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Does this mean that proofs by contradiction equivocate when they reason about things like rational number with square 2?
– Conifold
Commented Feb 9, 2017 at 2:01
I'm not seeing the connection between proof by contradiction and equivocation. Maybe you could spell it our more?
– virmaior
Commented Feb 9, 2017 at 2:37
If inconsistent definition is guilty of equivocation then "rational number with square 2" is guilty of equivocation. This seems to mean that Euclid's proof of irrationality of the square root of 2 equivocates when it defines such a number and then derives a contradiction by reasoning about it. If the equivocation is in using rationality in some parts of the proof and square 2 in others (although, frankly, they mix in this case) then any conjunctive definition can be said to equivocate.
– Conifold
Commented Feb 9, 2017 at 2:52
I don't think that's an accurate description of what's happening there. Or may be to add something, an equivocation is when you accomplish your conclusion by changing the definition of the term. The proof of the existence of irraitonal numbers does not depend on that.
– virmaior
Commented Feb 9, 2017 at 3:30
We may disagree on that, but why does it matter if it is an accurate description of what Euclid does, or whether the proof depends on it? The point is that it can be (and often is) described in this manner, along with many other contradiction proofs. Where then is the definition of the term changed? It seems the same (inconsistent) conjunction is used throughout.
– Conifold
Commented Feb 9, 2017 at 3:59

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