Abstract

SummaryThe working logician begins with whatever operations are necessary to make computation possible. He does not inquire into the foundations which the carrying out of his operations assumes; no axioms, no assumptions, just the computations themselves. Yet in logic of all places the starting‐point should be defensible. After examining the logical assumptions, the constructions of proofs, individuals and classes, and the metaphysical assumptions, the conclusion is reached that the net effect of operational logic is to assimilate logic to mathematics rather than to consider mathematics an extension of logic. The price to be paid for this preference is to leave them both unexplained. It would mean that the metaphysics of mathematics would have to proceed without logic.