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shminux comments on [SEQ RERUN] Math is Subjunctively Objective - Less Wrong
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Comments (15)
What he is really asking is "why do we think that Peano arithmetic is true?".
I've never quite grokked this, is "true" an abbrevation for "true in this universe"? Because asking if a mathematical theory is "true" otherwise is just wrong.
(ETA: Any reason for the downvotes? This is a genuine question.)
It seems to me that he's talking at least as much about the fact that S(S(0))+S(S(S(0)))=S(S(S(S(S(0))))) is a theorem of PA, and asking what it means for that to be "true".
Peano arithmetic does not have a truth value. Peano arithmetic provides the definition of 2,3,5,+,and =.
In other words, if you don't accept Peano arithmetic, then you cannot decode what I mean by 2+3=5
Depends on your definition of true:
This statement is clearly not about accepting PA, but about counting sheep.