logicism
Sign in to saveIn 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.
~50 min read
Article
17 sectionsContents
- Overview
- Origin of the name 'logicism'
- Intent, or goal, of logicism
- History
- Epistemology, ontology and logicism
- An example of a logicist construction of the natural numbers: Russell's construction in the ''Principia''
- Preliminaries
- The definition of the natural numbers
- Criticism
- The unit class, impredicativity, and the vicious circle principle
- A solution to impredicativity: a hierarchy of types
- Gödel's criticism and suggestions
- Neo-logicism<!--'Neo-Fregeanism', 'Neo-Fregeanism', 'Neo-logicism', 'Neo-Logicism', 'Neologicism', 'Scottish School (philosophy of mathematics)', 'Stanford–Edmonton School', 'Stanford-Edmonton School', 'Abstractionist Platonism', and 'Modal neo-logicism' redirect here-->
- See also
- References
- Bibliography
- External links
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 == Dedekind's path to logicism had a turning point when he was able to construct a model satisfying the axioms characterizing the real numbers using certain sets of rational numbers. This and related ideas convinced him that arithmetic, algebra and analysis were reducible to the natural numbers plus a "logic" of classes. Furthermore by 1872 he had concluded that the naturals themselves were reducible to sets and mappings. It is likely that other logicists, most importantly Frege, were also guided by the new theories of the real numbers published in the year 1872.