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Logic
Valid inference, and what follows from what.
- ApologyPlato's account of Socrates's defense speech at his 399 BCE trial in Athens, the foundational text on the relation between philosophy and the political community that condemns it.BooksPhilosophy
- AporiaThe Greek term for productive perplexity — the recognition, often arrived at through dialectical questioning, that one does not in fact know what one thought one knew.ConceptsPhilosophyClassical Greek
- BoethiusThe late-antique Roman philosopher whose Consolation of Philosophy, written while awaiting execution, became one of the most-read texts in the medieval West, and whose translations and commentaries on Aristotle were the principal source for Latin scholastic logic for seven centuries.FiguresPhilosophyLate Antiquity
- CapitalMarx's three-volume major theoretical work of systematic political economy, analyzing the structure, dynamics, and internal contradictions of capitalist society.BooksPhilosophy
- Critical TheoryThe twentieth-century tradition founded by the Frankfurt School Institute for Social Research that integrates Marxist analysis, Hegelian dialectic, Freudian psychoanalysis, and Weberian sociology into a critical theory of contemporary society.TraditionsPhilosophy20th Century
- Decisive TreatiseAverroes's late-twelfth-century juridical defense of philosophy from within Islamic legal categories, arguing that systematic rational inquiry is religiously obligatory for those qualified and laying out the doctrine of interpretation that reconciles philosophical conclusions with scriptural authority.BooksPhilosophy
- DeductionReasoning in which the conclusion cannot be false if the premises are true.ConceptsPhilosophy
- DialecticReasoning conducted through opposition — by question and refutation, or by the development of a position through its own contradictions.ConceptsPhilosophyCross-Era
- Foundations of ArithmeticFrege's 1884 informal statement of the logicist program, arguing that arithmetic is reducible to logic and providing the conceptual foundation for the formal derivation later attempted in the Grundgesetze.BooksPhilosophy
- Functions, and why subscripts are functionsWhat the arrow in f from A to B means, why every column of a table is a function from a row to a value, and why a subscript is the same thing written differently.Math
- G.W.F. HegelThe German Idealist philosopher whose dialectical system attempted to articulate the unfolding of absolute spirit through history, nature, and consciousness as a single rational structure.FiguresPhilosophy19th Century
- Gottlob FregeThe German mathematician and philosopher whose 1879 Begriffsschrift invented modern predicate logic, whose attempt to derive arithmetic from logic founded the analytic philosophy of mathematics, and whose theory of sense and reference founded the analytic philosophy of language.FiguresPhilosophy19th Century
- HeraclitusThe Pre-Socratic philosopher of Ephesus who held that everything is in flux, that opposites are unified in their tension, and that an underlying logos orders the whole.FiguresPhilosophyPre-Socratic
- Hitchens's razorWhat can be asserted without evidence can be dismissed without evidence.ConceptsMind
- Karl MarxThe German philosopher, economist, and revolutionary whose materialist transformation of Hegelian dialectic and analysis of capitalism produced one of the most influential intellectual frameworks of the modern era.FiguresPhilosophy19th Century
- LogicThe study of valid inference — the rules by which conclusions follow from premises.ConceptsPhilosophy
- MarxismThe substantial philosophical and political tradition founded by Marx and Engels that takes the analysis of historical material conditions, class structure, and economic production as the foundation of social theory and political practice.TraditionsPhilosophy19th Century
- Nested sums, and the loop they describeTwo sigmas side by side are two nested loops.Math
- Peter AbelardMedieval logician who located morality in intention, and whose position on universals settled the dispute for a century.FiguresPhilosophy1079–1142
- PhaedoPlato's dialogue on the immortality of the soul, set on the day of Socrates's execution and containing the first systematic statement of the Theory of Forms.BooksPhilosophy
- Phenomenology of SpiritHegel's 1807 foundational work tracing the dialectical development of consciousness through successive shapes from sense-certainty through absolute knowing.BooksPhilosophy
- PlatoThe Athenian philosopher who turned Socrates's questioning into a comprehensive philosophical system and founded the institution that taught it for nine centuries.FiguresPhilosophyClassical Greek
- Products, quantifiers, grouping and joinsPi is sigma with multiplication and identical grammar.Math
- PythagorasThe Pre-Socratic philosopher and religious teacher whose Pythagorean movement combined mathematical inquiry, ascetic practice, and the doctrine of the transmigration of souls, and whose influence on subsequent philosophy and mathematics has been continuous through the Western tradition.FiguresPhilosophyPre-Socratic
- Reading a real formulaTaking the revenue formula apart mark by mark, the three checks worth running on any formula of that shape, a set of mixed exercises with no new notation, and a cheat sheet of everything in the series.Math
- RepublicPlato's encyclopedic dialogue on justice, the soul, education, the ideal city, and the philosophical knowledge required to govern it.BooksPhilosophy
- Sets, and why a table is oneThe marks for membership, subsets, size and the Cartesian product — and the one idea the rest of the series rests on: a database table is a set of tuples, which is what the word relational means.Math
- Sigma, and what it is really doingThe summation sign has exactly four parts, and every sigma you will ever meet has the same four.Math
- SkepticismThe tradition of suspending judgment where evidence does not settle a question — Pyrrhonism seeking tranquillity through balanced arguments, Academic skepticism arguing that nothing can be known.TraditionsPhilosophyc. 360 BC – present
- SocratesThe Athenian philosopher who turned philosophy from cosmology to the examined life — and was executed by the city he refused to stop questioning.FiguresPhilosophyClassical Greek
- SophistryFifth-century BC Greek teachers of rhetoric and argument who taught for a fee, and who first argued that law and custom are human conventions rather than natural facts.TraditionsPhilosophy5th–4th century BC
- SyllogismAristotle's three-line deductive argument form (e.g., All M are P; All S are M; therefore All S are P).ConceptsPhilosophy
- The sorites paradoxOne grain of sand is not a heap, and adding one grain never turns a non-heap into a heap — yet a million grains is a heap.ConceptsPhilosophy