Mirqāt The Ascent of Logic

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.

  1. c. 350 BCE Canon Greek

    Aristotle

    Organon

    The founding corpus of Western logic: the categories, the proposition, and the syllogistic of demonstration.

    in Ancient Logic
  2. c. 250 BCE Canon Greek

    Chrysippus & the Stoics

    Logical Fragments

    The first propositional logic: connectives and inference schemata, two millennia before Frege.

    in Ancient Logic
  3. c. 270 Canon Greek

    Porphyry

    Isagoge (Introduction)

    The introduction to Aristotle’s logic that every logician (Greek, Arabic, and Latin) began with for fifteen centuries.

    in Ancient Logic
  4. c. 520 Canon Latin Commentary

    Boethius

    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
  5. c. 940 Canon Arabic

    al-Fārābī

    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
  6. c. 1027 Canon Arabic

    Ibn Sīnā (Avicenna)

    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
  7. c. 1030 Canon Arabic

    Ibn Sīnā (Avicenna)

    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
  8. c. 1095 Canon Arabic

    al-Ghazālī

    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
  9. c. 1120 Canon Latin

    Peter Abelard

    Dialectica

    The boldest logic of the Latin twelfth century, with an original theory of the conditional and of meaning.

    in Medieval Logic
  10. c. 1170 Canon Arabic Commentary

    Ibn Rushd (Averroes)

    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
  11. c. 1245 Canon Latin

    Peter of Spain

    Summulae Logicales

    The standard logic textbook of the Latin Middle Ages: the Western parallel to al-Abharī’s Īsāghūjī.

    in Medieval Logic
  12. c. 1250 Canon Arabic

    al-Abharī

    Īsāghūjī

    إيساغوجي

    The little primer that taught logic to the Islamic world for seven centuries. Memorized, glossed, beloved.

    in Medieval Logic
  13. c. 1250 Canon Arabic

    Sirāj al-Dīn al-Urmawī

    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
  14. c. 1250 Canon Arabic Commentary

    Naṣīr al-Dīn al-Ṭūsī

    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
  15. c. 1265 Canon Arabic

    al-Kātibī al-Qazwīnī

    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
  16. c. 1290 Canon Arabic

    Shams al-Dīn al-Samarqandī

    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
  17. c. 1305 Canon Latin

    Ramon Llull

    Ars Magna (The Great Art)

    A combinatorial “logic machine” of rotating figures, a distant ancestor of Leibniz’s dream of calculation.

    in Medieval Logic
  18. c. 1320 Canon Arabic

    Ibn Taymiyya

    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
  19. c. 1323 Canon Latin

    William of Ockham

    Summa Logicae

    The summit of Latin scholastic logic: a rigorous theory of supposition and the semantics of terms.

    in Medieval Logic
  20. c. 1335 Canon Arabic Commentary

    Quṭb al-Dīn al-Rāzī

    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
  21. c. 1360 Canon Arabic

    al-Taftāzānī

    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
  22. c. 1535 Canon Arabic

    al-Akhḍarī

    al-Sullam al-Munawraq

    السُّلَّمُ المُنوْرَق

    Logic in verse. The rhymed ladder by which countless students first climbed into the science.

    in Medieval Logic
  23. c. 1686 Canon Latin

    Gottfried Wilhelm Leibniz

    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
  24. 1837 Canon German

    Bernard Bolzano

    Theory of Science (Wissenschaftslehre)

    Anticipated logical consequence, analyticity, and the semantic conception of validity a century before Tarski.

    in Mathematical Logic
  25. 1843 Canon English

    John Stuart Mill

    A System of Logic

    The great codification of inductive logic and the methods of empirical inference.

    in Philosophical Logic
  26. 1847 Canon English

    Augustus De Morgan

    Formal Logic

    The laws of negation that bear his name, and the first serious logic of relations.

    in The Modern Revolution
  27. 1854 Canon English

    George Boole

    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
  28. 1879 Canon German

    Gottlob Frege

    Begriffsschrift

    The birth of modern logic: quantifiers, bound variables, and a fully formal language of predicates.

    in The Modern Revolution
  29. 1883 Canon German

    Georg Cantor

    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
  30. 1899 Canon German

    David Hilbert

    Grundlagen der Geometrie

    The modern axiomatic method made exact, and the launch of Hilbert’s formalist program.

    in The Modern Revolution
  31. 1907 Canon Dutch

    L. E. J. Brouwer

    On the Foundations of Mathematics

    Intuitionism: the constructivist challenge that denies the law of excluded middle its unrestricted reign.

    in Non-Classical Logics
  32. 1908 Canon German

    Ernst Zermelo

    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
  33. 1910–13 Canon English

    Whitehead & Russell

    Principia Mathematica

    The monumental logicist attempt to derive mathematics from logic, and the theory of types it required.

    in The Modern Revolution
  34. 1921 Canon German

    Ludwig Wittgenstein

    Tractatus Logico-Philosophicus

    Truth-tables, logical atomism, and a vision of the proposition as a picture of fact.

    in Philosophical Logic
  35. 1931 Canon German

    Kurt Gödel

    On Formally Undecidable Propositions

    The incompleteness theorems: every sufficiently strong, consistent formal system leaves truths it cannot prove.

    in Mathematical Logic
  36. 1933 Canon Polish

    Alfred Tarski

    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
  37. 1934 Canon German

    Rudolf Carnap

    The Logical Syntax of Language

    Logic recast as the exact syntax of scientific language. The high-water mark of logical positivism.

    in Philosophical Logic
  38. 1934–35 Canon German

    Gerhard Gentzen

    Collected Papers

    Natural deduction and the sequent calculus: the founding of structural proof theory and cut-elimination.

    in Proof Theory
  39. 1936 Canon English

    Alonzo Church

    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
  40. 1936 Canon English

    Alan Turing

    On Computable Numbers

    The Turing machine: a precise definition of computation, and the undecidability of the halting problem.

    in Computational Logic
  41. 1963 Canon English

    Saul Kripke

    Semantical Considerations on Modal Logic

    Possible-worlds semantics: the model theory that finally gave modal logic firm mathematical ground.

    in Modal Logic
  42. 1971 Canon English

    Saunders Mac Lane

    Categories for the Working Mathematician

    Category theory presented as a foundational language. Objects, arrows, and the universal among them.

    in Category Theory
  43. 1972 Study English

    Herbert Enderton

    A Mathematical Introduction to Logic

    The gold-standard textbook for first-order logic, completeness, and the beginnings of model theory.

    in Mathematical Logic
  44. 1984 Canon English

    Per Martin-Löf

    Intuitionistic Type Theory

    Dependent type theory: a constructive foundation in which proofs are programs and propositions are types.

    in Category Theory
  45. 2001 Study English

    Graham Priest

    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
  46. 2013 Canon English

    The Univalent Foundations Program

    Homotopy Type Theory

    Types as spaces, and the univalence axiom: a new, computational foundation for mathematics.

    in Cutting-Edge Research