A Mereological Reading of the Dictum de Omni et Nullo

When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates the assertoric syllogistic. I argue that this mereological validation offers advantages over recent discussions in Morison, Malink, Ebert and Vlasits

Greek and Roman Logic

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry

What Is a Perfect Syllogism in Aristotelian Syllogistic?

The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status over the other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus

The Study of Ancient Greek Texts in Early Ottoman Constantinople

H εργασία αποτελεί επισκόπηση των έργων σχετικά με τα αρχαία ελληνικά κείμενα στην Κωνσταντινούπολη κατά το δεύτερο μισό του 15ου αιώνα. Μαρτυρίες από τα σωζόμενα χειρόγραφα που περιέχουν αρχαία ελληνικά κείμενα, τα συγγράμματα των Ελλήνων διανοουμένων της εποχής όπως ο Αμιρούτζης, ο Γεώργιος Τραπεζούντιος, ο Ματθαίος Καμαριώτης, καθώς και πληροφορίες που παρέχονται από τον σύγχρονό τους Κριτόβουλο, αποδεικνύουν ότι οι λόγιοι της εποχής και οι μαθητές τους ενδιαφέρονταν για ευρύ φάσμα θεμάτων, από την αρχαία ελληνική γλώσσα και τη λογοτεχνία μέχρι τις επιστήμες και τη φιλοσοφία. Η μελέτη των αρχαίων ελληνικών κειμένων δεν περιοριζόταν στην Αυλή των Οθωμανών Σουλτάνων, αλλά και στους εκπαιδευτικούς κύκλους των Ελλήνων διανοουμένων.

The Study of Ancient Greek Texts in Early Ottoman Constantinople

H εργασία αποτελεί επισκόπηση των έργων σχετικά με τα αρχαία ελληνικά κείμενα στην Κωνσταντινούπολη κατά το δεύτερο μισό του 15ου αιώνα. Μαρτυρίες από τα σωζόμενα χειρόγραφα που περιέχουν αρχαία ελληνικά κείμενα, τα συγγράμματα των Ελλήνων διανοουμένων της εποχής όπως ο Αμιρούτζης, ο Γεώργιος Τραπεζούντιος, ο Ματθαίος Καμαριώτης, καθώς και πληροφορίες που παρέχονται από τον σύγχρονό τους Κριτόβουλο, αποδεικνύουν ότι οι λόγιοι της εποχής και οι μαθητές τους ενδιαφέρονταν για ευρύ φάσμα θεμάτων, από την αρχαία ελληνική γλώσσα και τη λογοτεχνία μέχρι τις επιστήμες και τη φιλοσοφία. Η μελέτη των αρχαίων ελληνικών κειμένων δεν περιοριζόταν στην Αυλή των Οθωμανών Σουλτάνων, αλλά και στους εκπαιδευτικούς κύκλους των Ελλήνων διανοουμένων.

Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972

Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic

Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study

The following is a critical and historical account of Aristotelian Essentialism informed by recent work on Aristotle’s modal syllogistic. The semantics of the modal syllogistic are interpreted in a way that is motivated by Aristotle, and also make his validity claims in the Prior Analytics consistent to a higher degree than previously developed interpretative models. In Chapter One, ancient and contemporary objections to the Aristotelian modal syllogistic are discussed. A resolution to apparent inconsistencies in Aristotle’s modal syllogistic is proposed and developed out of recent work by Patterson, Rini, and Malink. In particular, I argue that the semantics of negation is distinct in modal context from those of assertoric negative claims. Given my interpretive model of Aristotle’s semantics, in Chapter Two, I provide proofs for each of the mixed apodictic syllogisms, and propose a method of using Venn Diagrams to visualize the validity claims Aristotle makes in the Prior Analytics. Chapter Three explores how Aristotle’s syllogistic fits within Aristotle’s philosophy of science and demonstration, particularly within the context of the Posterior Analytics. Consideration is given to the Aristotelian understanding of the relationship among necessity, explanation, definition, and essence. Chapter Four applies Aristotelian modal logic in contemporary contexts. I contrast Aristotelian modality and essentialism with contemporary modalism based upon the semantics of possible worlds, e.g. Kripke and Putnam. I also develop an account of how Aristotelian modal logic can ground a sortal dependent theory of identity, as discussed by Wiggins