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metalogical antinomy

First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… … Wikipedia
Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… … Wikipedia
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.[1] According to… … Wikipedia
Truth — For other uses, see Truth (disambiguation). Time Saving Truth from Falsehood and Envy, François Lemoyne, 1737 Truth has a variety of meanings, such as the state of being in accord with fact or reality … Wikipedia
Doxastic logic — is a modal logic concerned with reasoning about beliefs. The term doxastic derives from the ancient Greek δόξα, doxa, which means belief. Typically, a doxastic logic uses Bx to mean It is believed that x is the case, and the set denotes a set of… … Wikipedia