ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...) of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such as (...) ‘moving’, which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle’s own proofs is revealed. The result is an applied logic which provides needed links between Aristotle’s views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle’s theory of modality, and the philosophy of logic in general. (shrink)

I present the realist conception of logic supported by Oswaldo Chateaubriand which integrates ontological and epistemological aspects, opposing it to mathematical and linguistic conceptions. I give special attention to the peculiarities of his hierarchy of types in which some properties accumulate and others have a multiple degree. I explain such deviations of the traditional conception, showing the underlying purpose in each of these peculiarities. I compare the ideas of Chateaubriand to the similar ideas of Frege, Tarski and Gödel. I suggest (...) a view of the logical properties in terms of the Aristotelian notion of focal meaning and I give a formal expression to the type of the entities in the hierarchy proposed by Chateaubriand. (shrink)

Normative political philosophy always refers to a standard against which a society's institutions are judged. In the first, analytical part of the article, the different possible forms of normative criticism are examined according to whether the standards it appeals to are external or internal to the society in question. In the tradition of Socrates and Hegel, it is argued that reconstructing the kind of norms that are implicit in practices enables a critique that does not force the critic's particular views (...) on the addressee and can also be motivationally effective. In the second part of the article, Axel Honneth's theory of recognition is examined as a form of such reconstructive internal critique . It is argued that while the implicit norms of recognition made explicit in Honneth's philosophical anthropology help explain progressive social struggles as moral ones, his theory faces two challenges in justifying internal critique. The Priority Challenge asks for the reasons why the implicit norms of recognition should be taken as the standard against which other implicit and explicit norms are to be judged. The Application Challenge asks why a social group should, by its own lights, extend equal recognition to all its members and even non-members. The kind of functional, prudential, conceptual, and moral considerations that could serve to answer these challenges are sketched. (shrink)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s (...) challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

This paper shows Socratic elenchus as an efficient and effective way of modeling rational knowledge seeking. Like ordinary conversations, the elenctic exchanges in the dialogues presuppose a degree of autonomy on the part of its participants. Socrates’ line of questioning often seems pertinent to a particular interlocutor because he is well aware of the fact that the interlocutor has goals and ambitions or is reputed to be an expert at something. In turn, Socrates’ line ofquestioning reflects his own goals and (...) ambitions. In Alcibiades Major Socrates is trying to turn Alcibiades towards a greater awareness of his limitations. Plato’s dialogues also force readers to consider their own solutions to the topics introduced in them. Consequently, the autonomy of a dialogue’s participants requires that interpreters not exaggerate one aspect of a dialogue’s structural features at the expense of other aspects. (shrink)

The ways in which the Aristotelian sciences are related to each other has been discussed in the literature, with some focus on the subalternate sciences. While it is acknowledged that Aristotle, and Plato as well, was concerned as well with how the arts were related to one another, less attention has been paid to Aristotle's views on relationships among the arts. In this paper, I argue that Aristotle's account of the subalternate sciences helps shed light on how Aristotle saw the (...) art of rhetoric relating to dialectic and politics. Initial motivation for comparing rhetoric with the subalternate sciences is Aristotle's use of the language of boundary transgression, germane to the Posterior Analytics, when discussing rhetoric’s boundaries, as well as the language of "over" and "under" found in APo. First, I discuss three passages in Rhetoric Book I and argue that Garver's (1988) account cannot be correct. Second, I look to the subalternate sciences, especially focusing on optics and the distinction between "unqualified" optics and mathematical optics. Third, I discuss rhetoric's dependence on both dialectic and politics. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

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. (shrink)

This dissertation examines the way Philip Melanchthon, author of the Augsburg Confession and Martin Luther's closest co-worker, sought to establish the relationship between faith and reason in the cradle of the Lutheran tradition, Wittenberg University. While Melanchthon is widely recognized to have played a crucial role in the Reformation of the Church in the sixteenth century as well as in the Renaissance in Northern Europe, he has in general received relatively little scholarly attention, few have attempted to explore his philosophy (...) in depth, and those who have examined his philosophical work have come to contradictory or less than helpful conclusions about it. He has been regarded as an Aristotelian, a Platonist, a philosophical eclectic, and as having been torn between Renaissance humanism and Evangelical theology. An understanding of the way Melanchthon related faith and reason awaits a well-founded and accurate account of his philosophy. Having stated the problem and finding it inadequately treated in the secondary literature, this dissertation presents an account of Melanchthon's philosophical development. Finding that his philosophy was ultimately founded upon his understanding of and method in rhetoric and dialectics, this dissertation explicates his mature accounts of these arts. It then presents an account of Melanchthon's philosophy as both humanistic (i.e., rhetorically based and practically rather than speculatively oriented) and fideistic (i.e, skeptical about the product of human reason alone, but finding certainty in philosophy founded upon, and somewhat limited by, Christian faith). After a final assessment of claims about Melanchthon's philosophy from the secondary literature, this dissertation considers how such a humanistic, fideistic philosophy might be helpful for Christians in a philosophically post-modern situation. (shrink)

This project is guided and motivated by the question concerning the nature of the phantasm as that which mediates between sensation and intellection in John Duns Scotus' account of cognition. Scotus embraces Aristotle's claim that the intellect cannot think without the phantasm. The phantasm is in a corporeal organ, yet the immaterial intellect must act with it to produce an intelligible species. In this project I examine the critical elements of Scotus' cognitive theory in order to understand the nature of (...) the phantasm. In the first chapter I discuss key elements of Aristotle's metaphysics and give a close, textual reading of De Anima guided by his claim that the relationship of the body and soul is highly specific. I then focus on his claim in De Anima 2.12 that sensation involves the reception of the sensible form without the matter. In the second chapter, I discuss Scotus' key theological notions that guide and inform his cognitive project. The beatific vision requires the presence of the divine essence in its own existence to the intellect. As the highest cognitive experience, the beatific vision is definitive of all cognitive experience making the presence of the object to the cognitive faculty of central importance. The discussion of the incarnation shows that the world is sacralized and thus, is a worthy object of cognitive attention in itself. In the third chapter, I discuss Scotus' understanding of the body-soul relationship focusing on his notion of person to both secure the unity of the human being and to ground the mediation between sensation and intellection. In the fourth chapter, I first discuss Aquinas' claim that sensation requires a spiritual change. While Scotus's account is in many respects the same as Aquinas', Scotus does not maintain that sensation is primarily passive and is thus, able to account for cognitive attention by way of his understanding of the unity of the sense organ, immanent actions, and sensation as intuitive cognition. What emerges in this discussion is Scotus' particular understanding of an intentio by which the nature of the phantasm can be understood. (shrink)

This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo period first reporting his original results. It ends with works published in 2015. (...) Some items are annotated as listed or with endnotes connecting them with other work and pointing out passages that, in retrospect, are seen to be misleading and in a few places erroneous. In addition, Section V, “Discussions”, is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 10 items published in the 1970s, 24 in the 1980s, 42 in the 1990s, 60 in the 2000s, and 70 in the current decade. The secondary bibliography is also annotated as listed or with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. Section VI, “Alternatives”, lists recent works on Aristotle’s logic oblivious of Corcoran’s research and, more generally in some cases, even of the Łukasiewicz-initiated tradition. As is evident from Section VII, “Acknowledgements”, Corcoran’s publications benefited from consultation with other scholars, most notably George Boger, Charles Kahn, John Mulhern, Mary Mulhern, Anthony Preus, Timothy Smiley, Michael Scanlan, Roberto Torretti, and Kevin Tracy. All of Corcoran’s Greek translations were done in collaboration with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. (shrink)

This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with (...) other work. In addition, Section V “Discussions” is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 8 items published in the 1970s, 22 in the 1980s, 39 in the 1990s, 56 in the 2000s, and 65 in the current decade. The secondary bibliography is annotated with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. As is evident from the Acknowledgements sections, all of Corcoran’s publications benefited from correspondence with other scholars, most notably Timothy Smiley, Michael Scanlan, and Kevin Tracy. All of Corcoran’s Greek translations were done in consultation with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications. (shrink)

JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran -/- This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies and the Journal of Symbolic Logic article from his (...) Buffalo period first reporting his original results; it ends with works published in 2015. A few of the items are annotated as listed or with endnotes connecting them with other work and pointing out passages that in-retrospect are seen to be misleading and in a few places erroneous. In addition, Section V, “Discussions”, is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 8 items published in the 1970s, 23 in the 1980s, 42 in the 1990s, 56 in the 2000s, and 69 in the current decade. The secondary bibliography is also annotated as listed or with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. Section VI, “Alternatives”, lists recent works on Aristotle’s logic oblivious of Corcoran’s research and, more generally, of the Lukasiewicz-initiated tradition. As is evident from Section VII, “Acknowledgements”, Corcoran’s publications benefited from consultation with other scholars, most notably Timothy Smiley, Michael Scanlan, Roberto Torretti, and Kevin Tracy. All of Corcoran’s Greek translations were done in collaboration with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. -/- REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications. Also, let me know of passages I should comment on. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

Vyrauja nuomonė, jog ankstyvoji Descartes’o filosofija angažuojasi metodologinėms problemoms, o tai laikytina naujosios epochos ženklu. Tačiau turint omenyje tokios problematikos išskirtinį aktualumą Aristoteliui bei faktą, kad Descartes’o metodologija aiškiai stokoja apibrėžtumo, jo santykis su ankstesniąja tradicija turėtų būti įvertintas naujai. Straipsnyje siekiama apginti požiūrį, kad „Proto vadovavimo taisyklėse“, savo pirmajame filosofiniame veikale, Descartes’as demonstruoja pastangas duoti tvirtą epistemologinį pagrindą teorinio mąstymo išlaisvinimui iš bet kokių formalių apribojimų. Pateikdamas naują mąstymo procedūrų traktuotę, Descartes’as numato perspektyvų įvairovės galimybę teoriniame reiškinių aiškinime ir (...) šiuo aspektu atsiskleidžia jo originalumas. (shrink)

In the Categories, Aristotle addresses two different cases of dual categorization, cases in which the same thing might appear in two different categories: relatives and secondary substances in the first case, qualities and relatives in the second. His treatment of these two cases is markedly different. Ackrill thinks dual categorization poses a dilemma for Aristotle’s project as a whole, but I argue that there is a dilemma only on particular understandings of Aristotle’s purpose in compiling the list of categories. I (...) investigate various interpretations of the categories to find one that explains Aristotle’s reactions to dual categorization, and suggest an interpretation of the peculiar four-fold system of classification in Chapter 2. (shrink)