# 851-0173-00L History of Formal Logic: The Emergence of Boolean Logic

Semester | Spring Semester 2021 |

Lecturers | J. L. Gastaldi |

Periodicity | non-recurring course |

Language of instruction | English |

Abstract | The invention of Boolean logic in the middle of the 19th century is considered a major event in the history of modern thought. However, Boole’s original system does not correspond to what we came to understand as Boolean logic. We will study the early history of Boolean logic in relation to the mathematics of its epoch, in search of an alternative philosophy of formal knowledge for the present. |

Objective | During the course, students will be able to: -Acquire a general perspective on the history of formal logic -Review relevant aspects of the history of modern mathematics -Obtain philosophical and historical tools for critically assessing the status of formal sciences -Develop a critical understanding of the notion of formal -Discuss the methodological capabilities of historical epistemology |

Content | The invention of Boolean logic in the middle of the 19th century is considered a major event in the history of modern thought. Boolean algebras and Boolean rings lay at the basis of propositional logic and digital communication, contributing in a decisive way to the theoretical and technical conditions of our time. However, if attention is paid to Boole’s own work, it will quickly appear that his Calculus of Logic does not correspond to what we came to understand as Boolean logic. Instead of disregarding those differences as inevitable mistakes of any pioneering enterprise, waiting to be corrected by successive developments, we will try to understand them as the sign of an alternative philosophy of logic and formal knowledge, which later developments excluded and forgot, and from which recent advances in formal sciences could take advantage. Such an inquiry will give us the occasion of exploring the philosophical and scientific landscape in which formal logic emerged in the first half of the 19th century (focusing on the works of Babbage, De Morgan and Boole), and to build a critical perspective on the notion of “formal”, at the crossroad of the history and philosophy of mathematics and logic. |