# Boole and Laws of Thought

George Boole, in the 1840s, proposed that variables could represent more than just numbers. Boole’s work, published in “An Investigation of the Laws of Thought” (1854), introduced algebra with two values: 1 (true) and 0 (false). Instead of traditional algebraic operations, Boolean algebra uses AND, OR, and NOT, also known as conjunction, disjunction, and complement. Conjunction (∧) is like multiplication, with any 0 resulting 0 (false). Disjunction (∨) is similar to addition, but 1∨1 is defined as 1. Complement (¬) exchanges values, swapping 0 for 1, and vice versa. These operations can be expressed in various ways, including truth tables and Venn diagrams, which show their relation to sets of x and y (varying groups of 1s and 0s). Boole derived other operations from composites of these basic ones. In the 1930s, Claude Shannon used Boolean equations to control switching circuits, creating the first logic gates, in the form of thermionic diodes. A logic gate can use anything as an input.

References:

Boole, G., 1854. An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities (Vol. 2). Walton and Maberly.