# 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·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
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]

## metamathematics

the logical analysis of the fundamental concepts of mathematics, as function, number, etc. — metamathematician, n. — metamathematical, adj.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 metamathematics - the logical analysis of mathematical reasoningmath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementpure mathematics - the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
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He discusses topics like Plato's "line," Leibnizian metaphysics, Berkeleyan metalogical signs and master arguments, the second-order idealism of David Hume, Kantian ethics and the "fate of reason," metamathematical interpretations of free will and determinism, and time-evolution in random universes.
Kurt Godel (1906-1978) powerfully demonstrated the paradoxically incomplete mathematics by ingeniously constructing a metamathematical argument about arithmetic (Gamwell, 2016).
Nonetheless, this points in the right direction: we can ask metamathematical questions, and since Godel, we know that the task of mathematicians is to investigate the properties of the real structures they create.
Lucas, that metamathematical theorems imply the existence of consciousness, a point supported by Penrose, based on his experience of mathematical intuition, and its role in guiding discovery in mathematics.
The proposition undecidable in the system PM is thus decided by metamathematical arguments" (p.