Kurt Gödel

Kurt Gödel was a person, mathematician, who worked on many foundational issues in formal logic. Some of his most interesting results are:

Gödelization, as a procedure to bootstrap a representation of a formal system inside the formal system itself.
The completeness theorem of the predicate calculus, which proves that the theorems of the predicate calculus are all and only the logically valid formulas.
The incompleteness theorem for first order theories sufficiently powerful to express arithmetics, which states that if a theory of this kind is consistent it is also incomplete, i.e. there are statements which cannot be neither proved nor disproved in it.
The proof that, given a formal theory that can express arithmetics, if we bootstrap in it a proposition expressing the consistency of the theory itself, this proposition cannot be proved in the theory, unless we adopt a definition of "proposition expressing the consistency of the theory itself" based on stronger hypotheses than those on which the formal theory is based upon.

Note that the above descriptions are by no way rigorous. The interested reader should refer to a good textbook on formal logic.

This page is linked from: Methods of Reflection