## A Theory of Formal Deducibility |

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### Contents

Formal Systems and Formal Reasoning | 6 |

The Finite Positive Connectives | 24 |

Quantifiers | 65 |

Copyright | |

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### Common terms and phrases

A A B adjoining adjunctor apply argument autonymous axiom axiom schemes called Carnap Chapter characteristic variable classical component compound propositions conclusion connectives consider deduction deduction theorem defined definition elementary propositions elementary statement elementary theorem elimination theorem episystems equivalent expression finite number formal system functors Gentzen Hence holds hypothesis induction inference infinitely inner system interpretation introduced intuitively L-system language Lemma mathematics metalanguage morphology natural system negation normal derivation notation notion noun occur free ordinary orem parametric constituents Peirce's law phrases possible postulates predicate predicate calculus premises prime propositions prime statement primitive frame primitive terms principal constituent proof scheme propositional algebra prosequence quantifiers refutable Remark rule of derivation rule of inference sense sequence Similar proof strict implication suppose suppositions term variable terminology theory tion truth tables U-language valid void