Those who made it

Aristotle أرسطو

Systematized the syllogism, making formal logic a rigorous discipline with rules for valid deduction.

in Ancient Logic

Their works Organon

Diodorus Cronus ديودورُس كرونُس

The Megarian whose “Master Argument” and theory of the conditional shaped ancient modal logic.

in Ancient Logic

Chrysippus خريسيبوس

Developed Stoic propositional logic and truth-functional connectives, anticipating modern sentential logic.

in Ancient Logic

Their works Logical Fragments

Galen جالينوس

Physician and logician who systematized the syllogistic and is traditionally credited with the fourth figure.

in Ancient Logic

Porphyry فُرفوريوس

His Isagoge, the introduction to the Categories, framed how logic was taught for fifteen centuries.

in Ancient Logic

Their works Isagoge (Introduction)

Boethius بوثيوس

Translated and glossed Aristotle’s logic into Latin, the bridge by which the West kept the Organon for seven centuries.

in Medieval Logic

Their works On Aristotle’s Logic (translations & commentaries)

al-Kindī الكِندي

The first philosopher of the Arabs, he translated and naturalized Greek logic into the Arabic language.

in Medieval Logic

al-Fārābī الفارابي

The “Second Teacher”: the great commentator who founded the Arabic Aristotelian tradition in logic.

in Medieval Logic

Their works Kitāb al-Qiyās (The Syllogism)

Avicenna (Ibn Sīnā) ابن سينا

Reworked and surpassed the Aristotelian organon, founding a modal and temporal syllogistic of his own.

in Medieval Logic

Their works al-Shifāʾ: The Logical-Ishārāt wa-l-Tanbīhāt (Pointers & Reminders)

al-Ghazālī الغزّالي

Made Aristotelian logic the very gateway to knowledge within Islam, in his Miʿyār al-ʿIlm.

in Medieval Logic

Their works Miʿyār al-ʿIlm (The Criterion of Knowledge)

Peter Abelard بيير أبيلار

The sharpest logician of the Latin twelfth century, with an original theory of the conditional, meaning, and universals.

in Medieval Logic

Their works Dialectica

Zayn al-Dīn al-Sāwī زين الدين الساوي

An early reformer of Arabic logic who pruned it back toward the genuinely demonstrative.

in Medieval Logic

Ibn Rushd (Averroes) ابن رشد

“The Commentator,” whose epitomes of the Organon shaped logic in both Islam and Latin Europe.

in Medieval Logic

Their works Talkhīṣ Manṭiq Arisṭū (Epitome of Aristotle’s Logic)

Fakhr al-Dīn al-Rāzī فخر الدين الرازي

A pivotal post-Avicennan logician and critic who reshaped the curriculum of the science.

in Medieval Logic

al-Khūnajī الخُونَجي

In Kashf al-Asrār he advanced the post-Avicennan theory of the conditional and the syllogism.

in Medieval Logic

al-Abharī الأبهري

Author of Īsāghūjī, the most-taught logic primer in the Islamic world for seven centuries.

in Medieval Logic

Their works Īsāghūjī

Sirāj al-Dīn al-Urmawī سراج الدين الأُرموي

His Maṭāliʿ al-Anwār became a standard advanced text of post-Avicennan logic, studied through its commentaries.

in Medieval Logic

Their works Maṭāliʿ al-Anwār (The Rising-Points of Lights)

Naṣīr al-Dīn al-Ṭūsī نصير الدين الطوسي

Polymath whose commentary on Avicenna’s Ishārāt became foundational to the later logical tradition.

in Medieval Logic

Their works Sharḥ al-Ishārāt (Commentary on the Pointers)

al-Kātibī al-Qazwīnī الكاتبي القزويني

His al-Shamsiyya became the single most-commented-upon logic text in Islamic history.

in Medieval Logic

Their works al-Risāla al-Shamsiyya

Peter of Spain بطرس الإسباني

His Summulae Logicales was the standard logic textbook of the Latin Middle Ages: the Western Īsāghūjī.

in Medieval Logic

Their works Summulae Logicales

Ramon Llull رامون لُل

His Ars Magna, a combinatorial machine of rotating figures, was a distant ancestor of Leibniz’s calculus of reason.

in Medieval Logic

Their works Ars Magna (The Great Art)

Ibn Taymiyya ابن تيمية

His Refutation of the Logicians mounted the most thorough pre-modern critique of the syllogism.

in Medieval Logic

Their works al-Radd ʿalā al-Manṭiqiyyīn (Refutation of the Logicians)

Shams al-Dīn al-Samarqandī شمس الدين السمرقندي

In Qisṭās al-Afkār he built an independent system of post-Avicennan logic, prized for its theory of definition.

in Medieval Logic

Their works Qisṭās al-Afkār (The Balance of Thoughts)

William of Ockham وليم الأوكامي

Built a rigorous theory of supposition and term-semantics at the summit of Latin scholastic logic.

in Medieval Logic

Their works Summa Logicae

Quṭb al-Dīn al-Rāzī قطب الدين الرازي

The great commentator whose Taḥrīr on al-Kātibī’s Shamsiyya became the standard gateway to post-Avicennan logic.

in Medieval Logic

Their works Taḥrīr al-Qawāʿid al-Manṭiqiyya (on al-Shamsiyya)

John Buridan جان بوريدان

The greatest Latin logician of the later Middle Ages: theories of consequence, supposition, and the sophismata.

in Medieval Logic

al-Taftāzānī التفتازاني

Master of the commentary tradition; his concise Tahdhīb al-Manṭiq taught the science for centuries.

in Medieval Logic

Their works Tahdhīb al-Manṭiq

al-Sayyid al-Sharīf al-Jurjānī السيّد الشريف الجرجاني

The great glossator, whose ḥawāshī on the standard logic texts set the terms of debate for centuries.

in Medieval Logic

Jalāl al-Dīn al-Dawānī جلال الدين الدواني

A leading glossator of the later tradition, whose ḥawāshī sharpened the logical debates of the Persianate world.

in Medieval Logic

al-Akhḍarī الأخضري

His versified primer, al-Sullam, taught logic to generations across the Muslim world.

in Medieval Logic

Their works al-Sullam al-Munawraq

Mullā Ṣadrā مُلّا صدرا

Brought logic into his transcendent philosophy, the late flowering of the Illuminationist tradition.

in Medieval Logic

Gottfried Wilhelm Leibniz لايبنتس

Dreamed of a universal symbolic language that would settle disputes by calculation: an ancestor of formal logic.

in The Modern Revolution

Their works Logical Writings (Generales Inquisitiones)

Bernard Bolzano برنارد بولتسانو

In near-total isolation, anticipated logical consequence, analyticity, and semantics a century early.

in Mathematical Logic

Their works Theory of Science (Wissenschaftslehre)

Arthur Schopenhauer آرثر شوبنهاور

His logic and “eristic dialectic” anticipated several distinctions logicians would later make precise.

in Philosophical Logic

Augustus De Morgan أوغست دي مورغان

Co-founded the algebra of logic; gave the laws of negation and the first serious logic of relations.

in The Modern Revolution

Their works Formal Logic

John Stuart Mill جون ستيوارت مِل

His System of Logic codified inductive logic and the methods of empirical science.

in Philosophical Logic

Their works A System of Logic

George Boole جورج بُول

Created Boolean algebra, the first algebraic system for logic, treating propositions and classes by calculation.

in The Modern Revolution

Their works An Investigation of the Laws of Thought

John Venn جون فِن

Gave the algebra of logic its diagrams, and read inference through the lens of probability.

in Algebraic Logic

Charles Sanders Peirce تشارلز ساندرز بيرس

Invented quantification and the logic of relations independently, and pioneered truth-functional analysis.

in The Modern Revolution

Ernst Schröder إرنست شرودر

Systematized the algebra of logic and the calculus of relations into a monumental treatise.

in Algebraic Logic

Georg Cantor كانتور

Created set theory and the theory of the infinite, laying foundational concepts for modern mathematics.

in Set Theory & Foundations

Their works Foundations of a General Theory of Sets

Gottlob Frege فريغه

Founded modern logic with quantifiers, bound variables, and a fully formal language of predicates.

in The Modern Revolution

Their works Begriffsschrift

Giuseppe Peano جوزيبه بيانو

Axiomatized arithmetic and gave logic much of its modern notation (∈, ∃, ⊃).

in The Modern Revolution

Alfred North Whitehead ألفرد نورث وايتهد

With Russell, co-authored Principia Mathematica, the great attempt to ground all mathematics in logic.

in The Modern Revolution

Their works Principia Mathematica

David Hilbert هلبرت

Founded the axiomatic method and the formalist program, and made proof itself an object of study.

in Proof Theory

Their works Grundlagen der Geometrie

Ernst Zermelo تسيرملو

Axiomatized set theory, the seed of the Zermelo–Fraenkel foundation of mathematics.

in Set Theory & Foundations

Their works Investigations in the Foundations of Set Theory

Bertrand Russell برتراند رسل

Found the paradox that bears his name and built type theory, then derived mathematics from logic in Principia.

in The Modern Revolution

Their works Principia Mathematica

Jan Łukasiewicz يان وكاشيفيتش

Founded many-valued logic and Polish notation, and reread Aristotle and the Stoics with modern tools.

in Non-Classical Logics

L. E. J. Brouwer براور

Founded intuitionism, denying the unrestricted law of excluded middle and demanding constructive proof.

in Non-Classical Logics

Their works On the Foundations of Mathematics

C. I. Lewis سي. آي. لويس

Founded modern modal logic with strict implication and the hierarchy of modal systems.

in Modal Logic

Stanisław Leśniewski ستانيسواف ليشنيفسكي

Founder of the Warsaw school’s systems (protothetic, ontology, and mereology), and Tarski’s teacher.

in Mathematical Logic

Thoralf Skolem تورالف سكولم

The Löwenheim–Skolem theorem and Skolem functions: pillars of model theory and its paradoxes.

in Mathematical Logic

Ludwig Wittgenstein لودفيغ فتغنشتاين

The Tractatus: truth-tables, logical atomism, and the limits of what logic can say.

in Philosophical Logic

Their works Tractatus Logico-Philosophicus

Rudolf Carnap رودولف كارناب

The Logical Syntax of Language: logic recast as the rigorous syntax of science.

in Philosophical Logic

Their works The Logical Syntax of Language

Emil Post إميل بوست

Proved the completeness of propositional logic, founded many-valued logic, and pioneered the theory of computation.

in Mathematical Logic

Haskell Curry هاسكل كَري

Built combinatory logic and saw the deep correspondence between proofs and programs: the Curry–Howard isomorphism.

in Proof Theory

Alfred Tarski تارسكي

Gave the semantic theory of truth and founded model theory, with the undefinability theorem at its core.

in Mathematical Logic

Their works The Concept of Truth in Formalized Languages

Alonzo Church تشرتش

Created the λ-calculus and Church’s thesis, foundations of computability and of type theory.

in Computational Logic

Their works An Unsolvable Problem of Elementary Number Theory

Kurt Gödel غودل

Proved the completeness of first-order logic and the incompleteness theorems: the limits of formal systems.

in Mathematical Logic

Their works On Formally Undecidable Propositions

Jacques Herbrand جاك إربران

Herbrand’s theorem reduced first-order provability to the propositional, a root of automated reasoning.

in Computational Logic

Willard Van Orman Quine ويلارد فان أورمان كواين

Reshaped logic and its philosophy: the critique of analyticity, and an austere first-order vision.

in Philosophical Logic

Gerhard Gentzen غنتسن

Invented natural deduction and the sequent calculus, and proved cut-elimination. Structural proof theory was born.

in Proof Theory

Their works Collected Papers

Saunders Mac Lane ماك لين

Co-founded category theory with Eilenberg, giving mathematics a language of objects and arrows.

in Category Theory

Their works Categories for the Working Mathematician

Stephen Cole Kleene ستيفن كول كليني

A founder of recursion theory: the Kleene hierarchy, normal form, and the regular sets that bear his star.

in Computational Logic

Alan Turing تورنغ

Formalized computability through the Turing machine and proved the undecidability of the halting problem.

in Computational Logic

Their works On Computable Numbers

Ruth Barcan Marcus روث باركان ماركوس

Founded quantified modal logic: the Barcan formula and the logic of direct reference, before Kripke’s semantics.

in Modal Logic

J. A. Robinson ج. أ. روبنسون

The resolution principle: the inference rule at the heart of automated theorem proving and Prolog.

in Computational Logic

Paul Cohen بول كوهين

Invented forcing, proving the independence of the continuum hypothesis and the axiom of choice from ZF.

in Set Theory & Foundations

Saul Kripke كريبكي

Developed possible-worlds semantics, finally giving modal logic firm mathematical ground.

in Modal Logic

Their works Semantical Considerations on Modal Logic

Per Martin-Löf مارتن-لوف

Developed intuitionistic type theory, a constructive foundation where proofs are programs.

in Category Theory

Their works Intuitionistic Type Theory

Jean-Yves Girard جان-إيف جيرار

Created linear logic and System F, deepening the correspondence between proofs and programs.

in Proof Theory