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VoiceOfRa comments on Deliberate Grad School - Less Wrong
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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?
In which you managed to misspell Turing the same way as in the previous one. ;-)
(As for the actual question, two territories can have some properties in common even if they don't spatially overlap. In the case of Andromeda there are some non-trivial such properties, i.e. the laws of physics. Mathematics is the study of the properties that all possible territories share, which all are technically tautological but not always immediately obvious to people without infinite computing power.)
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.
Instead of assuming that I didn't, you could also have assumed that I just misunderstood it.