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dankane 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."
Basically, you're saying that for an elephant, apples behave like clouds, because the elephant has a concept of apple that is like our concept of cloud. (I hope real elephants aren't this dumb). I like this a lot, it clarifies what I felt was missing from the cloud analogy.
Having it explicitly stated is helpful. It leads to the insight that at bottom, outside of directly useful concepts and into pure ontology/epistemology, there are no isolated individual integers. There is only relative magnitude on a broad continuum. This makes approaching QM much simpler.
Mmmm. This is all projected onto elephants, but maybe something like what you say. I was just pointing to a possible alternate processing mode. An elephant might well recognize quantity, but probably not through counting, which requires language. Quantity might be recognized directly, by visual comparison, for example. Bigger pile/smaller pile. More attraction vs. less attraction, therefore movement toward bigger pile. Or smell.
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.