The Burden of Proof

Nobody believes anything non-trivial because of "proof"

  • Many people say the only way they will believe in God is if they have "proof."

  • What is proof?

  • What your high school science teacher taught you:
    1. Formulate hypothesis
    2. Gather data
    3. Data are consistent with a hypothesis if you're at least 95% sure that it wouldn't have happened if the hypothesis was false
    4. Are data consistent with hypothesis? If yes, accept hypothesis. If not, reject.

  • Nobody actually does this when forming their beliefs and choosing actions.
    • The data alone are never that convincing.
    • If we imposed this standard of proof, we would be paralyzed.

  • An example from physics:
    • Einstein never accepted quantum mechanics to be true. Hence the famous declaration, "God does not play dice with the universe."
    • But he saw all the same experimental data everybody else did.
    • Even data in physics -- which is as clean as any you'll find -- do not speak for themselves.

  • An example from economics:
    • "The most fundamental rule of economics is that a rise in price leads to less quantity demanded."
      --Stephen Dubner and Steven Levitt.

      (This is called the Law of Demand.)

    • Deirdre McCloskey, The Rhetoric of Economics, on the Law of Demand's wishy-washy empirical performance:

      1. "Sometimes, certain very sophisticated statistical tests of the law applied to entire economies... have resulted, after a good deal of handwringing and computer-squeezing, in the diagonal elements of certain matrices being negative at the 5 percent level of significance. And sometimes they have not."

      2. "Less comprehensive but more numerous demonstrations of the law have been attempted market by market... Again, the curves sometimes give the right slope, and sometimes don't."

      3. "Some economists have tried to subject the law to a few experimental tests. After a good deal of throat-clearing they have found it to be true for clearheaded rats and false for confused humans... an interesting result which no one worries about too much."

    • 99.99% of economists believe in the Law of Demand. Economists don't need "proof" to be convinced of something.

  • An example from history:
    • Hannibal crossed the Alps with elephants in 218 B.C., an incredible feat.
    • Our only documentation of that deed:
      • Polybus: written 70 years after crossing
      • Livy: written 200 years after crossing

    • We don't have the original manuscripts of Polybus and Livy.
      • Earliest copy of Polybus: 1100 years after original publication
      • Earliest copy of Livy: fragment copied 400 years after original publication

    • From textual comparison, it's clear that Polybus and Livy drew from the same primary source for their account
      • So there is really only one testimony that has been retold twice.

    • Polybus and Livy contradict each other on exactly which route Hannibal took over the Alps.

    • Despite these problems, historians generally accept that Hannibal crossed the Alps with elephants.

  • Examples from mathematics:
    • Surely in mathematics, all proof is iron-clad, isn't it?
    • Mathematicians Philip Davis and Reuben Hersh: "The line between complete and incomplete proof is always somewhat fuzzy, and often controversial."
    • "Since its invention it had been generally agreed that the calculus gave correct answers, but no one had been able to give a satisfactory explanation of why this was so."
      --Encyclopedia Britannica

      This state of affairs lasted for over a century after the invention of calculus by Newton and Leibniz.

      • Mathematicians agreed that calculus gave "correct" answers even without proof!

    • Today, mathematicians claim that all possible "finite simple groups" have been classified.
      • Proof of the "enormous theorem" is scattered over 30 years of journal articles and 15,000 pages
      • Realistically, proof is unverifiable

    • 100 years after it was conjectured, the "four color theorem" is now considered to have been proven.
      • No human being has actually read through the entire proof
      • The proofs are generated by computer programs
      • Do you think there is 100% certainty that there are no bugs in those programs?

  • Examples from philosophy:
    • One of the main lessons of modern philosophy is that there don't seem to be any good arguments for
      • the existence of other minds
      • the existence of other people
      • the existence of the past
      • the existence of an external world

    • How do I know that I am not just a brain in a vat (i.e. in the Matrix)?
    • Yet we believe that other minds and people exist, that the outside world exists, and that the past exists
    • "Strong rationalism" is the philosophy that nothing should be believed unless it can be proved rationally by logic or empirically by sensory experience
    • Most philosophers today think that strong rationalism is nearly impossible to defend

  • Even God visibly showing Himself isn't sufficient to produce belief without a leap of faith.
    • In 1988, the atheist philosopher A. J. Ayer had such an adventure when he choked on a piece of smoked salmon and his heart stopped for a few minutes. Soon afterward, Ayer reported that his near-death experience, in which he saw a red light that seemed to govern the universe, "slightly weakened my conviction that my genuine death... will be the end of me." But he later dismissed it as a hallucination caused by a temporary lack of oxygen in his brain.
      --Jim Holt, New York Times Magazine, July 29, 2007

    • ...to my thinking, miracles are never a stumbling-block to the realist. It is not miracles that dispose realists to belief. The genuine realist, if he is an unbeliever, will always find strength and ability to disbelieve in the miraculous, and if he is confronted with a miracle as an irrefutable fact he would rather disbelieve his own senses than admit the fact. Even if he admits it, he admits it as a fact of nature till then unrecognised by him. Faith does not, in the realist, spring from the miracle but the miracle from faith. If the realist once believes, then he is bound by his very realism to admit the miraculous also.
      --Fyodor Dostoevsky, The Brothers Karamazov

  • What is sufficient, then, for belief?
    • A preponderance of evidence in favor. Airtight proof almost never exists.
    • Within nearly every decision and action in life is a leap of faith made to bridge the otherwise impassable gap between evidence and conviction.

Reality is too complicated to allow for the luxury of so-called "proof."



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