Wittgenstein gets credit for the truth table, but Peirce sketched one decades earlier
Ludwig Wittgenstein is usually credited with inventing the truth table, in the Tractatus he finished in 1918. Yet research by Irving Anellis points to Charles Sanders Peirce drawing a truth table matrix in 1883, and a discovery in 1997 caught Wittgenstein and Bertrand Russell sketching them together on the back of a lecture transcript.
A truth table lists every possible combination of true and false for a set of inputs, one row per combination, and gives the result of a logical operation in a final column. That makes it easy to check whether an expression holds in every case, which is what logicians mean by valid, and to prove that two expressions are equivalent.
The history is tangled. The Tractatus appeared in print in 1921, the same year Emil Leon Post proposed a similar system independently. In 1997 John Shosky found tables on the reverse of a typed page from Russell's 1912 lecture on logical atomism: the one for negation in Russell's hand, the one for material implication in Wittgenstein's. Peirce, though, had an equivalent implication table in an unpublished manuscript from 1893, and an indirect table for the conditional in notes from 1883 to 1884 tied to a paper published in 1885.
Engineers rely on the idea constantly. A lookup table in a digital circuit is simply a truth table stored in hardware, and design software can pack one into an integer, one bit per row: a 32-bit number holds the complete table for five inputs. Binary addition fits the same mould, with the result bit behaving exactly like exclusive-or and a separate carry bit.
The catch is size. Every extra input doubles the number of rows, so tables become impractical for functions with many inputs, where binary decision diagrams or equations are more economical. Moving beyond two values makes it worse: adding two single digits takes four rows in binary but nine in base 3.
Source: Truth table
