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>Let's imagine I had shown that something was either one or two. You seem to be claiming I could not take positive proofs assuming each of them and turn it into
by ebola1717 11y ago
>Let's imagine I had shown that something was either one or two. You seem to be claiming I could not take positive proofs assuming each of them and turn it into a full proof.
When you break it down to the logical axioms, you can't use cases like that. Try it yourself. You get something like this:
Let A: (k > 0)
B: (k = 0)
k is a whole number, therefore A v B.
A -> X !=2
B -> X !=2
Okay, from here, you need to deduce X != 2. Traditionally we do this by applying proof by cases, but as I showed in my other comment, this requires the law of the excluded middle.
I don't see any other propositional logic axioms we can apply to achieve the same result.
- ikeboy 11y ago>Traditionally we do this by applying proof by cases, but as I showed in my other comment, this requires the law of the excluded middle. I think that's because you don't know A v B. But in my case you can directly prove A v B. The form is (A v B, A -> C, B -> C) -> C. https://en.wikipedia.org/wiki/Proof_by_exhaustion https://en.wikipedia.org/wiki/Proof_by_exhaustion says that this is called a direct proof.