Proving a Negative


Many atheist likes to think that he cannot prove a negative.  He cannot prove the non-existence of God — likewise, he cannot prove that “the tooth fairy does not exist”.  I have made it a motto that “What you can’t prove (or disprove) isn’t science”.  All scientific theories make testable predictions, and all scientific theories can be falsified.  This is what makes the scientific method so incredibly effective.

However, it just occurred to me that theoretically, you can actually prove a negative.  Maybe I’m wrong.  But x is either T or F.  If x is not T, then x is F, or ~T.  So if x can be proven to not be T, then x has to be ~T.

Proving a negative. “There is no Greatest Prime”:

  • Assume that prime numbers are finite and that “P” is the largest prime. For the sake of example, let’s say the largest prime number is P = 7. That would mean that 2, 3, 5, and 7 are the only prime numbers, and 7 is the largest of them; that there are no prime numbers bigger than 7.
  • Create a new number, “Q”, by multiplying all the known primes together, and adding “1”. e.g. Q = (2 * 3 * 5 * 7) +1 = 211
  • Divide Q by any of the known prime numbers. It will never divide evenly and always have a remainder of “1”. e.g. 211/2 = 105R1, 211/3 = 70R1, 211/5 = 42R1, and 211/7 = 30R1
  • If a number is indivisible by any primes, that means that it, itself, is a prime number.
  • P = 7 cannot be the largest prime because Q = 211 is larger than P and is prime. This is true for any value of P.
  • Therefore, there cannot be a largest prime. Reductio Ad absurdum, our initial assumption that there can be a “largest” prime is incorrect. The prime numbers go on forever.

So, I’m guessing that you can prove a negative when the mechanism through which the negative can be proven wrong has been (or can be) proposed.  “The theory of evolution is not true.” (x = ~T).  There’s a negative, and one which can be proven, because evolution is a scientific theory, and it can be falsified; there exists several criteria by which it can be shown that x is not T.

The non-existence of God, like the non-existence of the tooth fairy, is a different case.  The idea of God cannot be falsified to begin with.  There is no way you can disprove God, because there is no criteria by which God can be disproven.  I can offer to you proof of absence of God, but you can easily respond that absence does not equate to non-existence.  Think about it.  There is no way I can disprove God.  The existence of some gods, Zeus for example, could perhaps be disproven, because Zeus lived on top of Mt. Olympus, and if I went up there, and searched the entire place, and didn’t find the bearded guy, then it could be said that the a criterion for non-existence has been met.  But perhaps Zeus lives in a different dimension.  Perhaps he lives in a different universe.  Perhaps he is beyond space and time.  Then it is simply impossible to prove the negative.  And there is no reason to.  Why?  Because you have never proven it to begin with.  Prove to me that God is beyond space and time.  See, you can’t.

It is therefore more feasible to present proof of absence, or proof of negligence, or proof of bad design, or proof that the Bible is inaccurate.  For example, on the basis of evidence, I can prove that a global flood never took place.  I can show you that the world is filled with untold suffering; that all of nature is a battlefield.  But I cannot disprove the existence of God, and a theist should not expect the atheist to be able to do so.

It must also be said that because Intelligent Design cannot be disproven, it is not science.  There exists no criteria by which ID can be disproven.  For instance, I could make a (very absurd) claim that the world is only 6,000 years old, only God designed it to look older than it actually is.  This claim can in fact fit with the evidence, but it certainly is not science, because it cannot be proven or disproven.  Intelligent Design claims that we were “designed” by an intelligent entity — it can perhaps fit with the evidence (somewhat; I beg to argue that the universe does not appear intelligently designed at all; and how does it square with the evidence for evolution?) — but since it cannot be disproven (designer may have wanted this, designer may have wanted that), I reserve the right to call it theology, or mythology, or merely an article of faith.  It is by no rational means a scientific theory — and by no rational means a scientific alternative to the theory of evolution.

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