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Proving a negative

  1. Jan 13, 2010 #1


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    I've found many different explanations for why a negative claim can/cannot be proven. I remember reading a comment on Richard Dawkins' website claiming that it is impossible to prove a negative, but there were many others who responded to said claim showing ways in which a negative could be proved.

    The following quote was one of the only explanations that has made sense to me.


    I'm hoping for input on whether or not this explanation is correct.
  2. jcsd
  3. Jan 13, 2010 #2


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    In mathematics, a negative can be easily be proven by for example the principle of contradiction.

    In real life, however, you will need a proper epistemological model before you can answer such questions, which must, of course, define the notion of a "proof".
    Last edited: Jan 13, 2010
  4. Jan 13, 2010 #3
    One has to be careful when using the word 'proof'. It means something very different in mathematics and deductive logic, than in does in science (inductive logic). Proof, in the most strict sense of the word, only exists in math and deductive logic.

    All men are mortal, socrates is a man, therefore socrates is mortal.

    When someone says that science proves something, what they are really saying is that the evidence points to this, or that, being true.

    All the ravens I have observed are black, therefore all ravens are black.

    Dawkins is making an argument about observation.
    A good example of what he means comes from Bertrand Russel.

    Lets say, I claim that there is a teapot orbiting the sun, somewhere in between earth and mars. And lets say you want to prove me wrong, so you get in a space ship and fly around the entire area, and find no teapot. I could still say that, it is there, you just weren't in the right place at the right time to see it.

    You can't prove it is not there, simply by failing observe it.

    Even with your orange example, you could have made a faulty observation. But the real problem with the orange example is that its making an argument about location, not existense.

    With regards to the argument about god, the question is not whether there is a god in the bowl. The question is, does the orange god exist, at all.

    If I ask, do unicorns exist?
    You can respond that you have never seen one.
    But you can't show that a unicorn doesn't exist somewhere in the universe.
    You can't prove that it doesn't exist.

    However, if you do see one, then you have empirical proof (some level of evidence) that one does exist.

    So Dawkins is saying, he sees no evidence for god, and since, even if he tried, he couldn't prove that god doesn't exist somewhere, its up to people who believe, to provide evidence that he does.
  5. Jan 13, 2010 #4
    God, in the Judeo-Christian sense, is a concept that generally runs into many logical fallacies.
  6. Jan 13, 2010 #5


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    I don't buy your "argument about location" bit -- it just looks like you're playing a word game.

    But anyways, going back to the original post, we can justifiably claim that there are no oranges in my bowl, because we we know that, with extremely high confidence, if there were oranges in the bowl, I would see them when I look.

    Thus, when I look and don't see any oranges, I have extremely high confidence that there are no oranges in my bowl.

    Now, let's switch -- let's use the ghost example from that thread. Can I claim that there are no ghosts in my bowl?

    No, I cannot make that claim: I don't have any solid tests like I did with the orange. I know that if there are ghosts in my bowl, there's a slim chance I might see them when I look -- but I have very little confidence in that test. Therefore I cannot contrapositive it and claim that there are no ghosts.

    Now, it would be wrong to claim there are no ghosts until someone proves otherwise. The fact I cannot find any way to justify that claim does not magically justify that claim!

    (but it would be fine to be skeptical of someone who claims there are ghosts, but cannot offer evidence for it)

    The right thing to do is to carry on without caring whether or not there are ghosts in my bowl. After all, if ghosts don't have consequences, then I never have any reason to consider their existence!
  7. Jan 14, 2010 #6
    I've always taken it as you can only prove a positive. In the case of the oranges in the bowl one could look at the bowl and see an empty bowl (for instance). You can then claim that you do not see a bowl of oranges but a bowl that is empty. You are asserting the existence of an empty bowl not the non-existence of the bowl with oranges. The person who asked that you fetch the bowl with oranges may then enter the room and bring you the bowl in contention to show you that there are orange fruits painted inside the bowl. Had you been certain of the nonexistence of the bowl with oranges in it you would have been wrong. By asserting what exists you are still correct. It seems obviously more logically consistent.
  8. Jan 14, 2010 #7
  9. Jan 14, 2010 #8
    My wording is probably bad. More or less what I mean is that you can observe a thing that exists and collect data/evidence of its existence. You, of course, can not observe and collect data on that which does not exist. One must observe that which does exist to speculate on that which does not.
  10. Jan 14, 2010 #9


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    Note that an important difference between the oranges proof and the God proof is the irrefutable acknowlegement that the area under discussion is within the scope of the observers.

    You can get your adversary to admit that the both of you have access to the entire bowl such that you can determine if there are oranges in it.

    In the case of God, you cannot convince any adversary that you can see the entire universe.
  11. Jan 15, 2010 #10
    Assuming the advocate provides what they consider to be affirmative evidence it can be tested by observation just the same. You are simply making observations about some small part of the bowl to draw conclusions about its over all contents instead of having access to the whole thing.
  12. Jan 15, 2010 #11


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    There is a big difference between saying "there is an orange in the bowl" and "oranges exist". Or conversely "there is no orange in the bowl" and "oranges do not exist".
  13. Jan 15, 2010 #12
    It seems we live in a world of unproven ideas.
  14. Jan 15, 2010 #13
    Going from observed to unobserved is inductive logic.
    This is different from direct observation.
  15. Jan 15, 2010 #14


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    Although someone who adheres to a "Oranges in the bowl" religion could always claim that THEY see oranges, and that the fact that you don't see them is because of your preconceptions, selective blindness, mental illness or some other reason....
    And you wouldn't be able to prove them wrong.
  16. Jan 15, 2010 #15
    One is still using direct observation, even if not of the whole, as the basis for reasoning and argument. If I observe a portion of the bowl and find that there is orange there then I can be fairly certain that there is some orange if not a whole or multiple specimens.
  17. Jan 15, 2010 #16


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    I've seen this happen too. The person making the claim has some ambiguous, ever-changing definition for the object/entity in question. I guess one has to clearly define 'god', 'orange', or 'ghost' before any claims for or against it's existence can be made?
  18. Jan 15, 2010 #17


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    Thank you, Hurkyl. I've never considered this before; it helps me.
  19. Jan 15, 2010 #18


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    This helps as well; thank you.

    If I understand correctly, the problem lies within how 'oranges' and the entity 'God' are defined? One has access to all aspects of an orange, whereas one does not have access to every aspect of everyone's perception of 'God'.
  20. Jan 16, 2010 #19


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    I was making it simpler. Nevermind God or oranges - these are the things being refuted, so you can't use them as a common component of a dialogue.

    But the bowl can be seen by both. You can prove there's nothing in the bowl (oranges or otherwsie) because both of you can agree on this. The problem with God is that you cannot see the entire universe, so you cannot prove it doesn't contain him.
  21. Jan 17, 2010 #20
    As pointed out earlier, it is not needed. Do you have to see the entire universe to know that no square circles exists? Not at all, since the concept of a square circle is intrinsically self-contradictory and can thus not exist anywhere in the entire universe. If this was the case with the god concept, a similar conclusion would follow.
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