Philosophy of Logic
History of logic
Ancient Egyptians inventing Geometry and triangulation in order to be able to delineate property lines destroyed by Nile flooding, through use of known objects such as the pyramids.
Precursors: Sophists, Socrates, and Plato contributing to theories of language and the axiomatic method. Euclid's Elements, using basic principles, axioms, and derived theorems.in Geometry. For Greeks the Elements was what science should look like.
Aristotle showed that all science had a geometric structure. Aristotle and the logic of predicates: theories of the structure of language; theories of opposition and conversion; development of syllogistic and modal logic.
Later development in the logic of predicates: contributions of Theophrastus and Galen.
Founding of the logic of propositions: contributions of Theophrastus and the Megarians; Stoic logic.
Arabic contributions; disputes between the ‘old logic’ and the ‘new loigc’ after the translation of Aristotle’s Organon; summations by William of Sherwood and Peter of Spain.
Medieval theories of language: the theory of categorematic and syncategorematic terms. The theory of supposition.
Developments in formal logic: the logic of predicates, propositions, and of modal expressions. Logical fallacies and paradoxes.
Modern logic from Renaissance to the 20th century
Influence of Neoplatonism and the rise of the natural sciences. The experimental method was born. Logics of Petrus Ramus and Port-Royal.
Mathematical logic during the Enlightenment. Much greater use of mathematical methods. Leibniz e.g. his general calculus of reasoning and general methodology. The search for clarity and use of diagrams.
19th century developments: expansions of syllogistic, Boole’s algebra of logic, refinements of the calculus, the study by Frege and Cantor. George Boole, 1854 The Laws of Thought using methods of algebra to the study of logic, which revolutionised logic (akin to Copernicus, Newton, Einstein in Physics).
Logic in the 20th century
Conflict of Logicism, the view mathematics is a continuation of logic, with Intuitionism and Formalism. Russell’s Logicism and the theory of types, Brouwer’s Intuitionism, Hilbert’s Formalism.
Logic of propositions and logic of prediates. Metalogical studies: the study of the properties of axiomatised systems, syntax and semantics as metalogical disciplines.
Logic in the East
Indian logic: in the sutras, special problems in grammar and special types of inference.
Chinese logic: it origins in reflections on the characteristics of controversies betweenthe majore philosophies of Confucianism, Taoism, and Moism, its neglect after the establishement of Neo-Confucianism in the 11th century.
Philosophy of logic
Organisation of logic as a discipline
Nature and variety of logic. The transfer towards Mathematical Logic. Varieties of logical symbolism.
Features and problems of logic: concerns with logical semantics or model theory, questions of the limitations of logic, Gödel’s (Godel) incompleteness theorems, the question of logic and computability.
Issues and developments in the philosophy of logic
Concerned with problematising notions such as reference, predication, identity, truth, negation, quantification, existence, necessity, definition and entailment. See Gottlob Frege. Links to Philosophy of Mind.
Problems in meaning and truth: logical semantics of modal concepts, logic and informativeness.
Problems of ontology: individuation and existence.
The place of logic among the sciences and disciplines
- Relation of logic to mathematics. Mathematical Logics. Godel's incompleteness theorem.
- Relation of logic to computer science: the connection between automata theory and logical study of formal languages, mechanical theorem proving.
- The role of logic in the methodology of the empirical sciences.
- Interrelations of logic and linguistic theory.
- Logic in psychology e.g. as a conceptual framework for psychological theorising
- The role of logic in legal and practical reasoning
- Diverse views about the place of logic in the educational curriculum.
- The relation of logic to metaphysics and to other branches of philosophy.