IISER MOHALI

Abstract: We trace the origins of formal logic in Aristotle’s Prior Analytics in 4th Century BCE. We begin with Aristotle’s definition of ‘deduction’ and two types of deduction: demonstration and dialectic. The difference is in the nature of the premises and not in the nature of the inference, which is the same in both types. We then advance to the basic structure of syllogistic logic in which 256 syllogisms are generated and the methods of determining the validity of these syllogisms are laid out. We also look at axiomatic geometry initiated by Euclid within a century after Prior Analytics. Then we jump to the 17th century and Leibniz’s attempts to algebraize logic to take it beyond the limitations of subject-predicate logic. Then, we jump to the 19th century emergence of modern logic with Boole’s algebraization of logic, which is completed by Frege’s axiomatization of logic with quantifiers. Finally, we introduce metalogic in which the consistency and completeness of formal systems of logic are proven. We also introduce the extensions of logic to modal logic, epistemic logic and deontic logic and the most recent developments in dynamic epistemic logic and dynamic deontic logic.