This follows from formal theorems in metamathematics as well as from the history of science.    From Wordnik.com.  [Smart Mobs » Blog Archive » The Peer-Production/Wisdom of Crowds Debate contd.] Reference

(Curry here makes an exception for metamathematics.).    From Wordnik.com.  [Philosophy of Mathematics] Reference

Its subject matter is mathematics and metamathematics, not physics and metaphysics.    From Wordnik.com.  [Evolution and Indoctrination] Reference

He talks about the lyrics of 1960s songwriter Randy Newman in terms of metamathematics.    From Wordnik.com.  [Professor Uses Mathematics to Decode Beatles Tunes] Reference

The intuitive-contentual operations with signs forms the basis of Hilbert's metamathematics.    From Wordnik.com.  [Hilbert's Program] Reference

By analogy with Hilbert's metamathematics, Tarski constructed metalogic as a distinct discipline.    From Wordnik.com.  [AXIOMATIZATION] Reference

Or, perhaps we could call it "psychological metamathematics" until we can think of a better name.    From Wordnik.com.  [why maths and science are hard] Reference

He also contributed to general metamathematics (the theory of consequence operation) and intuitionistic logic.    From Wordnik.com.  [Lvov-Warsaw School] Reference

Hilbert found a much more important field to which his “metamathematics” was to be applied, namely arithmetic and analysis.    From Wordnik.com.  [Chores] Reference

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.    From Wordnik.com.  [Category Theory] Reference

In standard metamathematics, an important role for a thorough understanding of the second incompleteness theorem has been played by Löb's theorem (Löb 1955).    From Wordnik.com.  [Paradoxes and Contemporary Logic] Reference

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.    From Wordnik.com.  [Incompatible Arrows, III: Lewis Carroll] Reference

The halting of these attempts and their futility were explained and sanctioned by the famous proof by K. Gödel (1931); the proof itself was drawn by the rigor - ous procedures of metamathematics and established that the proposition which states the noncontradictori ness of a system in which arithmetic can be developed is not decidable within this system.    From Wordnik.com.  [AXIOMATIZATION] Reference

Research into this type of question -- the subject being generally called ` metamathematics '-- continues apace.    From Wordnik.com.  [VERBATIM: The Language Quarterly Vol IV No 3] Reference

And interestingly, a major influence of metamathematics shows up in his work on Lisp, giving rise to the notion that "Numbers are Symbols Too.".    From Wordnik.com.  [Planet Lisp] Reference

One of the big intellectual foundations of functionalism is the work in computability theory that form the core of computer science and modern metamathematics.    From Wordnik.com.  [the Foresight Institute] Reference

Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics.    From Wordnik.com.  [Nothingandall] Reference

4 Early partial formalizations and metamathematics.    From Wordnik.com.  [The Development of Intuitionistic Logic] Reference

Paradoxes: between metamathematics and type-free foundations (1930 “ 1945).    From Wordnik.com.  [Paradoxes and Contemporary Logic] Reference

Paradoxes: between metamathematics and type-free foundations (1930 “ 1945) 5.1 Paradoxes and diagonalization.    From Wordnik.com.  [Paradoxes and Contemporary Logic] Reference

The problems of making its meaning more precise, of removing the confusions and misunderstandings connected with it, and of establishing its fundamental properties belong to another branch of science ” metamathematics (Tarski 1983d, p. 110).    From Wordnik.com.  [Alfred Tarski] Reference

In the ancient "the half-life function" of t h e scrolls his name also appears with higher forces of energy. t h e scriptures of Enoch, where guistics, metamathematics, meta - cosmological accounts are given of gnosticism all seek out the wisdom o t h e r life stations of intelligence. of a greater evolving universe a n d There is a story handed down in a yet all of these metasciences a r e h i d d e n mystical scroll of Light tautological a n d h e n c e limited i n which tells us how in the darkness nature; they are n o t able to bring of primordial creation Metatron the reality of universal energy b r o u g h t the Father's Plan of crea - down into the scientific experience tion to the outer worlds by al - of material realities.    From Wordnik.com.  [Recently Uploaded Slideshows] Reference

1907, 99n. 1, 173)/(Brouwer 1975, 61n. 1, 94), where the latter is the mathematical study of the language of the former in abstraction from its original meaning; this way, Brouwer made fully explicit the distinction between mathematics and (what became known as) metamathematics (e.g.    From Wordnik.com.  [The Development of Intuitionistic Logic] Reference

(Hilbert himself called this "metamathematics.".    From Wordnik.com.  ['A Matter of Temperament'] Reference