Is logical thinking a way to discover or to debate? The answers from philosophy and mathematics define human knowledge.
According to A History of Formal Logic by the distinguished J M Bocheński, the golden periods for logic were the ancient Greek period, the medieval scholastic period, and the mathematical period of the 19th and 20th centuries.
Descartes hits the nail on the head when he claims that the logic of the Schools is not really a logic of discovery.
From the perspective of the 21st century, medieval scholastic logic is perhaps more deserving of the title ‘logic’ than the work done under this heading in the early modern period, given that it comes closer to the level of rigour and formal sophistication that came to be associated with logic from the late 19th century onwards.
Boole was responding to a growing interest in logic among mathematicians, and he mostly remained Kantian in his thought, but his work undoubtedly represents a turning point in the history of logic: it kicks off the mathematical period singled out by Bocheński as one of the most prolific periods in the history of logic.
While Boole used mathematics to analyse logic, Frege’s project was to use logic to analyse mathematics.
To return to Bocheński’s characterisation of the three grand periods in the history of logic, two of them, the ancient period and the medieval scholastic period, were closely connected to the idea that the primary application of logic is for practices of debating such as dialectical disputations.
Originally published at Cogly.
