Paul Johnson on Logic

“What would be the consequences for the theory of truth, asked one worried logician,’… of the adoption of a non-standard system’? Another, observing systems of modal logic, observed: ‘One gets an uneasy feeling as one discerns and studies more of the systems belonging to this family that it is literally a family, and has the power of reproducing and multiplying, proliferating new systems [of logic] without limit.’ In a world in which even the rules of logic shifted and disintegrated, it is not surprising that modern times did not develop in ways the generation of 1920 would have considered ‘logical’.”

“Moreover, growing uncertainty surrounded even the one too which the academic philosophers felt they could trust: logic. Two centuries before, Kant had asserted in his Logik (1800): ‘There are but few sciences that can come into a permanent state, which admits of no further alteration. To these belong Logic … We do not require any further discoveries in Logic, since it contains merely the form of thought.’ As late as 1939, a British philosopher asserted: ‘Dictators may be powerful today, but they cannot alter the laws of logic, nor indeed can even God do so.’ Thirteen years later the American philosopher Willard Quine calmly accepted that the definition of logic was undergoing fundamental change: ‘What difference is there in principle between such a shift and the shift whereby Kepler succeeded Ptolemy, or Einstein Newton, or Darwin Aristotle?’ In the decades that followed, many rival systems to classical logic emerged: Bochvar’s many-valued logic, new systems by Birkhoff and Destouches-Février and Reichenbach, minimal logic, deontic logics, tense logics. It became possible to speak of empirical proof or disproof of logic.”