Concept
Mathematical logic
Overview
subfield of mathematics
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
When it is admitted that classes are not things, the question arises: What do we mean by statements which are nominally about classes? Take such a statement as, "The class of people interested in mathematical logic is not very numerous." Obviously this reduces itself to, "Not very many people are interested in mathematical logic." For the sake of definiteness, let us substitute some particular number, say 3, for…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
Names Mathematical logic several times; states what Mathematical logic is.
In geometry, instead of the tedious apparatus of fallacious proofs for obvious truisms which constitutes the beginning of Euclid, the learner should be allowed at first to assume the truth of everything obvious, and should be instructed in the demonstrations of theorems which are at once startling and easily verifiable by actual drawing, such as those in which it is shown that three or more lines meet in a point.
Bertrand Russell, Mysticism and Logic and Other Essays
The author is tied to Mathematical logic in the knowledge graph.
Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Mathematical logic is; the author is tied to Mathematical logic in the knowledge graph.
Philosophers who discussed Mathematical logic
- Ernest Nagel
- Gottfried Wilhelm Leibniz
- Gershom Scholem
- Hans Reichenbach
- Kurt Gödel
- Jaakko Hintikka
- Per Martin-Löf
- René Descartes
- Michael Dummett
- Jan Łukasiewicz
- Aristotle
- George Boolos
- Solomon Feferman
- T. M. Scanlon
- Cornelius Castoriadis
- C. I. Lewis
- Alfred North Whitehead
- Saul Kripke
- Gottlob Frege
- Amartya Sen
- Richard Boyd
- Rudolf Carnap
- Alfred Tarski
- Richard Montague
Related ideas
- Formal language
- First-order logic
- Alan Turing
- Georg Cantor
- Gottfried Wilhelm Leibniz
- Gödel's completeness theorem
- Harvard University Press
- Giuseppe Peano
- Skolem's paradox
- Philosophy
- Carl Gustav Hempel
- Springer Science+Business Media
- Integer
- Karl Menger
- Compactness theorem
- Zermelo–Fraenkel set theory
- Hans Reichenbach
- Computability theory
- John von Neumann
- Infinitesimal
- Truth value
- Kurt Gödel
- Intuitionistic logic
- Foundations of mathematics
Opposing perspectives
Place in the tradition
Part of Analytic philosophy.