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eli_sennesh comments on Deliberate Grad School - Less Wrong
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Two correct maps of the same territory, designed to highlight the same regularities and obscure the same sources of noise, will be either completely the same or, in the noisy case, will approximate each-other.
Just because there's no Realm of Forms doesn't mean that numbers can be different for different people without losing their ability to compressively predict regularities in the environment.
What is the territory, that numbers are a map of? I can use them to assemble a map, for example, s=0.5at^2 as a map, or model, of uniformly accelerating bodies, but the components of this are more like the ink and paper used to make a map than they are like a map.
I have a bunch of maps, literal printed maps of various places, and the maps certainly exist as physical objects, alongside the places that they are maps of. They exist independently of me, and independently of whether anyone uses them as a map or as wrapping paper. Likewise, it seems to me, numbers.
If there is no Realm of Forms, what territory are you referring to?
The ordinary physical universe, presumably.
As TheAncientGeek said, the ordinary physical universe. "Abstract" objects abstract over concrete objects.
And where is the ordinary physical universe do these abstractions live?
Again: they abstract over concrete objects. You get a map that represents lots of territories at the same time by capturing their common regularities and throwing out the details that make them different.
So do you claim these abstractions actually exist?
The abstract maps exist. The abstract territory does not.
In which case we're back to the question of why numbers are the same for everyone? You said:
Except you claim there's no same territory. The aliens in the Andromeda galaxy will have the same numbers as us, as will the sentient truing machines that evolved in a cellular automata. So what common territory are they all looking at?
The physical world: see here.
(Another attempt, this time read the comment before responding.)
Where in the physical word is the common territory between us and the Andromeda aliens? And how about the sentient truing machines that evolved in a cellular automata who aren't even in the same universe as us?
How about you try reading the comment your responding to next time. It's even extremely short so you don't have much of an excuse.