Conventionalism in Geometry and the Interpretation of Necessary Statements

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Conventionalism in Geometry and the Interpretation of Necessary Statements Max Black Philosophy of Science, Vol. 9, No. 4. (Oct., 1942), pp. 335-349. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28194210%299%3A4%3C335%3ACIGATI%3E2.0.CO%3B2-L Philosophy of Science is currently published by The University of Chicago Press.

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CONVENTIONALISM I N GEOMETRY AND T H E INTERPRETATIOK

OF NECESSARY STATEMENTS MAX BLACK

1. DESCRIPTION

O F A NECESSARY STATEMEST.

DIFFICULTY O F RECONCILIIGG THE

MEABISGFULFESS O F NECESSdRP STATEMENTS WITH THE

DEFISIKG P X I N C I P L E S O F EMPIRICISM

The statemelits traditionally labelled "necessary," among them the valid theorems of mathematics and logic, are identified as "those whose truth is independent of experience." The "truth" of a necessary statement has to be independent of the truth or falsity of experiential statements; a necessary statement can be neither confirmed nor refuted by empirical tests. The admission of genuinely necessary statements presents the empiricist with a troublesome problem. For an empiricist may bc defined, in terms of the current idiom, as one who adheres to some version, however "weal