tautology

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In science, these two types of organization of data (description and explanation) are connected by what is technically called tautology. …
..Von Neumann, in his famous book [“The theory of games and economic behaviour. 1944), expressly points out the differences between his tautological world and the more complex world of human relations. All that is claimed is that if the axioms be such and such and the postulates such and such, then the theorems will be so and so. In other words, all the tautology affords is connections between propositions. The creator of the tautology stakes his reputation on the validity of these connections.
Tautology contains no information whatsoever, and explanation (the mapping of description onto tautology) contains only the information that was present in the description. The “mapping” asserts implicitly that the links which hold the tautology together correspond to relations which obtain in the description. Description, on the other hand, contains information but no logic and no explanation. For some reason, human beings enormously value this combining of ways of organizing information or material.
To illustrate how description, tautology, and explanation fit together, let me cite an assignment which I have given several times to classes. I am indebted to astronomer Jeff Scargle for this problem, but I am responsible for the solution. The problem is:

A man is shaving with his razor in his right hand. He looks into his mirror and sees his image shaving with his left hand. He says, “Oh, there’s been a reversal of right and left. Why is there no reversal of top and bottom?”

(Mind & Nature: 76-77)

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