|Proof Theory: mathematics, logic is about the existence or nonexistence of finite strings of symbols allowing to derive a statement. Therefore, proof theory is a part of the syntax, as opposed to the model theory, which belongs to the semantics. See also model theory, syntax, semantics._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Object language/metalanguage/Field: e.g. proof theory: there is no object level. - Object level: here the statements are without reference to sentences or formulas - and not on axioms, rules of inference or derivatives.
Proof theory: working with math. entities._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980