Stuart_Armstrong comments on The Last Number - Less Wrong

4 Post author: Stuart_Armstrong 10 April 2010 12:09PM

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Comment author: Stuart_Armstrong 10 April 2010 11:13:40PM 0 points [-]

Can that statement be proved if arithmetic is inconsistent?

Comment author: [deleted] 11 April 2010 04:49:38AM 0 points [-]

From an inconsistent system (such as ZFC would be if arithmetic were), yes. An inconsistent system has no models.

Comment author: Stuart_Armstrong 11 April 2010 07:46:23AM 0 points [-]

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.