# Hilbert II

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Glossary

### Basic Rule, Meta Rule

From the formal viewpoint mathematical logic is nothing else then string manipulation. On initial given strings (axioms) simple rules are applied to get new strings (derived propositions). These rules are called basic rules and could also be applied on the new strings to get further strings and so on. Some of those deductions are done always the same way and lead to a new rule that enables shorter derivations. With common mathematical methods it will be proved, that with this new meta rule no entirely new strings could be deduced. Each application result of the new rule could also be gained by (perhaps cumbersome) use of basic rules.

Therefore it is always possible to replace the use of meta rules by basic rules. This transformation can also be done automatically. Whoever distrusts the proof of the meta rule could derive a string also with the basic rules alone. The situation gets complicated by the introduction of language extensions, which the meta rule could premise. It is also possible that the transformation can not be done in reality because the appropriate derivation with basic rules is simply too long. See also first order predicate calculus.

### Predicate Calculus

Basis for the mathematical argumentation is the so called predicate calculus. It is based on the propositional calculus. It is a system of symbolic logic that represents individuals and predicates and quantification over individuals as well as the relations between propositions.

### QEDEQ

QEDEQ is an extension of Q.E.D. to get a symmetric word. Q.E.D. stands for Latin "quod erat demonstrandum". This made-up word occurs seldom in texts, that way an internet search for QEDEQ normally leads to pages that are connected with this project.

update 2014-01-20 09:20:48+0100