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