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 ?
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.
Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic, Lodon, UK, 1998.
The author has organized the main body of his text in nine chapters devoted to mathematics, analysis, commonsense sets, interpretability and logic, formalism, metamathematics, second order logic, iterative hierarchies, structuralism, sets and structures, Cantors continuum hypothesis, and a wide variety of other related subjects.
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).
Introduction to Metamathematics, Amsterdam: North Holland Pub.
There was also a case, once reported in a staid medical journal, of a Birkenhead man who, after suffering an electric shock from a faulty fridge, found he could perform phenomenal feats of mental computation and became an expert in the fields of integral calculus, non-Euclidean geometry and metamathematics.
metaparadigm), also in infinite unextended concepts such as metatime, metaspace, metaconsciousness, metainformation and metalife, following on, inter alia, Godel's metamathematics and Devereux's metafamiliarity.
Greenberg, On Formally Undecidable Propositions of Law: Legal Indeterminacy and the Implications of Metamathematics, 43 HASTINGS L.
Furthermore, when Godel explained his achievements for an article by Hao Wang, he pointed out: "How indeed could one think of expressing metamathematics in the mathematical systems themselves, if the latter are considered to consist of meaningless symbols which acquire some substitute of meaning only through meta-mathematics" (Feferman, 1988, p.
Rasiowa, Helena y Roman Sikorski (1963), The Mathematics of Metamathematics, Varsovia, Polonia, Panstwowe Wydawnictwo Naukowe.