|Derivability: question which statements can be obtained according to the rules of a calculus.|
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|Thiel I 97
Derivability/Hilbert/Thiel: The methods used for the proof of the non-derivability of a formula from others by means of given derivation rules have been given for the first time by Bernays in the Hilbert school. Bernays postdoctoral thesis for the proof of the independence of axiom systems of classical propositional logic. Neither of these axioms is to be derived from the others.
Classic: ~~p > p
effective: p > ~~p ....+...I 98 102
Axiomatic derivations of logical sentences were unrivaled up to the twenties in this form, then alternative procedure calculus of the "natural concluding" were developed, whose rule usually bring exactly one logical symbol into a conclusion chain or eliminate. The actual kind of mathematical approach is closer than the axiomatic approach.
Philosophie und Mathematik Darmstadt 1995