Paradox of the 99 Foot Tall Man

99 Foot Tall ManLet’s say you form a hypothesis that no human being can ever grow to be 100 feet tall. You begin to collect data by measuring the height of every human you encounter, and you find that the vast majority of them are under eight feet tall. No matter how many humans you measure, you have not proved your hypothesis completely, but as you collect data on thousands upon thousands of people who are under eight feet tall, you are becoming more and more certain that your hypothesis must be correct. Each person you measure who is less than 100 feet tall is one piece of confirming evidence.

One day you meet a man who is nine feet tall. You are surprised, because he is the tallest person you have ever met, by several inches. Does this change your opinion about your hypothesis? Surely not. The existence of a nine foot tall human does not make a 100 foot tall human more probable. The nine foot tall man is an outlier in terms of human height, but he is also another piece of confirming evidence for your hypothesis.

The next day, however, you meet a man who is 99 feet tall. How does this affect your confidence in the hypothesis?

From one perspective, this should have the same effect as every other human you have met: he is yet another person who is not 100 feet tall, just like the nine foot tall man and the tens of thousands of people who are shorter. But surely, if this really happened, you would actually feel much less confident about your hypothesis. If humans can grow to be 99 feet tall, why not one foot taller?

Labyrinths of ReasonThis paradox, in which a piece of evidence seems to both strengthen and weaken a hypothesis, was invented by Paul Berent, and is described in William Poundstone’s Labyrinths of Reason. Like Hempel’s Raven Paradox , it is a problem of  inductive reasoning. Just as seeing ten thousand black ravens does not prove that all ravens are black, seeing ten thousand humans under 100 feet tall does not prove that all humans are under 100 feet tall. These hypotheses are both generalizations that can never be fully proven. Evidence can only provide incremental support for them, or disprove them (in the case of a white raven or a 100 foot tall man).

What the 99 foot tall man illustrates is that not all evidence is equal. Black ravens and people under ten feet tall provide support for the hypotheses. Meeting a 99 foot tall man is like finding an albino crow. It is not just another confirming instance. Instead, the nature of the evidence casts doubt on the hypothesis.

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