the fact that 1 + 1 = 2, or even consider it a fact at all?
Okay, I don' t have to speculate or argue. I'm an alien, and I don't consider it a "fact," unless fact is defined to include the consequences of language. I.e, as an alien, I can see your process, and, within your process, I see that "1 + 1 = 2" is generally useful to your survival. That I'll accept as a fact. However, if you believe that 1 + 1 = 2 is a "fact," such that 1 + 1 <> 2 is necessarily "false," I think you might be unnecessarily limited, harming long-term survival.
It's also useful to my survival, normally. Sometimes not. Sometimes 1 + 1 = 1, or 1 + 1 = 0, work better. I'm not kidding.
The AI worth thinking about is one which is greater than human, so that a human can recognize the limitation of fixed arithmetic indicates to me that a super-human AI would be able to do that or more.