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I thought it was impossible to prove a negative, generally?
by jonathonf 8y ago
I thought it was impossible to prove a negative, generally?
- gerdesj 8y agoI think you have got a bit confused here. For example Fermat's Last Theorem is effectively "a negative": "no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2"
- deleted 8y ago[deleted]
- rtkwe 8y agoThat phrase applies basically everywhere else except math. It's only possible to prove a negative in mathematics because it's a fully logical system. On a side note Fermat's Last Theorem isn't a good counterexample because it hasn't been proven yet either.
- pitaj 8y agoIt's proven: https://www.theguardian.com/science/2016/mar/15/british-mathematician-andrew-wiles-abel-prize-fermats-last-theorem-proof https://www.theguardian.com/science/2016/mar/15/british-math... https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_...
- rocqua 8y agoIf you really want to get down to it, math doesn't work either. Godel's second incompleteness theorem means we can never be sure whether any mathematical system is 'fully logical'.
- checkyoursudo 8y ago"You cannot prove a negative" basically means that you cannot prove that some claim or statement is, was, and always will be false (without perfect knowledge of the past, present, and future). That parenthetical is an important and almost always unstated axiom. The general inability to prove a false statement does not mean you cannot prove that the answer to some equation is a number below zero. I am not really aware of the phrase being used in the context of math, but rather more often with examinations or experiments that are susceptible to evidence. To be sure, "you cannot prove a negative" is itself unproven. It more a rule of thumb to remind you not to assume that though some statement is false now that it always was false and always will be false. It's not perfect, but it's also not a law of logic or anything. It's just a guideline.
- ReverseCold 8y agoIf there are n possibilities and you can prove that y are always true, then the n-y remaining are never true.
- rzzzt 8y agohttps://en.wikipedia.org/wiki/Closed-world_assumption https://en.wikipedia.org/wiki/Closed-world_assumption
- andrewaylett 8y agoCareful with that phrasing -- you need to prove that _only_ y are true.
- ebullientocelot 8y agoThis is true without perfect observation. In math you have perfect observation (sometimes), so you can do something like Fermat's Last Theorem. Once you enter the physical world, not so much.
- DoctorOetker 8y agoI don't see a hard line between math, then physics, then the 'real' world. They are levels of formalization. Both in math and in the real world we don't have 'perfect observation'. There is plenty of conjectures in math and the real world that lack a proof of something being true or false. I think "can't prove a negative" is one of the least informative ways of trying to say something, I assume he meant to say "absence of evidence is not evidence of absence" or perhaps "absence and evidence don't commute"
- andrewaylett 8y agoA classical method is to derive a contradiction from the converse.
- EGreg 8y agoPlease elaborate
- andrewaylett 8y agoBasically just https://en.wikipedia.org/wiki/Proof_by_contradiction https://en.wikipedia.org/wiki/Proof_by_contradiction