Logic in the 19th century

The nineteenth century was one of the most active periods for logic in Western philosophy. It is regarded foremost as being the first time logic became ‘symbolic’ and ‘mathematical’.

There was tremendous diversity and conflict in logic in this period – indeed there were substantial debates over whether there even is a subject called ‘formal logic’ and over what the most basic logical forms were. There was an explicit discussion in the early part of the century of whether logic should be extensional or intensional, opinion eventually settling on a purely extensional conception. By the end of the century, many of these debates had been resolved or had withered away, and the most widespread conception and practice of logic coalesced in the early twentieth century into a view we now identify with the works of Frege, Russell and Whitehead.

The nineteenth century brought, for the first time, from Boole and Frege, distinct proposals on how to symbolize logic that were both extensively developed and had widespread influence. Boole is correctly regarded as the father of modern symbolic logic. Frege shared two concerns of many nineteenth-century mathematicians – avoiding incorrect derivations and providing rigorous and clear foundations for the infinitesimal and derivative calculus – and therefore sought to develop a very clear notion of mathematical ‘proof’. His notation has not been taken up but his influence, especially on the move towards symbolization, has been considerable.

De Morgan was the first logician extensively and symbolically to discuss the logic of relations. However, a systematic algebraic notation for relations was provided only later by Peirce, and developed also by Schröder.