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You Can Prove a Negative [pdf]

• TerryADavis 11y ago
  The nigger brain cannot understand what a NIST certified random number is. I fucken hate niggers.
• awptimus 11y ago
  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.
  • _delirium 11y ago
    Yeah, the first half of this seems to be mostly for color rather than really debunking the slogan. Not even the most naive users of the slogan "you can't prove a negative" literally think that you cannot prove negatively phrased mathematical or logical claims, such as "1 + 2 != 5".
    • awptimus 11y ago
      It's just missing the better alternative. It's much more correct and useful to say "given all evidence the probability there are yeti is almost zero" correctly doesn't rule it impossible and correctly asserts that we shouldn't behave as if they do. I mean, if we're fine when the entire physics community go nuts with excitement when we make a mistaken measurement of a neutrino going faster than light, why worry about a person who thinks they saw a yeti try to find a yeti?
    • coldtea 11y ago
      >Not even the most naive users of the slogan "you can't prove a negative" literally think that you cannot prove negatively phrased mathematical or logical claims, such as "1 + 2 != 5". What happens is that the most "naive users of the slogan" don't take their thinking that far, that's why they believe it. It's not that don't think you cannot prove negatively phrased mathematical or logical claims, it's they don't understand that that would be a counter-example to their "can't prove a negative" claim.
  • deleted 11y ago
    [deleted]
  • TelmoMenezes 11y ago
    And likewise you can't prove a positive. In fact, you can't prove anything with statistics, and science is not about proof. Mathematics is about proof. Science is doubt. All theories are forever on probation -- or until they are falsified by new experiments.
    • awptimus 11y ago
      Not true. Given a hypothesis "there exists" the first observed instance is proof of the positive. The inverse however, again, requires you to sample the entire population and collect all data.
      • duaneb 11y ago
        Depending on what you're observing, it's only statistical probability you actually observed anything. There is no such thing as an inductive proof; there is no way you can prove anything exists to another person. I suggest Hume and the writings of the logical positivists. This will wipe the idea of being able to "prove" with science or observation right out of your brain. No matter how much information you have, you don't have enough to predict the future. If our planet collides with some huge energy burst, all the people who said "I know for a fact that the earth will still be moving around the sun at the approximately same rate and mass" will have been PROVEN false. But there is no such trick to prove anything about tomorrow.
        • awptimus 11y ago
          Other people don't factor into this. Proving to them is not necessary. Once an event occurs, it occurred. Your knowledge of what that event or the total state of that event might be uncertain, but the event's occurrence is no longer probabilistic.
          • duaneb 11y ago
            Yea, but you are probably talking about a completely different event than the other person, or whatever happened in your memory, or maybe just a past version of yourself. The world is not naturally quantized into discrete events, causes, and effects, and it is in this disagreement over simple assumptions that "this event happened" that cause people to disagree about "certain" things. Look at how utterly useless witness testimony can be, no matter how hard they swear up and down, if the memory is suspect at all. So, if you want to lie to yourself, I guess you could "prove" something to yourself. But you know you can't trust your observations for about a billion different reasons. Why is this important? Because you can always know if a bridge has failed, but you never know if it's not going to fail. Never. No matter how certain you are, unless you can form a deductive proof showing that the structure will NEVER fail (which I suspect is impossible for a computer, let alone a human), you will always have doubt. If you don't recognize the doubt, you are lying to yourself. Furthermore, once you realize how.... loosely science binds together, you realize that the "laws" we think we "know" are broadly accurate but fall to pieces in the details. So no, proving a negative is not possible. It's not a proof unless you can show the state of the universe, which is again impossible without consensus, which is itself probabilistic and flawed. If you are 100% certain that an event has happened in any way that you could deductively prove something, that gamma ray burst could easily mess with your plans. A non-deterministic universe is one of increasing, but always <100%, certainty.
• animefan 11y ago
  Similarly in frequentist statistics "you can only disprove a hypothesis" is false. 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. 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
  • darkmighty 11y ago
    It really depends on the statistical model of the quantities you're working with. If somehow your model dictates that x and y must be discrete, you can get certainty of measurement (i.e. prove x=y) even with some noise. In this case I think both sides are right, so the argument should be used in context. You can only prove things about the real world (and not an axiomatic system for example) assuming there are no unknowns. In some (perhaps most) cases those unknowns are not there, but in some important cases unexpected behavior may occur in spite of "overwhelming evidence", because the assumptions made by the conclusions failed. It would be a much simpler discussion to state "When you want to prove something, make your assumptions clear, and test them well. Everything that hopes for rigor is proved within a well defined set of assumptions, so it's not like nothing can be proved either.".
  • coldtea 11y ago
    >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. If they are so close that your test has no power, then they might as well be the same for the purposes of your test.
• jsprogrammer 11y ago
  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.
  • ginolomelino 11y ago
    The paper very specifically addresses that problem at length.
    • jsprogrammer 11y ago
      It's more that it avoided the issue by deflecting to a different example, while assuming unproven and fallacious (to the original point) premises to construct an inductive argument, which the author later admits is not any kind of proof according to the original question.
    • themodelplumber 11y ago
      I wouldn't say it addresses the problem at length. At best it goes one level deeper than "you can't prove a negative" to say "you _can_ actually offer some evidence or probability for said negative" but even then it hands off the threshold of [what's been proven vs. not proven at that point] to epistemology. After that, the author concludes that you should never dismiss an inductive argument just because you think any probability it provides is immaterial. After all, we rely on induction all the time in day-to-day life! Well, duh. So let's hear it for induction, everybody. At least it gives us some probability. I dunno. It's just not as intriguing a line of thinking as I hoped it would be based on the title of the paper. Despite all the excitement about proving a negative, the author goes completely silent on the issue of how much probability proves what!
  • Retra 11y ago
    Then how would you prove that such a proof cannot exist?
    • jsprogrammer 11y ago
• pg_is_a_butt 11y ago
  .edu?? is this a globe university thing? this is a complete joke
• scoofy 11y ago
  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.
  • Retra 11y ago
    That's one model of the process. Another is that the distinction between negative and positive claims is entirely artificial, and that there are really only "claims" and the truth of them is determined by their effectiveness at constructing reliable models of reality. And thus any demonstration of self-contradiction is a disprove of a claim, whether negative or not.
    • scoofy 11y ago
      Negative and positive claims are not artificial or equivalent, one is making a claim about positive existence, the other is making claims about lack of existence. Of course we can manufacture the universal quantifier insofar as it's a mapping of the existential quantifier. That is to say, proving something is "not nonexistent" is not a statement that requires the universal quantifier, it's a claim that has simply mapped the equivalency of the existential quantifier, using the universal one. This is still only a statement about positive knowledge.
      • deleted 11y ago
        [deleted]
• ThePhysicist 11y ago
  In physics (and other natural sciences) you can ONLY prove negatives in fact, so to a physicist this statement is not surprising at all. 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. 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.
  • scoofy 11y ago
    You're reference for negative here is wrong. When you prove that something is not the case, then you do so by demonstrating an there exist something contrary to your hypothesis. This is positive knowledge, not negative knowledge. This is a very convoluted philosophical concept, but it's essential Karl Popper's argument. We don't, and can't prove negatives, but what we mean by that, as i discuss below, is that we cannot apply the universal quantifier with any certainty.
    • Retra 11y ago
      What exactly do you mean by "positive knowledge" or "negative knowledge?"
      • scoofy 11y ago
        Positive knowledge is: there is an instance of x (where not existing is not a predicate of x, as existence is not a predicate) Negative knowledge is: there is not an instance of x (where not existing is not a predicate of x)
• wfo 11y ago
  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. 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. 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. 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.
  • Kenji 11y ago
    About the part with god, there's a specific expression for that: God of the gaps. As our (scientific) understanding increases, a proposed god people want to believe in has to lose one characteristic after another because they would not hold up against reason and evidence.
    • cristianpascu 11y ago
      True, my father told me that the day science came up with the tunneling effect, he stoped believing in a loving God. How can one believe in God when we have computers so powerful that we can post pictures of cats on the internet?