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The T-schema is often expressed in natural language, but it can be formalized in many-sorted predicate logic or modal logic; such a formalisation is called a T-theory. T-theories form the basis of much fundamental work in philosophical logic , where they are applied in several important controversies in analytic philosophy .
Analyses or descriptions of an existing theory would be considered meta-theories. [2] If the subject matter of a theoretical statement consists of one or multiple theories, it would also be called a meta-theory. [3] For mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. [4]
Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory but not the object theory. [citation needed] A formal system is determined by a formal language and a deductive system (axioms and rules of inference). The formal system can be used to ...
In general a deduction theorem needs to take into account all logical details of the theory under consideration, so each logical system technically needs its own deduction theorem, although the differences are usually minor. The deduction theorem holds for all first-order theories with the usual [2] deductive systems for first-order logic. [3]
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...
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In mathematics, the term theory is used differently than its use in science ─ necessarily so, ... One form of philosophical theory is a metatheory or meta-theory. A ...