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I quit after the first paragraph. If you assume "proof by contradiction" to be a valid form, then you also assume that mathematics is consistent. Nothing to se
by acchow 13y ago
I quit after the first paragraph.
If you assume "proof by contradiction" to be a valid form, then you also assume that mathematics is consistent. Nothing to see here... Move along...
Edit: In case some people missed it... In our logical framework, an inconsistent theory can prove both Φ and ¬Φ. Notice that you are using our logical framework; you are assuming it to be consistent. Yes. Assuming the framework to be consistent, you can prove that the framework is consistent. Shocking.
- jeffcoat 13y agoDid you see the first line? "That mathematics is thought to be consistent justifies the use of Proof by Contradiction." So the original author agrees with you. You're right too, though: most of the value of that post is in the first paragraph, which is a very concise presentation of an interesting (apparent) paradox.
- acchow 13y agoI stopped reading after the first paragraph, so I don't know what the rest of it says. You're right, he does agree with me. But he presents it with a shroud of mystery. I was turned off by his attempt at demonstrating a paradox (a la alarming title "contra Gödel et. al.) and using word play to trick the reader into believing there is one. But there is no paradox.
- stiff 13y agoThe claimed paradox is that this proof contradicts Goedels result "if mathematics is consistent, then it cannot infer its own consistency.". This is not what the paper is about anyway, though.
- stiff 13y agoYou don't at all assume a logical framework to be consistent when "using" it, ie. considering the theorems that follow from it and its properties.