On Three-Valued Logic

Introduction

Łukasiewicz published the short paper in 1920 in the Lwów journal “Ruch Filozoficzny”. Besides “true” (1) and “false” (0) it introduces a third value (1/2), interpreted as “possible”, for contingent statements about the future, so that some classical laws, such as the law of excluded middle, no longer hold generally. The problem goes back to Aristotle’s discussion of tomorrow’s sea battle in “On Interpretation” 9. The motive was philosophical: Łukasiewicz wanted to show that indeterminism and human freedom can be stated consistently, against the view that every true sentence is true eternally. Together with Emil Post’s independent work (1921), the paper stands at the beginning of modern many-valued logic, which Łukasiewicz later extended to infinitely many values.

Connections

Builds on

• Organonc. 350 BCE · Aristotle

More works by Jan Łukasiewicz

• 1951Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic