metamathematics


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met·a·math·e·mat·ics

 (mĕt′ə-măth′ə-măt′ĭks)
n. (used with a sing. verb)
The branch of mathematics that deals with the logic and consistency of mathematical proofs, formulas, and equations.

met′a·math′e·mat′i·cal adj.
met′a·math′e·ma·ti′cian (-mə-tĭsh′ən) n.

metamathematics

(ˌmɛtəˌmæθɪˈmætɪks)
n
(Mathematics) (functioning as singular) the logical analysis of the reasoning, principles, and rules that control the use and combination of mathematical symbols, numbers, etc
ˌmetaˌmatheˈmatical adj
ˌmetaˌmathemaˈtician n

met•a•math•e•mat•ics

(ˌmɛt əˌmæθ əˈmæt ɪks)

n. (used with a sing. v.)
the study of fundamental concepts of mathematics, as number and function.
[1885–90]
met`a•math`e•mat′i•cal, adj.

metamathematics

the logical analysis of the fundamental concepts of mathematics, as function, number, etc. — metamathematician, n. — metamathematical, adj.
See also: Mathematics
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.metamathematics - the logical analysis of mathematical reasoning
math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
pure mathematics - the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
Translations
References in periodicals archive ?
In contrast with this, meta- can actually be traced back in history in a way explaining how constructions like metamathematics, metacommunication, meta-analysis (metanalysis*), metapolitics, metaphrastic, metamorphize, metaphor, metathesis, metamorphism, or metamorphosis have come up.
This volume collects the author's writings on metamathematics and the history of philosophy, focusing on classical, medieval, and Enlightenment philosophy, with two mathematical chapters offering proofs on related problems of uncertainty and time-evolution and theoretical physics.
Pelletier, "Metamathematics of fuzzy logics by Petr Hajek," Bulletin of Symbolic Logic, vol.
Tarski, Alfred (1983), Logic, Semantics, Metamathematics, J.
Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic, Dordrecht, The Netherlands, 1998.
Lucas was considering the consequences of Godel's famous incompleteness theorem (52,53) in metamathematics, which states that any system of axioms containing arithmetic must necessarily contain statements that can be seen to be true but are unprovable.
Introduction to Mathematics of Metamathematics. Amsterdam: North-Holland Publ.
Even if we use a physical object to describe a physical object, or a formal structure to describe a formal structure (as in metamathematics), the distinction between our sets (a) and (b) prevents the model from criticisms like Postal's.
Kleene, Introduction to metamathematics, North-Holland (1959), Chapt.
--, 1956, Logic, Semantics, Metamathematics, Oxford University Press, Oxford.
(Note that metametaphysics is not another discipline, it is part of metaphysics (as metamathematics is part of mathematics).