Part Ten X › Division I I › Section 10/11 10/11

History and Philosophy of Logic

Subject Outline

AHistory of logic
- 1Ancient logic
  - aPrecursors of ancient logic: contributions of the Sophists, Socrates, and Plato to theories of language and the axiomatic method
  - bAristotle and the logic of predicates: theories of the structure of language, theories of opposition and conversion, development of syllogistic and modal logic
  - cLater developments in the logic of predicates: contributions of Theophrastus and Galen
  - dFounding of the logic of propositions: contributions of Theophrastus and the Megarians, Stoic logic
- 2Medieval logic
  - aDevelopment of medieval logic: Arabic contributions, disputes between the "old logic" and the "new logic" after the translation of Aristotle's Organon, summations by William of Sherwood and Peter of Spain
  - bMedieval theories of language and their relation to the development of logic: the theory of categorematic and syncategorematic terms, the theory of supposition
  - cMedieval developments in formal logic: the logic of predicates, of propositions, and of modal expressions; logical fallacies and paradoxes
- 3Modern logic from the Renaissance to the 20th century
  - aLogic in the Renaissance: the influence of Neoplatonism and of the rise of the natural sciences, the logics of Petrus Ramus and of Port-Royal
  - bThe rise of mathematical logic during the Enlightenment: contributions of Leibniz (e.g his general calculus of reasoning and general methodology), the search for clarity and the use of diagrams
  - cDevelopment of mathematical logic in the 19th century: expansions of syllogistic, Boole's algebra of logic, refinements of the calculus, the study by Frege and Cantor of the relation between logic and the foundations of mathematics
- 4Logic in the 20th century
  - aThe conflict of Logicism, the view that mathematics is a continuation of logic, with Intuitionism and Formalism: Russell's Logicism and the theory of types, Brouwer's Intuitionism, Hilbert's Formalism
  - bDevelopments in the logic of propositions and in the logic of predicates
  - cMetalogical studies: the study of the properties of axiomatized systems; syntax and semantics as metalogical disciplines
- 5Logic in the East
  - aIndian logic: its origins in the commentaries on the scriptural texts called sutras, special problems in grammar and special types of inference, interest in the logical implications of the notion of negation
  - bChinese logic: its origins in reflections on the characteristics of controversies between the major philosophies of Confucianism, Taoism, and Moism; its neglect after the establishment of Neo-Confucianism in the 11th century ad
BPhilosophy of logic
- 1The organization of logic as a discipline
  - aThe nature and varieties of logic: differing conceptions of its field and scope, varieties of logical symbolism
  - bFeatures and problems of logic: concerns with logical semantics or model theory, questions of the limitations of logic, Godel's incompleteness theorems, the question of logic and computability
- 2Issues and developments in the philosophy of logic
  - aProblems in meaning and truth: logical semantics of modal concepts, logic and informativeness
  - bProblems of ontology: problems concerning individuation and existence
  - cAlternative logics: modal logics, intuitionistic logic