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> my understanding is if you deduce something true from an assumption it means nothing. Your understanding is not complete. If you start from a set of assumpt
by bregma 7y ago
> my understanding is if you deduce something true from an assumption it means nothing.
Your understanding is not complete.
If you start from a set of assumptions and perform a series of logical deductions to reach a conclusion, you have proven that given the assumptions are true, the conclusion is true. You have a proof of correctness under the assumptions.
If you can go on to demonstrate your conclusion is false (say, with a single counterexample) then it will prove that at least one of your original assumptions is false. You now have some provably reliable knowledge .
- thaumasiotes 7y ago>> my understanding is if you deduce something true from an assumption it means nothing. > Your understanding is not complete. > If you start from a set of assumptions and perform a series of logical deductions to reach a conclusion, you have proven that given the assumptions are true, the conclusion is true. You have a proof of correctness under the assumptions. 04091948 is completely correct here. If you assume P and prove Q, then you've proven that P implies Q. If you assume P and prove True, then you've proven that P implies True. This is the same thing as proving nothing, since everything implies True.
- deleted 7y ago[deleted]
- QuesnayJr 7y agoIt's the article that has it backwards. You can deduce true from any premise. In terms of the Curry-Howard isomorphism, I can write a program from any input to the one-element type by throwing away the input and returning the one element. I think the previous comment was alluding to "resolution", where you prove a statement true by assuming it is false, and then deriving a contradiction. That only works in classical logic, though.