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Eliezer_Yudkowsky comments on Logical Pinpointing - Less Wrong
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Do we need a process for figuring out which objects are likely to behave like numbers? And as good Bayesians, for figuring out how likely that is?
Er, yes? I mean it's not like we're born knowing that cars behave like integers and outlet electricity doesn't, since neither of those things existed ancestrally.
Wait, what? We may not be born knowing what cars and electricity are, but I would be surprised if we weren't born with an ability (or the capacity to develop an ability) to partition our model of a car-containing section of universe into discrete "car" objects, while not being able to do the same for "electric current" objects.
I'm pretty sure that we're born knowing cars and carlike objects behave like integers.
I think our eyes (or visual cortex) knows that certain things (up to 3 or 4 of them) behave like integers since it bothers to count them automatically.
The ancestral environment included people (who behave like integers over moderate time spans) and water (which doesn't behave like integers)..
The better question would have been "how do people identify objects which behave like integers?".
The same way we identify objects which satisfy any other predicate? We determine whether or not something is a cat by comparing it to our knowledge of what cats are like. We determine whether or not something is dangerous by comparing it to our knowledge of what dangerous things are like.
Why do you ask this question specifically of the integers? Is there something special about them?
Water does behave like very large integers.
So does electricity. (And it does so exactly, whereas water contains different isotopes of hydrogen and oxygen...)
Anyway, I seem to recall seeing a Wikipedia article about some obscure language where the word for 'water' is grammatically plural, and thinking 'who knows if they've coined a backformed singular for "water molecule", at least informally or jocularly'.
(Note also that natural languages don't seem to have fixed rules for whether nouns like "rice" or "oats" --i.e. collections of small objects you could count but you would never normally bother to-- are mass nouns or plural nouns.)
If you're going to insist that different isotopes disrupt the whole number quality of water, then fractional-charge quasiparticles would like a word with your allegation that electricity can be completely and exactly modeled using integers.
Touché.