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Stuart_Armstrong comments on The Last Number - Less Wrong
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Comments (57)
What about the statement of the type: "the reals are a model of peano arithmetic"?
Nice pun.
Pun? Where?
"Arbitrary real-world statements", "the reals are a model of peano arithmetic".
What about it?
Can that statement be proved if arithmetic is inconsistent?
From an inconsistent system (such as ZFC would be if arithmetic were), yes. An inconsistent system has no models.
That would imply that 4.2 is an object of Peano arithmetic; but there is a simpler way of getting this.
The first-order statement: "there exists an x, such that x times 10 is 42" can be phrased in artithmetic. Therefore if arithmetic is inconsistent, it is true. And I define 4.2 to be a shorthand for this x.