This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the (...) ancient logic texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the (...) system is deducible by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his (...) understanding of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general (...) propositions. We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

We consider semantic and syntactic transformations of the concept of "the logical" in the ancient philosophy in the form of crypto-logos, para-logismos, dia-logos, and syl-logismos. We interpret Heraclitus' concept of Logos as a cryptologos through which intuitive insight (epístasthai gnóomen) reveals hidden or implicit harmony (harmoníe aphanés) in nature (phýsis) as a conceptual unity of ontic opposites (tà enantía). In Pramenides' paraconsistent concept of the identity of Being and thought, we point to para-logical hypotheses about the One that are (...) carried out through antithetical deductions of thought and which maintain the dynamics of the ontic determinations of being (ón) in the statics of the conceptual determinations of Being (tò eînai). As the beginning of the explicative granulation of ''the logical'' we consider Plato's concept of the dialectical skill (dialektikè tékhne) of dividing concepts of genus into species and sub-species that logically represent ontic opposites in problem-formulated questions. Finally Aristotle's concept of lógos as a statement-making sentence / proposition (lógos apophantikós) made explicit the Being (tò eînai), or the Being as Being (tò ón hê ón), in semantic and syntactic figures and modes of syllogistic inferences in which ontological (eînai), ontic (ón), conceptual (logikôos) and linguistic (légomenon) correspondence is shown. We conclude that with these changes in the concept of lógos, the path has been taken from the hidden or implicit Truth of the phenomena of nature and the world (pân) to explicit truthfulness of propositions as the unhiddeness (alétheia) of Being trough the semantical and syntactical visibility of the logical structures of being, thought and language in scientific knowledge based on demonstration (apoódeiksis). (shrink)

At least since Socrates, philosophy has been understood as the desire for acquiring a special kind of knowledge, namely wisdom, a kind of knowledge that human beings ordinarily do not possess. According to ancient thinkers this desire may result from a variety of causes: wonder or astonishment, the bothersome or even painful realization that one lacks wisdom, or encountering certain hard perplexities or aporiai. As a result of this basic understanding of philosophy, Greek thinkers tended to regard philosophy as (...) an activity of inquiry (zētēsis) rather than as a specific discipline. Discussions concerning the right manner of engaging in philosophical inquiry – what methodoi or routes of inquiry were best suited to lead one to wisdom – became an integral part of ancient philosophy, as did the question how such manners or modes of inquiry are related to, and differ from, other types of inquiry, for instance medical or mathematical. In this special issue of History of Philosophy & Logical Analysis, we wish to concentrate in particular on ancient modes of inquiry. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of (...) propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can (...) be found in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much (...) of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

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. (shrink)

ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention (...) to the complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

The logic of academic writing is the argumentative strategy on which our papers, our sections, and our paragraphs are based. It is a strategy, as it is a plan that connects different steps and has a specific goal, namely convincing the audience of an original and important idea. And it is argumentative, for two reasons. First, we can defend our idea and we can convince our audience only through arguments, which only in very few disciplines are formal deductions. In (...) most cases, the arguments that we use are based on premises accepted by a community and the conclusions are drawn from principles that in the ancient dialectics were called “maxims,” principles shared by everyone. Second, a paper is a dialogue between the author and his or her readers. An idea can be considered as interesting and worth reading only when it addresses a topic that is perceived as important by the readers and tackles a problem that is open and needs to be solved. Our arguments are acceptable when they start from the premises of our community of readers, avoiding repeating what is obvious for them or taking for granted what is obscure or unknown to them. In this book, we present the argumentative approach to academic writing that we used in classroom. What characterizes it and makes it unique is the perspective that is adopted. We do not start from preexisting ideas that only need to be presented in a way that is suitable to an academic public. We intend to show that writing academically is a consequence of thinking academically, or rather “strategically.” We want to explain how the linguistic and presentational devices are the result of a much deeper plan underlying them, and how mastering the logic of a paper leads to understanding and even developing academic styles. The logic of academic writing is not aimed at teaching how to use language and write texts academically, but at enabling readers to create their own style based on their own argumentative strategies. (shrink)

An ancient argument attributed to the philosopher Carneades is presented that raises critical questions about the concept of an all-virtuous Divine being. The argument is based on the premises that virtue involves overcoming pains and dangers, and that only a being that can suffer or be destroyed is one for whom there are pains and dangers. The conclusion is that an all-virtuous Divine (perfect) being cannot exist. After presenting this argument, reconstructed from sources in Sextus Empiricus and Cicero, this (...) paper goes on to model it as a deductively valid sequence of reasoning. The paper also discusses whet her the premises are true. Questions about the possibility and value of proving and disproving the existence of God by logical reasoning are raised, as well as ethical questions about how the cardinal ethical virtues should be defined. (shrink)

This book is written for those who wish to learn some basic principles of formal logic but more importantly learn some easy methods to unpick arguments and assess their value for truth and validity. -/- The first section explains the ideas behind traditional logic which was formed well over two thousand years ago by the ancient Greeks. Terms such as ‘categorical syllogism’, ‘premise’, ‘deduction’ and ‘validity’ may appear at first sight to be inscrutable but will easily be (...) understood with examples bringing the subjects to life. Traditionally, Venn diagrams have been employed to test arguments. These are very useful but their application is limited and they are not open to quantification. The mid-section of this book introduces a methodology that makes the analysis of arguments accessible with the use of a new form of diagram, modified from those of the mathematician Leonhard Euler. These new diagrammatic methods will be employed to demonstrate an addition to the basic form of syllogism. This includes a refined definition of the terms ‘most’ and ‘some’ within propositions. This may seem a little obscure at the moment but one will readily apprehend these new methods and principles of a more modern logic. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial (...) philosophic problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. (shrink)

A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhaṅgī, and the Mādhyamika catuṣkoṭi. It is argued that the irrationality currently imputed to these logics relies upon some philosophical preconceptions inherited from Aristotelian metaphysics. This misunderstanding can be corrected in two steps: by recalling their assumptions about truth; by reconstructing their ensuing theory of judgment within a common conceptual framework.

Johannes Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. Steuchius first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that (...) dialectic was among the first of the arts the Arabs practiced. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the (...) many fallacious ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

This book is an anthology with the following themes. Non-European Tradition: Bussanich interprets main themes of Hindu ethics, including its roots in ritual sacrifice, its relationship to religious duty, society, individual human well-being, and psychic liberation. To best assess the truth of Hindu ethics, he argues for dialogue with premodern Western thought. Pfister takes up the question of human nature as a case study in Chinese ethics. Is our nature inherently good (as Mengzi argued) or bad (Xunzi’s view)? Pfister ob- (...) serves their underlying agreement, that human beings are capable of becoming good, and makes precise the disagreement: whether we achieve goodness by cultivating autonomous feelings or by accepting external precepts. There are political consequences: whether government should aim to respect and em- power individual choices or to be a controlling authority. Early Greek Thinking: Collobert examines the bases of Homeric ethics in fame, prudence, and shame, and how these guide the deliberations of heroes. She observes how, by depending upon the poet’s words, the hero gains a quasi- immortality, although in truth there is no consolation for each person’s inevi- table death. Plato: Santas examines Socratic Method and ethics in Republic 1. There Socrates examines definitions of justice and tests them by comparison to the arts and sciences. Santas shows the similarities of Socrates’ method to John Rawls’ method of considered judgments in reflective equilibrium. McPherran interprets Plato’s religious dimension as like that of his teacher Socrates. McPherran shows how Plato appropriates, reshapes, and extends the religious conventions of his own time in the service of establishing the new enterprise of philosophy. Ac- cording to Taylor, Socrates believes that humans in general have the task of helping the gods by making their own souls as good as possible, and Socrates’ unique ability to cross-examine imposes on him the special task of helping others to become as good as possible. This conception of Socrates’ mission is Plato’s own, consisting in an extension of the traditional conception of piety as helping the gods. Brickhouse and Smith propose a new understanding of Socratic moral psychology—one that retains the standard view of Socrates as an intellectualist, but also recognizes roles in human agency for appetites and passions. They compare and contrast the Socratic view to the picture of moral psychology we get in other dialogues of Plato. Hardy also proposes a new, non-reductive understanding of Socratic eudaimonism—he argues that Socrates invokes a very rich and complex notion of the “Knowledge of the Good and Bad”, which is associated with the motivating forces of the virtues. Rudebusch defends Socrates’ argument that knowledge can never be impotent in the face of psychic passions. He considers the standard objections: that knowledge cannot weigh incom- mensurable human values, and that brute desire, all by itself, is capable of moving the soul to action. Aristotle: Anagnostopoulos interprets Aristotle on the nature and acquisition of virtue. Though virtue of character, aiming at human happiness, requires a complex awareness of multiple dimensions of one’s experience, it is not properly a cognitive capacity. Thus it requires habituation, not education, according to Aristotle, in order to align the unruly elements of the soul with reason’s knowledge of what promotes happiness. Shields explains Aristotle’s doctrine that goodness is meant in many ways as the doctrine that there are different analyses of goodness for different types of circumstance, just as for being. He finds Aristotle to argue for this conclusion, against Plato’s doctrine of the unity of the Good, by applying the tests for homonymy and as an immediate cons- equence of the doctrine of categories. Shields evaluates the issue as unresolved at present. Russell discusses Aristotle’s account of practical deliberation and its virtue, intelligence (phronesis). He relates the account to contemporary philo- sophical controversies surrounding Aristotle’s view that intelligence is neces- sary for moral virtue, including the objections that in some cases it is unnecessary or even impedes human goodness. Frede examines the advantages and disadvantages of Aristotle’s virtue ethics. She explains the general Greek con- ceptions of happiness and virtue, Aristotle’s conception of phronesis and compares the Aristotle’s ethics with modern accounts. Liske discusses the question of whether the Aristotelian account of virtue entails an ethical-psy- chological determinism. He argues that Aristotle’s understanding of hexis allows for free action and ethical responsibility : By making decisions for good actions we are able to stabilize our character (hexis). Hellenistic and Roman: Annas defends an account of stoic ethics, according to which the three parts of Stoicism—logic, physics, and ethics—are integrated as the parts of an egg, not as the parts of a building. Since by this analogy no one part is a foundation for the rest, pedagogical decisions may govern the choice of numerous, equally valid, presentations of Stoic ethics. Piering interprets the Cynic way of life as a distinctive philosophy. In their ethics, Cynics value neither pleasure nor tradition but personal liberty, which they achieve by self-suffi- ciency and display in speech that is frank to the point of insult. Plotinus and Neoplatonism: Gerson outlines the place of ordinary civic virtue as well as philosophically contemplative excellence in Neoplatonism. In doing so he attempts to show how one and the same good can be both action-guiding in human life and be the absolute simple One that grounds the explanation of everything in the universe. Delcomminette follows Plotinus’s path to the Good as the foundation of free will, first in the freedom of Intellect and then in the “more than freedom” of the One. Plotinus postulates these divinities as not outside but within each self, saving him from the contradiction of an external foundation for a truly free will. General Topics: Halbig discusses the thesis on the unity of virtues. He dis- tinguishes the thesis of the identity of virtues and the thesis of a reciprocity of virtues and argues that the various virtues form a unity (in terms of reciprocity) since virtues cannot bring about any bad action. Detel examines Plato’s and Aristotle’s conceptions of normativity : Plato and Aristotle (i) entertained hybrid theories of normativity by distinguishing functional, semantic and ethical normativity, (ii) located the ultimate source of normativity in standards of a good life, and thus (iii) took semantic normativity to be a derived form of normativity. Detel argues that hybrid theories of normativity are—from a mo- dern point of view—still promising. Ho ̈ffe defends the Ancient conception of an art of living against Modern objections. Whereas many Modern philosophers think that we have to replace Ancient eudaimonism by the idea of moral obligation (Pflicht), Ho ̈ffe argues that Eudaimonism and autonomy-based ethics can be reconciled and integrated into a comprehensive and promising theory of a good life, if we enrich the idea of autonomy by the central elements of Ancient eudaimonism. Some common themes: The topics in Chinese and Hindu ethics are perhaps more familiar to modern western sensibilities than Homeric and even Socratic. Anagnostopoulos, Brickhouse and Smith, Frede, Liske, Rudebusch, and Russell all consider in contrasting ways the role of moral character, apart from intellect, in ethics. Brickhouse / Smith, Hardy, and Rudebusch discuss the Socratic con- ception of moral knowledge. Brickhouse / Smith and Hardy retain the standard view of the so called Socratic Intellectualism. Shields and Gerson both consider the question whether there is a single genus of goodness, or if the term is a homonym. Bussanich, McPherran, Taylor, and Delcomminette all consider the relation between religion and ethics. Pfister, Piering, Delcomminette, and Liske all consider what sort of freedom is appropriate to human well-being. Halbig, Detel, and Ho ̈ffe propose interpretations of main themes of Ancient ethics. (shrink)

In a world filled with information overload and complex problems, the ability to think logically is a superpower. "A Little More Logical" is your guide to mastering this essential skill. This engaging and accessible open educational resource is perfect for students, teachers, and lifelong learners who want to improve their critical thinking abilities and make better decisions in all aspects of life. -/- Through a series of fun and interactive chapters, "A Little More Logical" covers a wide range of topics, (...) from the basics of constructing sound arguments to the application of logic in fields like ethics, science, and computing. You'll learn how to spot and avoid common fallacies, analyze real-world arguments, and use logical reasoning to solve problems and make informed choices. -/- But this book isn't just about abstract concepts – it's about the human story behind logic. You'll discover the fascinating lives and ideas of diverse thinkers, from ancient philosophers to modern-day pioneers, who have shaped the development of logical reasoning throughout history. With thought-provoking examples, engaging exercises, and plenty of humor along the way, "A Little More Logical" makes the study of logic both rigorous and entertaining. -/- Whether you're a student looking to ace your philosophy class, a teacher searching for high-quality educational resources, or a curious reader who wants to sharpen your mind, "A Little More Logical" is the perfect companion on your journey to becoming a more effective thinker. Unlock the power of logical thinking today with this one-of-a-kind open educational resource! (shrink)

Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach (...) to philosophy, let us return to the reasons to be reluctant at it. (shrink)

Already in ancient philosophy, there was a transition from the implicit and hidden action of the Logical ( lógos) in nature ( phýsis) to the scientific and explicit expression of the logical structures of thought, action, the world and language. Heraclitus' heno-logic with Logos as hidden implicit principle of homologization of opposites ( tà enantía) in nature differs from Parmenides' paraconsistent logic developed in a hypothetical hemidyalectics given in the formula ''All is One'' ( hén pánta eînai). (...) Plato's concept of dia-logic (dialektikè téchne ) with a new concept of Logos as the one genus of beings ( hén tí génon toôn ontoôn) in which the word not-Being (negation) got its place enabled production of dyadic logical structure by the granulation of genera into opposite species and sub-species that it contains. Aristotle's concept of triadic-logic as syl-logistics ( syllogismós) and demonstrative science (epistéme apodeiktikê ) give a new approach by new granulation of the concept of Logos into triadic logical structure: (1) the structure of being (substratum-attributes relation), (2) the structure of thought (substance-second substances relation), and (3) the structure of propositions (subject-predicate relation). Plato's dialectic and Aristotle's syllogistic both deconstructed the implicit ontological unity of the world (pan, kosmos, sphairos ) given through the concept of Logos in Pre-Socratic philosophy in order to make that unity in explicit form given by the logical and semantical structures of the propositions about the world, about the thought and about the language. The hidden implicit of the nature, which had to be known intuitively, was transformed into unhidden explicit inferential logical structures given in the semantics and pragmatics of scientific demonstration. (shrink)

Human cognitive process as a combination of the triad Knower - Knowing - Known and the language learning process as a combination of the triad Subject -Verb - Object will be understood in the light of ancient Indian wisdom as revealed in the Upanishads and will be presented. -/- A physics awareness of Advaita (No Two) concept will be used to model human mental processes such as – Knowing / Learning, Perception / Thinking / Logic, Understanding / Experiencing (...) / Awareness of meaning of a sentence. This awareness will further be used to prepare a flow-chart / block-diagram involving gross energy -transformations in human cognitive process. -/- This awareness will be corresponded to the awareness of Sri Aurobindo and Sri Ramana Maharshi on human consciousness. Implications of this model to natural language comprehension field of artificial intelligence will be presented combining with the ideas of connectionism. -/- . (shrink)

‘Reasoning’ can be considered a general concept that, upon speaking, is the ‘enraonar’, a Catalan word that should not be mistaken with ‘explain’ nor with ‘discuss’ which imply more detail, and cover different situations. This article is presented as an essay on the ancient ideal of ‘enraonar’. To that end, it is explained in what sense ‘enraonar’ and reason are one of the most complex phenomena thought has to deal with. Here it is argued that these natural phenomena require (...) a systematic and ‘scientific’ study, and that withoutthis knowledge computer science cannot simulate people’s every-day ‘enraonar’. (shrink)

The history of philosophy risks a self-opacity whereby we overestimate or underestimate our proximity to prior modes of thinking. This risk is relevant to assessing Hegel’s appropriation by McDowell and Priest. McDowell enlists Hegel for a quietist answer to the problem with assuming that concepts and reality belong to different orders, viz., how concepts are answerable to the world. If we accept Hegel’s absolute idealist view that the conceptual is boundless, this problem allegedly dissolves. Priest enlists Hegel for a dialetheist (...) answer to the problem with assuming that truth and falsity are mutually exclusive, viz., how certain sentences are both true and false. If we accept Hegel’s dialectical view that certain contradictions are necessary, this problem allegedly dissolves. For both McDowell and Priest, we find a true friend in Hegel. I argue that McDowell’s and Priest’s appropriations of Hegel overestimate Hegel’s affinity with quietism and dialetheism. McDowell reads Hegel as a quietist who silences metaphysical claims and the skeptical questions they raise against commonsense, but neglects Hegel’s adaptation of ancient skepticism against commonsense. Priest reads Hegel as a dialetheist who subordinates formal logic to dialectical logic by affirming the truth of certain contradictions, but neglects Hegel’s commitment to resolving contradictions for the sake of truth qua whole. I diagnose their misreadings in terms of what Hegel regards as the three moments of logic and argue that while McDowell jumps to its third moment, Priest stalls at its second moment. According to Hegel’s Encyclopedia Logic, logic has three “moments”: the abstractive moment of the understanding, which “stops short” at fixed categories; the negative moment of dialectic, which discovers the “genuine nature” of the categories, viz., that each “passes over, of itself, into its opposite”; and the positive moment of speculation, which grasps the “unity” of categories through the “dissolution” of their inner opposition. Hegel warns that if these moments are “kept separate from each other […] they are not considered in their truth”. I suggest that quietist and dialetheist readings of Hegel fail to consider truthfully the unified moments of his logic. In his quietist critique of metaphysics, McDowell enlists Hegel to dissolve the problem with assuming the duality of concept and reality. But McDowell helps himself directly to the third moment of logic, where the unity of the categories, and hence the boundlessness of the conceptual, would be fully articulated. Since he arrives at the third moment prematurely, ignoring its prior moments, he obscures its truth (§1). In his dialetheist critique of formal logic, Priest enlists Hegel to dissolve the problem with assuming the duality of truth and falsity. But Priest restricts himself gratuitously to the second moment of logic, where contradictions within the categories are not yet resolved. Since he stalls at the second moment, severed from its final moment, he obscures its truth (§2). I argue we can extricate Hegel from quietist and dialetheist misreadings only if we grasp the truth of the three moments of logic. (shrink)

While it is widely agreed that Hegel’s philosophy is a philosophy of freedom, the significance and scope of Hegel’s theory of freedom is disputed. Most scholarly work on this topic has been devoted to the socio-political philosophy of the Philosophy of Right. But Hegel also speaks of freedom in a way which extends beyond the concerns of his socio-political thought. This dissertation demonstrates how Hegel’s theory of freedom is more fully grasped when it is understood as a comprehensive philosophy which (...) also involves an ontology (a logic of being) and a phenomenology (a direct experience of this logic). The free state which Hegel outlines in the Philosophy of Right is still only a limited manifestation of a freedom which also pervades other aspects of human experience. A way of thinking which is “free” (in the sense that it does not restrict itself by assuming false methodological limitations) is itself essential to our capacity for rational self-determination. Moreover, this “speculative” perspective has only been achieved through the gradual cultivation (Bildung) of the free personality throughout history. -/- This dissertation therefore investigates why Hegel thinks that freedom is at issue in abstract philosophical thought (in his logical works) as well as in concrete historical phenomena (in the Phenomenology of Spirit). This logic and appearance of freedom explicates Hegel’s statement in the Preface of the Phenomenology that the absolute is not only substance, but also subject. Having shown that both the ancient freedom of the “social substance” and the modern freedom of the “pure I” are untenable on their own terms, Hegel advances a logical and phenomenological theory of freedom in which these one-sided truths are reconciled with each other. The “substantial subject” of Hegelian freedom more fully actualizes the purely subjective freedom of the Enlightenment, enabling true individual self-determination. Freedom appears not just as the right to make arbitrary choices, but as substantial thought and conviction. (shrink)

A new method of adult and children mental development is investigated – the trilogy of mind, which basic operation is the logic operation of comparison. This method was created considering Aristotle's understanding of philosophy as “the science about the first reasons and origins” of cognition, the beginning of presocratic cognition of the surrounding world. This new method is an effective mean of mental thinking development that is oriented at the understanding of natural and social processes with the help of (...) general scientific comparative notions – kinds of opposition, worked out in ancient times. (shrink)

This short work presents a popular fringe theory as a source of case studies for use in teaching informal logic in an introductory course. It puts forward ancient astronaut theory as the candidate source, together with a characterization of why it fits the bill. The televised material associated with that theory is well suited to being used as case studies given that they are easy to follow, contain a surprising number of arguments and fallacies, and keep students reliably (...) engaged. The paper includes an overview of the forms of argumentation and fallacies that these cases may be used to teach, along with a sketch of how to best implement them in the classroom. (shrink)

The paper provides both a description of conspiracy beliefs and an insight into their cultural significance. On one side, it highlights their specific formal features, on the other, and this constitutes its peculiarity in the recent literature on the topic, it considers them within the broader genre of general conceptual beliefs, whose main characteristics are weak methodology and logical structure, strong affective and dispositional constraints, epistemic closure and mauvaise foi, and whose main function is practical and self-representative (not epistemic). The (...) paper also claims that political theory and social sciences had some influence in legitimizing certain ideas and stereotypes that are exacerbated in conspiracy beliefs, while other te(le)ological conceptions, such as finalism and providence, may be an important source of ideas that turn out to be widely spread in contemporary criticism towards those same beliefs. (shrink)

Euthyphro is a Socratic interlocutor claiming enormous religious expertise, while his portrayal in the eponymous dialogue raises questions the reliability of his beliefs. This paper closely examines how Euthyphro justifies his case against his father, identifying an argument that relies on the concept of miasma (pollution). In so far as miasma is considered in isolation, Euthyphro has a good argument. Unfortunately, there is more than miasma at stake when considering why one could prosecute one’s own parent. Introducing the other relevant (...) concepts, honor and shame, we find his case reflects a dilemma at the source of ancient Greek religious thought. It would not be possible for Euthyphro or anyone else to know what to do in his case. (shrink)

Ayurveda is considered one of the ancient systems of knowledge in India. Various compendiums of Ayurveda i.e., Charaka, Sushruta, or Vagbhatta have enumerated an education system based on Gurukuls i.e., An Educator and their pupils. It is evident from them that a very systematized and organized form of medical education starting from selection to induction and then to effective teaching and training were given during that ancient era. The triad of education viz. Adhyayan (studying), Adhyapan (teaching) and Sambhasha (...) (an argument based on logic) is key to knowledge and the learning process as per Charaka. The selection of students and teachers was based on some set of fixed criteria necessary to be fulfilled. Induction was done prior to admission and proper disciplinary, and ethical rules were practiced. For the development of knowledge and skills in branches of Ayurveda, problems-based case discussion, identification, causes, and treatment of diseases, their principles were taught. Yogya (a set of dummy objects) was used to practice prior to the final surgery. (shrink)

Between the end of the nineteenth century and the first twenty years of the twentieth century, stimulated by the impetuous development of logical studies and taking inspiration from Leibniz's idea of a characteristica universalis, the three founding fathers of the analytic tradition in philosophy, i.e., Frege, Russell, and Wittgenstein, started to talk of a logically perfect language, as opposed to natural languages, all feeling that the latter were inadequate to their (different) philosophical purposes. In the second half of the twentieth (...) century, however, the very idea of a logically perfect language ceased for various reasons to seem attractive to analytic philosophers. Thus, it might appear that this idea could be classified together with the many other bizarre ideas that from time to time surface in the history of philosophy-an idea that perhaps had a beneficial impact on the development of twentieth century logic, but which can now be put to rest. In this brief note, I contend that this conclusion may be too hasty. Indeed, if a well-known empirical hypothesis advanced in 1975 by Jerry Fodor turns out to be true, then there is a logically perfect language, after all. More precisely, I argue that, if it exists, Fodor's language of thought possesses the main characteristics a logically perfect language is required to have. (shrink)

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. (shrink)

Flannery’s volume looks in two directions. On the one hand, as Flannery announces in the book’s introduction, the chapters in the volume were intended to shed light on three specific ‘background’ issues in contemporary ethics and the interpretation of Thomas Aquinas, namely, Aquinas’ notion of ethical theory (as articulated especially in Summa Theologica 1-2.6-21), the ramifications of physical actions on moral evaluation in contemporary ethics (for instance, whether the fact that an abortion consists specifically in the crushing of a fetus’ (...) skull rather than some other form of terminating the fetus has moral relevance), and the understanding of Aquinas’ ‘principle of double effect’ (Summa Theologica 2-2.64.7). On the other hand, the eight chapters (and two appendices) are all devoted to the exegesis of passages in Aristotle’s corpus (primarily the ethical treatises, but with substantial discussions of passages from the Prior Analytics, the Physics, and the Metaphysics insofar as they shed light on passages in the eth-ical corpus). Although the exegetical chapters are motivated by contemporary and Thomistic background issues, the exegesis appears entirely grounded in Aristotle’s (rather than Aristotelian) texts. (shrink)

Since Mates’ seminal Stoic Logic there has been uncertainty and debate about how to treat the term anapodeiktos when used of Stoic syllogisms. This paper argues that the customary translation of anapodeiktos by ‘indemonstrable’ is accurate, and it explains why this is so. At the heart of the explanation is an argument that, contrary to what is commonly assumed, indemonstrability is rooted in the generic account of the Stoic epistemic notion of demonstration. Some minor insights into Stoic logic (...) ensue. (shrink)

We develop some of Williamson’s ideas regarding how propositional calculus aids in comprehending Aristotelian logic. Specifically, we enhance the utilisation of truth tables to examine the structure of opposition diagrams. Using ‘conditioned truth tables’, we establish logical dependency relationships between the truth values of different propositions. This approach proves effective in interpreting various texts of the Organon concerning the doctrine of opposition.

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...) interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call (...) any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

The work of this dissertation, in a broad sense, seeks to rescue what may be in the original project or nucleus of philosophy, from its Socratic arising: the idea of elucidative rationality. This rationality is aimed at expressing our practices in a way that can be confronted with objections and alternatives. The notion of expression is central to this rationality. This centrality is elucidated by the contemporary philosopher Brandom (1994, 2000, 2008a, 2013), from his view of the semantic inferentialism. With (...) this view, this dissertation, in a strict sense, investigates evidences that leads to the distinction of the inferentially expressivist tradition of syllogistic. In this semantic inferentialism, logic is the “organ of semantic self-consciousness”. In this sense, logic does not define the rational, in the most basic sense, but allows us to be aware, through inferential articulation, of the conceptual contents, which govern all our thoughts. Evidences presented in the work of this dissertation seek to show that the syllogism is marked by the logical-elucidative character of this semantic self-consciousness, because of its expressive role as inseparable from the notion of inference. In the first part of this dissertation, then, the tradition of syllogistics is examined, in which the expression is the main notion. This study is based on the tradition of syllogistics, composed of the Aristotelian school of Campinas, organized by Angioni (2014a), the logical economist Keynes (1906), and the “formalist” schools, represented mainly by the logician Łukasiewicz (1957, 1929/1963) and by Corcoran (1972, 1974, 2009, 2015). The main claims of the Campinas school are analyzed: the non-epistemological, but explanatory, exposition of (scientific) knowledge, in the syllogism, the secondary role of the notion of truth, the priority of the predicative structure, and the suggestion of approaching of the syllogistic to the relevant system of logic. In this analysis, we add the discussion about the reasoning of the epagogic type, important to the practical understanding of the “first principles”. The key points of Keynes are also discussed: the semantic priority of propositional judgment and the explanatory role of deductive inference. The second part of this dissertation discusses the relation between expression, inference and the expressive role of logic, based on the semantic inferentialism of Brandom. In order to discuss this relationship, propaedeutic questions are raised, related to the semantic role of sentences and subsentences (terms and predicates) in language, to different conceptions of logical validity, beyond the truth-functional aspect, to the logical demarcation of symbolic rules, to demarcation of logic, the idea of “formal logic”, and the removal of formal semantics from natural language concern. Next, the theoretical framework of Brandom's semantic inferentialism is presented. In this framework, the idea of philosophical semantics, pragmatisms of the semantic and conceptual type, expressivisms of the rationalist, logical and propositional conceptual type, and the semantically primitive notion of incompatibility come into play. Thus, to those who are interested in the correspondence between ancient logic and modern logic, the work of this dissertation offers a useful contribution, especially to projects of formalization of the syllogistics, which need not appeal against or in favor of a strictly formal approach to logic. (shrink)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s (...) Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

An overview of the ancient philosophers and their philosophical system (divided into the fields of logic, physics, and ethics) comprising the living, organic, enduring, and evolving body of interrelated ideas identifiable as the Stoic perspective.

I examine two startling claims attributed to some philosophers associated with Megara on the Isthmus of Corinth, namely: Ml. Something possesses a capacity at t if and only if it is exercising that capacity at t. M2. One can speak of a thing only by using its own proper A6yor;. In what follows, I will call the conjunction of Ml and M2 'Megaricism' .1 The lit­ erature on ancient philosophy contains several valuable discussions of Ml and M2 taken individually (...) .2 But there is no discussion of them together, much less of their logical relations. I intend to remedy that lack, and to show why it is a lack worth remedying. My aims are both philosophical and historical. Inevitably, in saying anything new and interesting about Megaric views, I will be adopting assumptions scarcely free from controversy, and indulging in quite a bit of charitable recon­ struction. But the resulting picture is of considerable interest. For it explains why, although Ml and M2 seem to have little to do with one another, it is in fact small wonder that anyone who held one would hold the other, for, as I attempt to show, they entail each other. It explains why the Megarics are associated in the primary literature with the names of such diverse philosophical ancestors as Parmenides and Protagoras. And it explains why, although they are both false, Ml and M2 were claims taken seriously by both Plato and Aristotle, who in developing their own views on modality and language saw reason to mention Megaricism, and to argue against it. (shrink)

ABSTRACT: Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985, with focus on his commentary on ancient paradoxes.

In this extended essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of (...) detailed evidence that there are numerous (over a hundred) and extensive parallels both in formulation and --more importantly-- in content between the Stoics and Frege, parallels so plentiful that one would be hard pressed to brush them off as coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope. -/- (Corrigendum: At school, Frege likely had seven, not ten, years of intensive Latin and four years of intensive ancient Greek courses.). (shrink)

Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored (...) in the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view. (shrink)

ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances (...) for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)

Aristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is not ill’ (...) are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics. (shrink)