History of Logic

Diodorus Cronus and Philo debated the truth-conditions of conditionals and modality, seeding propositional logic and famous paradoxes.

The founder of logic analysed valid inference into the syllogism, giving reasoning its first formal system — dominant for two thousand years.

Aristotle's successor extended the syllogism to hypothetical and modal forms, taking the first steps beyond his teacher's system.

Aristotle's collected logical works — the 'instrument' of thought — laid out terms, propositions, and the theory of the syllogism.

The Stoics developed a logic of whole statements linked by 'if', 'and', and 'or' — the ancestor of modern propositional calculus.

The great Stoic built a logic of propositions and inference schemes — an approach only fully rediscovered in the modern era.

The great physician also wrote on logic, systematising the syllogistic figures and defending reasoning as the physician's essential tool.

Porphyry's introduction to Aristotle's Categories framed the medieval problem of universals and became the standard first logic textbook for a thousand years.

By translating and commenting on Aristotle, Boethius handed the logic of antiquity to the Latin Middle Ages that followed.

The Persian philosopher reworked Aristotelian logic, developing an original theory of modal and temporal reasoning far ahead of its time.

The sharpest logician of the early scholastics analysed meaning, entailment, and the logic of conditionals with new rigour.

His compact textbook of terminist logic taught supposition theory to generations of students and dominated the medieval curriculum.

The 'Subtle Doctor' sharpened medieval modal logic and the analysis of consequence, influencing debates on necessity and possibility.

Master of the theory of supposition and of 'Ockham's razor', he pushed medieval logic to a high point of technical subtlety.

He advanced the theory of consequences and tackled self-referential paradoxes like the Liar, prefiguring modern semantic puzzles.

Francis Bacon proposed a new inductive method against Aristotle's deductive 'Organon', laying the logical groundwork of empirical science.

Leibniz dreamed of a 'characteristica universalis' and a calculus of reasoning, so that thinkers could settle disputes by saying 'let us calculate'.

The most influential logic textbook of its age fused Aristotelian rules with Cartesian method and early ideas about probability.

He formalised the logic of relations and gave the duality laws — De Morgan's laws — still taught in every logic and computing course.

Boole recast logic as algebra where variables take the values true and false — the mathematics that would one day run every computer.

John Stuart Mill codified inductive reasoning into his famous methods of agreement and difference — the logic of experimental inquiry.

Boole's masterwork built an algebra of logic and probability, the direct ancestor of the Boolean logic inside digital circuits.

William Stanley Jevons refined Boole's algebra and built a 'logical piano' that mechanically drew conclusions — a forerunner of the computer.

Frege invented modern predicate logic with quantifiers, the greatest advance in logic since Aristotle, and tried to derive arithmetic from it.

Peano's axioms for the natural numbers and his crisp logical notation shaped how mathematics is written to this day.

This slim book introduced quantifiers and a fully formal language of proof — the birth of modern mathematical logic.

John Venn's overlapping circles gave symbolic logic and set relations an intuitive picture still taught in every classroom today.

Independently of Frege, Peirce developed quantifiers and the logic of relations, and introduced truth tables and the study of signs.

Schröder's monumental 'Algebra of Logic' synthesised Boole, Peirce, and De Morgan into the most complete treatment of its era.

Bertrand Russell's paradox of 'the set of all sets that don't contain themselves' exposed a crack in Frege's foundations of mathematics.

Russell and Whitehead's three volumes tried to derive all mathematics from logic, taming paradox with a theory of types.

L. E. J. Brouwer rejected the law of excluded middle for infinite sets, founding a constructive logic where to prove is to build.

This surprising result showed that first-order theories cannot pin down the size of their models, exposing the limits of formal description.

Tarski gave a rigorous definition of truth for formal languages and founded model theory, linking logic to mathematical structure.

Church invented the lambda calculus, proved key problems unsolvable, and — with Turing — pinned down the very notion of computability.

His incompleteness theorems proved no consistent formal system rich enough for arithmetic can prove all truths — nor its own consistency.

Turing's abstract machine defined the limits of mechanical reasoning and proved the halting problem undecidable, founding computer science.

Gerhard Gentzen invented natural deduction and the sequent calculus, giving proof its modern structure and founding proof theory.

Claude Shannon showed that Boolean algebra describes electrical switching circuits — the insight that made digital computers possible.

Robinson's resolution method gave machines a single, mechanisable rule of inference, launching automated reasoning and logic programming.

The discovery that proofs are programs and propositions are types fused logic with computation, shaping modern type theory and proof assistants.

Stephen Cook proved satisfiability of logic formulas is NP-complete, framing the P vs NP problem at the heart of computational complexity.

The language Prolog let programmers state facts and rules in logic and let the machine deduce the answers — reasoning as computation.

Per Martin-Löf built a constructive type theory that unified logic, computation, and mathematics — the foundation of today's proof assistants.

Kripke's possible-worlds semantics gave modal logic — the logic of necessity and possibility — a rigorous and enormously fruitful foundation.

Lotfi Zadeh let truth take any value between 0 and 1, giving machines a way to reason with vagueness in control systems and AI.

As machines argue and persuade, classical logic and the study of fallacies become practical tools for thinking clearly among algorithms.