Page:Mars - Lowell.djvu/29

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7
AS A STAR

theory is not whether there be a possibility of its being false, but whether there be a probability of its being true. This, which is evident enough when squarely envisaged, is too often lost sight of in discussing theories on their road to recognition. Negative evidence is no evidence at all, and the possibility that a thing might be otherwise, no proof whatever that it is not so. The test of a theory is, first, that it shall not be directly contradicted by any facts, and secondly, that the probabilities in its favor shall be sufficiently great.

As to what constitutes sufficiency it is important to bear in mind one point, namely, that the odds that a thing is true from the fact that two or more witnesses agree on the same statement is not the sum of the odds that each tells the truth, but the product of those odds.[1] Therefore, if the chances for the truth of a theory, in consequence of its explaining a certain set of details, be three to one, and because of its explaining another set,—for the purposes of argument unrelated to the first,—four to one, then the chances in its favor from its explaining both sets are not seven to one but twelve to one. If it explains a third set whose independently resulting odds are of five to one, the chances in its favor, from its explaining all three sets, not twelve to one but sixty to one; if a fourth set be added, with further odds of five to

  1. See Lacroix, Traité Elémentaire des Probabilités, p. 220.