CORCORAN-NAMBIAR ON PARADIGM SHIFTS IN LOGIC

Did Boole create a new paradigm to replace Aristotle’s? Or did he merely show the untenability of the Aristotelian paradigm thus inadvertently revealing a vacuum to be filled by Peano, Russell, or someone else? We raise these and related questions in the course of reviewing Peckhaus’s rich study:“The mathematical origins of nineteenth-century algebra of logic”. It is widely agreed that a revolutionary paradigm-shift took place in logic in the 1800s. Logical research before 1800 was dominated by a single paradigm whose core is traceable to ancient Greek logic, principally Aristotelian. Logical research after 1900 has been dominated by a radically different paradigm governing the work of logicians such as Frege, Peano, Russell, Hilbert, Gödel, Tarski, and Church. Justifying the word ‘mathematical’ in its title, the paper under review observes, whereas “the old logic” had been pursued almost exclusively by people regarded as philosophers, “the new logic” involved many people regarded as mathematicians. The paper addresses the issue of identifying the paradigm-shift: when did “the new logic” begin, who were the leading actors, what were the motivations, how did the paradigm gain acceptance?