Published online by Cambridge University Press: 14 March 2022
Two initially different arguments for indeterminism are often based either upon the Uncertainty Relations or the statistical interpretation of the wave equation of quantum mechanics. Both arguments ultimately involve three factors: (1) the assumption that elementary entities are enough like classical particles for it to make sense to say they are either determined or indetermined, (2) the fact that no exact measurements are possible of quantities supposed to characterize elementary entities, (3) the pragmatic supposition that determinism is false unless exact predictions are theoretically possible.
If it is legitimate to use (3) to prove indeterminism, then an equally legitimate argument can be based upon (2) which denies (1). Thus, it is doubtful that quantum mechanics supports indeterminism, though it may show that the concepts of ‘determined’ and ‘indetermined’ are inapplicable to the world.
1 John von Neumann, Mathematische Grundlagen der Quantenmechanik (Berlin, 1932), pp. 167-173; Mathematical Foundations of Quantum Mechanics (tr. Robert T. Beyer, Princeton, 1955), pp. 313-325.