No, you actually cannot prove a negative. It is definitionally impossible to do so.
To generate proof of something, you must make an assertion and then follow a repeatable procedure to arrive at your conclusion. You cannot arrive at a falsehood, due to a falsehood being definitionally impossible.
We can't prove that 4 + 4 is not equal to 9. What we can prove instead is that 4 + 4 is equal to 8, and we can also prove that the + operator cannot generate different outputs given the same inputs. We "prove the negative" by proving positive assertions that negate the negative.
The positive assertion that would have to be proven, to prove the negative statement of "Pence is not a pedophile", would be to assert that at no time in Pence's life has he fucked a child. The proof of this... well, that would be an excerpt from the memory of an omniscient being, I suppose.
Can you provide a concrete example of a proof of a negative assertion? I've heard the occasional claim that negative proofs are possible, but I've never seen/been patient enough to locate one. I work in programming and it's extremely against my experience that a negative can be proven; I'm frequently reframing tasks from negative to positive in order to find bugs (e.g. if a user asserts that "X doesn't work", the process of fixing the issue is entirely finding areas that can be proven to function correctly, until the only area that remains is the one that is broken)
The best I've arrived at is falsification as expressed in my math example above, and I think also in the extrapolation of Karl Popper's argument, if I'm interpreting that correctly. If all we have to work with is a negative, then the negative -itself- can't be proven by addressing the negative -itself-. You have to come at it from the angle of a positive assertion, like "Pence has always had a reliable witness to his behavior".
So you can "arrive at proof that a negative statement is false", but I think the common sentiment of "you can't prove a negative" is aimed at the attempt to directly prove/disprove a negative assertion itself, and isn't meant to imply that it's impossible to arrive at proof etc.
I didn't read any bitchiness from what you've said, I think you're doing a'ight :)
No, you actually cannot prove a negative. It is definitionally impossible to do so.
To generate proof of something, you must make an assertion and then follow a repeatable procedure to arrive at your conclusion. You cannot arrive at a falsehood, due to a falsehood being definitionally impossible.
We can't prove that 4 + 4 is not equal to 9. What we can prove instead is that 4 + 4 is equal to 8, and we can also prove that the + operator cannot generate different outputs given the same inputs. We "prove the negative" by proving positive assertions that negate the negative.
The positive assertion that would have to be proven, to prove the negative statement of "Pence is not a pedophile", would be to assert that at no time in Pence's life has he fucked a child. The proof of this... well, that would be an excerpt from the memory of an omniscient being, I suppose.
Can you provide a concrete example of a proof of a negative assertion? I've heard the occasional claim that negative proofs are possible, but I've never seen/been patient enough to locate one. I work in programming and it's extremely against my experience that a negative can be proven; I'm frequently reframing tasks from negative to positive in order to find bugs (e.g. if a user asserts that "X doesn't work", the process of fixing the issue is entirely finding areas that can be proven to function correctly, until the only area that remains is the one that is broken)
The best I've arrived at is falsification as expressed in my math example above, and I think also in the extrapolation of Karl Popper's argument, if I'm interpreting that correctly. If all we have to work with is a negative, then the negative -itself- can't be proven by addressing the negative -itself-. You have to come at it from the angle of a positive assertion, like "Pence has always had a reliable witness to his behavior".
So you can "arrive at proof that a negative statement is false", but I think the common sentiment of "you can't prove a negative" is aimed at the attempt to directly prove/disprove a negative assertion itself, and isn't meant to imply that it's impossible to arrive at proof etc.
I didn't read any bitchiness from what you've said, I think you're doing a'ight :)
I think then that we are in agreement! We just went about our definitions from different angles.