Metalogic

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Metalogic is the study of the metatheory of logic. While logic is the study of the manner in which logical systems can be used to decide the correctness of arguments, metalogic studies the properties of the logical systems themselves. According to Geoffrey Hunter, while logic concerns itself with the "truths of logic," metalogic concerns itself with the theory of "sentences used to express truths of logic"'

The basic objects of study in metalogic are formal languages, formal systems, and their interpretations. The study of interpretation of formal systems is the branch of mathematical logic known as model theory, while the study of deductive apparatus is the branch known as proof theory.

Results in metalogic

Results in metalogic consist of such things as formal proofs demonstrating the soundness of particular formal language.

Major results in metalogic include:

• The completeness and consistency of first-order logic.
• The undecidability of first-order logic.
• The deduction theorem.
• Gödel's completeness theorem.
• Gödel's incompleteness theorems.

References

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Last updated on Wednesday January 16, 2008 at 19:09:34 PST (GMT -0800)
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