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By Brian Skyrms

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Suppose now we are given still more information, to the effect that Mr. X is a me mbe r of the Armenian Club of Allentown and that 99 percent of the me mb ers of the Armenian Club are actually Armenians. Upon addition of this information the epistemic probability that Mr. X is an Armenian again becomes quite high, for it is now equal to the inductive probability of the following argument: Mr. X is an Oriental rug dealer in Allentown, Pa. Allentown, Pa. , is in the United States. Ninety percent of the Oriental rug dealers in the United States are Armenian.

And once we have this premise, scientific induction on level 2 leads us to the conclusion that they will be reliable in the future. Thus, what has been shown is that if any system of inductive logic has suc­ cessful rules on level 1 , then scientific induction provides a justifying argument for these rules on level 2. Indeed, we can generalize this principle and say that if a system of inductive logic has successful rules on a given level, then scien­ tific induction provides a justifying argument on the next highest level.

This argument was given high inductive probability by rules of level 1 of scien­ tific inductive logic. We knew its premises to be true, and we took its conclu­ sion as a pre diction. The lOOth jub-jub bird can thus be correctly described as purple - or as the color that makes the conclusion of argument jj-99 true- or as the color that results in a successful prediction by the rules of level 1 of sci­ entific inductive logic. Let us also suppose that similar arguments had been advanced in the past: jj-98, jj-97, etc.

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