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Eugine_Nier comments on A wild theist platonist appears, to ask about the path - Less Wrong
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Formal system A: The number 2 exists. Formal system B: The number 2 does not exist.
I cannot fathom how you can call these systems consistent. Each has a theorem whose negation is a theorem in the other. What possible meaning of 'consistency' describes this situation?
Map of America: Washington, D.C. exists. Map of Europe: Washington, D.C., doesn't exist.
Each is a consistent map of its part of the territory. I never said they describe the same part.
As far consistency, would you say PA is as likely to be inconsistent as consistent, because if you believe that PA is just a game of symbols that doesn't describe anything there seems to be no reason for it to be consistent.
Consistent with what? I believe it is consistent with itself, yes; but then again so is my toy variant with the mod-two arithmetic. If they're describing a single reality they should be consistent with each other.
Your analogy fails, because PA and the toy system both agree in describing 0 and 1 as next to each other. But PA asserts that 2 is next to 1, while the toy system explicitly denies that it is so. The map of Europe doesn't in fact make a claim about the existence of Washington; it just says that if it exists, it's outside the map. But the toy system makes an explicit claim about the number 2. It's not that it's outside the range of the system; the system aggressively asserts that it covers the place where 2 would be if it existed, and also that there ain't no number there.
Can you tell me your basis for this belief?
Answered here.