## Aristotle's Modal Syllogistic (Google eBook)Aristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity--and is today widely regarded as incoherent. Combining analytic rigor with keen sensitivity to historical context, Marko Malink makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle's philosophy. Aristotle's modal syllogistic differs significantly from modern modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics--specifically, its theory of predicables (definition, genus, differentia, proprium, and accident) and the ten categories (substance, quantity, quality, and so on). The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle's modal propositions, one that verifies the ancient philosopher's claims of the validity and invalidity of modal inferences. While it acknowledges some limitations of this reconstruction, Aristotle's Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts. |

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### Contents

The Assertoric Syllogistic | |

Categorical Propositions | |

The dictum de omni | |

The Orthodoxdictum Semantics | |

The Heterodox dictum Semantics | |

The Preorder Semantics | |

The Apodeictic Syllogistic | |

Essence Terms and Substance Terms | |

Universal Negative Necessity Propositions | |

Particular Necessity Propositions | |

The Validity of XQMMoods | |

TwoSided Possibility Propositions | |

OneSided Possibility Propositions | |

Aristotles Terms | |

### Common terms and phrases

ª ā abstract dictum semantics Alexander in APr animal apodeictic dictum apodeictic syllogistic apredicated Aristotle Aristotle’s claims assertoric propositions assertoric syllogistic Barbara NXN Baroco NNN biped Bocardo NXN categorical propositions categorical terms Celarent NXN chapter claims of validity contradictory conversion rules copula counterexample crosscategorial deductive system definition dictum de omni differentia e predicated ecthesis ecthetic proofs essence terms essential predication example firstorder follows genus hence heterodox dictum semantics implies incompatible inconcludence inferences interpretation inthe invalidity justified major premise Mikkalos modal opposition modal syllogistic moods mpaw necessity propositions negative nonessence terms nonsubstance terms Nortmann Npropositions nullo NXsubordination ofthe orthodox dictum semantics paronymous passage plurality associated possibility propositions predicable semantics predicate term predicated essentially premise pair preorder semantics Prior Analytics problematic syllogistic reductio semantic value subject term substance term Tcategory z(Abz z(Acz