# Disproving via negative, but not proving via positive

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## 3 Replies - 862 Views - Last Post: 29 December 2014 - 09:14 AM

### #1 Sammdahamm

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# Disproving via negative, but not proving via positive

Posted 29 December 2014 - 08:22 AM

I apologize for the poor quality title, but if I knew how better to phrase the question, I wouldn't be asking the question in the first place. Also I'm not 100% sure if this question is in the right area, but please correct me if this is the case.

Whilst revising relational databases I came across this point regarding functional dependencies:

Quote

Given some allowable instance r of R and an FD f, we
can try to use r to check if f does not hold over R, but
we cannot normally use r to check if f does hold over R.

I'm sure there is a formal name for this. Not just for this particular case, but for when you can disprove an entire theory by proving it wrong in a single case, but cannot prove it to be true by proving it once.

Sorry if this is terribly phrased, but it's really bugging me that I can't think of the correct term.
Sam

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## Replies To: Disproving via negative, but not proving via positive

### #2 jon.kiparsky

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## Re: Disproving via negative, but not proving via positive

Posted 29 December 2014 - 09:01 AM

Sammdahamm, on 29 December 2014 - 10:22 AM, said:

when you can disprove an entire theory by proving it wrong in a single case, but cannot prove it to be true by proving it once.

This is generally true, of course, and it's so generally true that I can't think of a name for it as a phenomenon. Since a rule is a claim that "in all cases, X", a single case in which ~X is enough to disprove the rule. This implies that a million cases in which X only tell us that "sometimes, X". There are some catchphrases which relate to this, I don't know if they're the ones you're looking for. "Black swan" is one. From linguistics, we have Chomsky's "no negative evidence" principle, which asserts that human beings must have inherent linguistic competence, since they make hypotheses from incomplete data, but never receive negative evidence allowing them to prune out incorrect hypotheses. (those of you with children will have noticed their surprising resilience to correction - this is completely normal). In philosophy, there is the argument about deductive versus inductive truth, and the related question about innate versus empirical knowledge. For this you're going to have to go back to some older material - Descartes, Hume, and so forth.

### #3 Sammdahamm

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## Re: Disproving via negative, but not proving via positive

Posted 29 December 2014 - 09:08 AM

jon.kiparsky, on 29 December 2014 - 09:01 AM, said:

Sammdahamm, on 29 December 2014 - 10:22 AM, said:

when you can disprove an entire theory by proving it wrong in a single case, but cannot prove it to be true by proving it once.

This is generally true, of course, and it's so generally true that I can't think of a name for it as a phenomenon. Since a rule is a claim that "in all cases, X", a single case in which ~X is enough to disprove the rule. This implies that a million cases in which X only tell us that "sometimes, X". There are some catchphrases which relate to this, I don't know if they're the ones you're looking for. "Black swan" is one. From linguistics, we have Chomsky's "no negative evidence" principle, which asserts that human beings must have inherent linguistic competence, since they make hypotheses from incomplete data, but never receive negative evidence allowing them to prune out incorrect hypotheses. (those of you with children will have noticed their surprising resilience to correction - this is completely normal). In philosophy, there is the argument about deductive versus inductive truth, and the related question about innate versus empirical knowledge. For this you're going to have to go back to some older material - Descartes, Hume, and so forth.

Thank you very much This is the reason why I will almost always choose to post questions on DIC instead of Stack Overflow/related sites. People seem much more friendly/helpful on here, whereas this question would have probably got something in the region of 10 down votes, and probably closed on SO.

Thanks again for answering such an ambiguous question,
Sam

### #4 jon.kiparsky

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## Re: Disproving via negative, but not proving via positive

Posted 29 December 2014 - 09:14 AM

It's true, I would certainly close this question on stack overflow, but if you're looking for a term or usage, the English Language Learners site on stack exchange is often helpful for questions of the form "What is the term for...?" - even if you're a native English speaker!

And that's why it's good that there's more than one website.