Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
- noun The branch of mathematics that deals with the logic and consistency of mathematical proofs, formulas, and equations.
from The Century Dictionary.
- noun The metaphysics of mathematics; the philosophy of non-Euclidean geometry and the like.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun A branch of
mathematics dealing with mathematical systems and their nature.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- noun the logical analysis of mathematical reasoning
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
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Examples
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This follows from formal theorems in metamathematics as well as from the history of science.
Smart Mobs » Blog Archive » The Peer-Production/Wisdom of Crowds Debate contd. 2006
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He also contributed to general metamathematics (the theory of consequence operation) and intuitionistic logic.
Lvov-Warsaw School Wole&324;ski, Jan 2009
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Hilbert found a much more important field to which his “metamathematics” was to be applied, namely arithmetic and analysis.
Chores 2009
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He talks about the lyrics of 1960s songwriter Randy Newman in terms of metamathematics.
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Soon it dawned on a few insightful souls, Gödel foremost among them, that this way of looking at things opened up a brand-new branch of mathematics — namely, metamathematics.
Incompatible Arrows, III: Lewis Carroll Sean 2008
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Its subject matter is mathematics and metamathematics, not physics and metaphysics.
Evolution and Indoctrination James F. McGrath 2008
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Or, perhaps we could call it "psychological metamathematics" until we can think of a better name.
why maths and science are hard Bill Kerr 2008
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In standard metamathematics, an important role for a thorough understanding of the second incompleteness theorem has been played by Löb's theorem (Löb 1955).
Paradoxes and Contemporary Logic Cantini, Andrea 2007
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On a different but important front, it can be argued that the distinction between mathematics and metamathematics cannot be articulated in the way it has been.
Category Theory Marquis, Jean-Pierre 2007
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(Curry here makes an exception for metamathematics.)
Philosophy of Mathematics Horsten, Leon 2007
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