In physics (and other natural sciences) you can ONLY prove negatives in fact, so to a physicist this statement is not surprising at all.<p>Example: If we observe an apple falling to the ground with the same acceleration many times we will try to generalize this observation and create a theory that explains this phenomenon and similar ones (such as Newton's laws and his theory of gravity). Unfortunately we can never prove such a theory in the mathematical sense since we can never be sure that the next time we perform a given experiment it will still yield the same result (it could be that the laws of physics change over time or work differently in other parts of the universe). However, we can easily falsify a given theory if we can produce even one single observation where the theory does not fit reality (which is precisely why general relativity was needed to replace the classical theory of gravity, which could not explain all experimental data [actually the new theory came even before the data in that case, which is amazing in itself]). So, in a sense, proving that something is not true is the only thing we can do with absolute certainty.<p>That said, theories that are proven wrong by experiment and replaced by other theories are still valid in their domain of applicability, so to say as an approxomation of the larger theory.
I think the article dances around what people really mean when they say "you can't prove a negative". The writer touches on it but somehow skirts the real issue. When we say "you can't prove a negative" you're really saying that in order to prove a statement of the form "not exists x P(x)", it's equivalent to proving "for all x not P(x)" and so you're really making a statement about EVERYTHING that has or does or could ever exist somehow. These proofs are either analytic and trivial (i.e. there doesn't exist a rectangular circle) or not proofs.<p>He suggests you get around this by providing an argument about unicorns and then goes on to talk about how premises don't always need to be justified, but the problem is proving the nonexistence of a thing -- and he provides a formal deductive example of a proof of nonexistence of a thing by instead substituting as a premise nonexistence of another thing (evidence). Sure, if you can prove no evidence for unicorns exists and that for unicorns to exist they MUST have left evidence you can prove they don't exist. But the first one is a reduction to the original problem -- in order to show something doesn't exist (be it unicorns or evidence for unicorns) you need complete and total knowledge about existence, which no human up to this point has had enough hubris to claim, and the second requires a level of certainty that doesn't really exist.<p>If we're discussing the existence of a thing that doesn't leave evidence (god) especially it's very fair to say you can't prove a negative and I think his attack on this tactic is a non-starter.<p>There has never been even the tiniest bit of evidence against the existence of god. There is certainly evidence against a god with specific qualities; a benevolent god, a god that wants this to happen, etc. But if you don't require god to have any specific qualities there isn't a shred.
This is an unnecessary. "You can't prove a negative" isn't a statement about logic, it's a statement statistical evidence (incorporating logic). You need to observe the entire population in order to reduce a probability to zero.
Similarly in frequentist statistics "you can only disprove a hypothesis" is false.<p>If you think you can disprove x > y, (where x and y are parameters like the mean of some quantity for two different populations) then it follows that you can prove x <= y.<p>On the other hand you cannot ever prove x = y since there will always be values of x and y that are so close that your test has no power. but you can still put bounds on how close x and y must be in this case
Induction allows us to use the existential quantifier, deductions allows us to add the universal quantifier. If we want to say something about the world, we are bound to empiricism, thus our deductive claims rest upon our inductive evidence. This is a framework. Any use of the universal quantifier (necessary for a negative claim), is unsupported by our empirical data. This is essentially Popper/Hume.
I think, "not being able to prove a negative" is more related to the idea that you cannot prove/disprove (ie. Assign an absolute truth value to) the non-existence of something. For example, you cannot prove that a God does not exist.