The Foundations of Scientific Inference by Wesley C. Salmon

Author:Wesley C. Salmon
Language: eng
Format: epub
ISBN: 9780822982944
Publisher: University of Pittsburgh Press

This example is not just an isolated case (although one contradiction ought to be enough), but it illustrates a general difficulty. A similar conflict can be manufactured out of any situation in which we have two magnitudes interdefined in such a way that there is a nonlinear relation between them. For a fixed distance, speed and time are reciprocal; for a square, area relates to the second power of the length of the side; etc. Figure 1 shows graphically the source of the paradox. For a nonlinear function, the value of the function for the mid-point (x1 + x2)/2 between two values of the argument x does not, in general, correspond to the mid-point (y1 + y2)/2 between the values of the function determined by those two values of the argument.

The whole set of paradoxes generated in the foregoing manner shows that the principle of indifference yields equivocal values for probabilities. The probability of averaging at least forty-five miles per hour over the mile is equal to one half and also to some number other than one half. Since axiom 1 of the probability calculus requires that probability values be unique, the classical interpretation violates the criterion of admissibility.

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