PHIL 2100 Lecture Notes - Lecture 3: Ibm Z, Gerhard Gentzen, Rule Of Inference
9 May 2016
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Formal languages: basic symbols + formation rules. Formal systems: formal language + deductive apparatus, (this generates a special subset of formulas that are the theorems of the system. ) Axioms are formulas that are starting points , or free theorems . Inference rules specify what moves are allowed: notice that formal systems can have only axioms, only inference rules, or some of each. My starting point was this: the formalization of logical deduction, especially as it has been developed by frege, russell, and hilbert, is rather far removed from the forms of deduction used in practice in mathematical proofs. In contrast, i intended rst to set up a formal system which comes as close as possible to actual reasoning. The result was a calculus of natural deduction. His student ja skowski, developed the desired natural system in on the rules of supposi- tions in formal logic" (1934). System : symbols: , (cid:4), , formulation rules:
