Unraveling Classical Logic: A Journey from Ancient Roots to Twentieth Century Precision

What is Classical Logic? A 15-Minute Overview

Classical logic, which I prefer to call Twentieth Century logic, is a distinctly European innovation. This discipline is not 'classical' in the traditional sense of deriving directly from ancient philosophies, nor is it similar to classical music, which emerged from the Enlightenment adorned with a veneer of sophistication in churches and courts. Instead, it signifies the rigorous mathematization of an ancient discipline, formalizing thought processes and striving for universal and necessary foundations.

Though not the logic of the Ancients, classical logic inherits and transforms the legacy of those early thinkers over millennia. My narrative, as detailed in Logic in the Wild, suggests that the genesis of logic lies in the necessity to excel in public debates, accompanying the emergence of politics and decision-making through deliberation. This deliberation process—formulating, articulating, and defending ideas—benefited from logical structures that guided coherent argumentation. Logic served as a repository of reliable argument forms, known as syllogistic logic.

During the medieval period, logic was a vibrant field of study, aiming to harmonize Christian dogmas with pagan philosophy and seeking coherence in their amalgamation. Logicians tackled paradoxes such as reconciling God's omniscience with human free will, divine justice with mercy, or creating a rock so heavy that he can't lift it.

The Enlightenment saw a temporary decline in logical pursuits as the burgeoning of new sciences, along with philosophical and mathematical advancements, diverted attention. Syllogistic logic sufficed for then-current needs. However, as mathematicians delved into increasingly complex theories, dealing with the infinitely small and large, they encountered foundational uncertainties. This prompted a reassessment of logical thought, gradually incorporating mathematical operations into logic.

At the dawn of the twentieth century, Frege identified language as a source of uncertainty in mathematical constructs, advocating for new, unambiguous logical languages. These formal languages allowed for the articulation of mathematical principles as necessary truths. With solid axioms and logical rules, mathematics could ensure the integrity of truths from premises to conclusions, providing a stable foundation. That was the dream.

But then, the same paradoxes that preoccupied medieval logicians, as they delved into the extremities of theological notions, resurfaced when twentieth-century mathematicians pushed the boundaries of truth. This historical echo turned twentieth-century logic into a quest for constructing theoretical towers, a narrative thoroughly explored in Logic in the Wild. Consequently, classical logic stands as the culmination of a century's mathematical effort to structure formal languages within these meticulously crafted theoretical structures. Time’s up!