The Canon · works of discovery
The mother books
The primary texts: works of discovery, not exposition. Read in the order they were written; each is a link in the chain.
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Organon
The founding corpus of Western logic: the categories, the proposition, and the syllogistic of demonstration.
in Ancient Logic -
Logical Fragments
The first propositional logic: connectives and inference schemata, two millennia before Frege.
in Ancient Logic -
Isagoge (Introduction)
The introduction to Aristotle’s logic that every logician (Greek, Arabic, and Latin) began with for fifteen centuries.
in Ancient Logic -
On Aristotle’s Logic (translations & commentaries)
The translations and commentaries through which the Latin West knew Aristotle’s logic for seven hundred years.
in Medieval Logic -
Kitāb al-Qiyās (The Syllogism)
كتابُ القياس
The “Second Teacher” founds the Arabic Aristotelian tradition by reading, correcting, and teaching the Organon anew.
in Medieval Logic -
al-Shifāʾ: The Logic
الشفاء: المنطق
A vast reworking of the organon, extended with a modal and temporal syllogistic of his own.
in Medieval Logic -
al-Ishārāt wa-l-Tanbīhāt (Pointers & Reminders)
الإشاراتُ والتنبيهات
His most influential late work, terse “pointers” that generations of logicians built their commentaries upon.
in Medieval Logic -
Miʿyār al-ʿIlm (The Criterion of Knowledge)
معيارُ العلم
Brings Aristotelian logic into Islamic orthodoxy, recast as the very measure of sound knowledge.
in Medieval Logic -
Dialectica
The boldest logic of the Latin twelfth century, with an original theory of the conditional and of meaning.
in Medieval Logic -
Talkhīṣ Manṭiq Arisṭū (Epitome of Aristotle’s Logic)
تلخيصُ منطق أرسطو
The Commentator’s epitomes of the Organon, which, in Latin, taught logic to all of medieval Europe.
in Medieval Logic -
Summulae Logicales
The standard logic textbook of the Latin Middle Ages: the Western parallel to al-Abharī’s Īsāghūjī.
in Medieval Logic -
Īsāghūjī
إيساغوجي
The little primer that taught logic to the Islamic world for seven centuries. Memorized, glossed, beloved.
in Medieval Logic -
Maṭāliʿ al-Anwār (The Rising-Points of Lights)
مطالعُ الأنوار
A standard advanced text of post-Avicennan logic, studied for centuries through its great commentary.
in Medieval Logic -
Sharḥ al-Ishārāt (Commentary on the Pointers)
شرحُ الإشارات
The definitive defence-and-commentary on Avicenna’s Ishārāt, itself foundational to all later Islamic logic.
in Medieval Logic -
al-Risāla al-Shamsiyya
الرسالةُ الشمسية
The single most-commented-upon logic text in Islamic history. The very standard of post-Avicennan logic.
in Medieval Logic -
Qisṭās al-Afkār (The Balance of Thoughts)
قسطاسُ الأفكار
An independent system of post-Avicennan logic, with its own treatment of definition and the syllogism.
in Medieval Logic -
Ars Magna (The Great Art)
A combinatorial “logic machine” of rotating figures, a distant ancestor of Leibniz’s dream of calculation.
in Medieval Logic -
al-Radd ʿalā al-Manṭiqiyyīn (Refutation of the Logicians)
الردُّ على المنطقيين
The most thorough pre-modern critique of the syllogism, anticipating, some argue, modern objections by centuries.
in Medieval Logic -
Summa Logicae
The summit of Latin scholastic logic: a rigorous theory of supposition and the semantics of terms.
in Medieval Logic -
Taḥrīr al-Qawāʿid al-Manṭiqiyya (on al-Shamsiyya)
تحريرُ القواعد المنطقية
The most studied commentary on al-Kātibī’s Shamsiyya, itself the gateway text for centuries of students.
in Medieval Logic -
Tahdhīb al-Manṭiq
تهذيبُ المنطق
A concise masterwork that distilled the whole science into a few pages, taught and glossed for centuries.
in Medieval Logic -
al-Sullam al-Munawraq
السُّلَّمُ المُنوْرَق
Logic in verse. The rhymed ladder by which countless students first climbed into the science.
in Medieval Logic -
Logical Writings (Generales Inquisitiones)
The first sustained calculus of reasoning: a symbolic algebra of concepts, two centuries ahead of its time.
in The Modern Revolution -
Theory of Science (Wissenschaftslehre)
Anticipated logical consequence, analyticity, and the semantic conception of validity a century before Tarski.
in Mathematical Logic -
A System of Logic
The great codification of inductive logic and the methods of empirical inference.
in Philosophical Logic -
Formal Logic
The laws of negation that bear his name, and the first serious logic of relations.
in The Modern Revolution -
An Investigation of the Laws of Thought
Logic recast as algebra. The birth of Boolean algebra, and of the whole algebraic tradition.
in The Modern Revolution -
Begriffsschrift
The birth of modern logic: quantifiers, bound variables, and a fully formal language of predicates.
in The Modern Revolution -
Foundations of a General Theory of Sets
The creation of set theory and the transfinite: rigorously, infinitely many sizes of infinity.
in Set Theory & Foundations -
Grundlagen der Geometrie
The modern axiomatic method made exact, and the launch of Hilbert’s formalist program.
in The Modern Revolution -
On the Foundations of Mathematics
Intuitionism: the constructivist challenge that denies the law of excluded middle its unrestricted reign.
in Non-Classical Logics -
Investigations in the Foundations of Set Theory
The first axiomatization of set theory: the seed that grows into ZF and the foundations of mathematics.
in Set Theory & Foundations -
Principia Mathematica
The monumental logicist attempt to derive mathematics from logic, and the theory of types it required.
in The Modern Revolution -
Tractatus Logico-Philosophicus
Truth-tables, logical atomism, and a vision of the proposition as a picture of fact.
in Philosophical Logic -
On Formally Undecidable Propositions
The incompleteness theorems: every sufficiently strong, consistent formal system leaves truths it cannot prove.
in Mathematical Logic -
The Concept of Truth in Formalized Languages
A rigorous semantic theory of truth, and the undefinability theorem: truth outruns any single language.
in Mathematical Logic -
The Logical Syntax of Language
Logic recast as the exact syntax of scientific language. The high-water mark of logical positivism.
in Philosophical Logic -
Collected Papers
Natural deduction and the sequent calculus: the founding of structural proof theory and cut-elimination.
in Proof Theory -
An Unsolvable Problem of Elementary Number Theory
The λ-calculus and the first undecidability result. A foundation of computation, and of type theory.
in Computational Logic -
On Computable Numbers
The Turing machine: a precise definition of computation, and the undecidability of the halting problem.
in Computational Logic -
Semantical Considerations on Modal Logic
Possible-worlds semantics: the model theory that finally gave modal logic firm mathematical ground.
in Modal Logic -
Categories for the Working Mathematician
Category theory presented as a foundational language. Objects, arrows, and the universal among them.
in Category Theory -
A Mathematical Introduction to Logic
The gold-standard textbook for first-order logic, completeness, and the beginnings of model theory.
in Mathematical Logic -
Intuitionistic Type Theory
Dependent type theory: a constructive foundation in which proofs are programs and propositions are types.
in Category Theory -
An Introduction to Non-Classical Logic
A single, lucid path through modal, many-valued, relevant, and fuzzy logics, building from the systems up.
in Non-Classical Logics -
Homotopy Type Theory
Types as spaces, and the univalence axiom: a new, computational foundation for mathematics.
in Cutting-Edge Research