School
Logicism
Overview
In philosophy of mathematics, logicism is a school of thought comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
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Until symbolic logic had acquired its present development, the principles upon which mathematics depends were always supposed to be philosophical, and discoverable only by the uncertain, unprogressive methods hitherto employed by philosophers. So long as this was thought, mathematics seemed to be not autonomous, but dependent upon a study which had quite other methods than its own. Moreover, since the nature of the…
Bertrand Russell, Mysticism and Logic and Other Essays
The author is tied to Logicism in the knowledge graph.
The first serious advance in real logic since the time of the Greeks was made independently by Peano and Frege--both mathematicians. They both arrived at their logical results by an analysis of mathematics. Traditional logic regarded the two propositions, "Socrates is mortal" and "All men are mortal," as being of the same form;[14] Peano and Frege showed that they are utterly different in form. The philosophical…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
The author is tied to Logicism in the knowledge graph.
The exercise of logical reason is always concerned with these absolutely general conditions. In its broadest sense, the discovery of mathematics is the discovery that the totality of these general abstract conditions, which are concurrently applicable to the relationships among the entities of any one concrete occasion, are themselves inter-connected in the manner of a pattern with a key to it. This pattern of…
Alfred North Whitehead, Science and the modern world
States what Logicism is; the author is tied to Logicism in the knowledge graph.
Philosophers who discussed Logicism
- Crispin Wright
- Willard Van Orman Quine
- Imre Lakatos
- Bertrand Russell
- Gottlob Frege
- Louis Couturat
- Jin Yuelin
Related ideas
- Empiricism
- World Congress of Philosophy
- First-order logic
- Felix Hausdorff
- Foundationalism
- Analysis
- Gottfried Wilhelm Leibniz
- Philosophical realism
- Giuseppe Peano
- Integer
- Immanuel Kant
- If and only if
- Zermelo–Fraenkel set theory
- Finitism
- Fictionalism
- Idealism
- Analytic philosophy
- Negation
- Formalism (philosophy of mathematics)
- Kurt Gödel
- Foundations of mathematics
- Ludwig Wittgenstein
- The Principles of Mathematics
- Function (mathematics)
Place in the tradition
Part of Outline of philosophy.
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