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- Jaroslav Peregrin, Absolute and Relative Concepts in Logic.It is a common wisdom that whereas consequence or entailment is a semantic concept, provability is a syntactic concept. However, what exactly does this mean? What is provability? In the traditional, intuitive sense, to prove something is to demonstrate its truth, and indeed the Latin word for proof is demonstratio. Hence in this sense, we cannot prove something unless it is true. Now in the course of his well known proof of the incompleteness of arithmetic, Gödel showed that provability within the axiomatic system of Peano arithmetic (PA) can be reconstructed as a number-theoretic predicate Pr and he showed that within the system there exists a statement G so that..No categoriesIn my reading list | Discuss this article | Edit | Categorize |My bibliography
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The whole development of modern logic is marked by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. The heart of theories of systems of formal logic are usually considered to be proofs of soundness and (in)completeness - in effect results concerning the relationship between proof-theoretically delimited theorems and model-theoretically delimited tautologies. Those founding fathers of modern logic who saw logic as primarily a matter of rules, people (...)
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