Este livro marca o início da Série Investigação Filosófica. Uma série de livros de traduções de textos de plataformas internacionalmente reconhecidas, que possa servir tanto como material didático para os professores das diferentes subáreas e níveis da Filosofia quanto como material de estudo para o desenvolvimento pesquisas relevantes na área. Nós, professores, sabemos o quão difícil é encontrar bons materiais em português para indicarmos. E há uma certa deficiência na graduação brasileira de filosofia, principalmente em localizações menos favorecidas, com relação (...) ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos traduções de textos importantes ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. O presente volume é constituído de três traduções de verbetes importantes sobre lógica, da Enciclopédia de Filosofia da Stanford: (1) A Lógica de Aristóteles, (2) Lógica Clássica, (3) Lógica Modal. (shrink)

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...) century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original...

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)

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 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)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

There have been and continue to be disagreements about how to consider the traditional square of opposition and the traditional inferences of obversion, conversion, contraposition and inversion from the perspective of contemporary quantificational logic. Philosophers have made many different attempts to save traditional inferences that are invalid when they involve empty classes. I survey some of these attempts and argue that the only satisfactory way of saving all the traditional inferences is to make the existential assumption that both the subject (...) and predicate classes and their complement classes are non-empty for all the propositions we admit. I briefly indicate the room for continued controversy over how properly to interpret Aristotle?s statements regarding these inferences, but find some plausibility in the views of Manley Thompson and A.N.Prior that Aristotle had in mind a particular arrangement of existential import unfamiliar to most contemporary logicians. (shrink)

There have been and continue to be disagreements about how to consider the traditional square of opposition and the traditional inferences of obversion, conversion, contraposition and inversion from the perspective of contemporary quantificational logic. Philosophers have made many different attempts to save traditional inferences that are invalid when they involve empty classes. I survey some of these attempts and argue that the only satisfactory way of saving all the traditional inferences is to make the existential assumption that both the subject (...) and predicate classes and their complement classes are non-empty for all the propositions we admit. I briefly indicate the room for continued controversy over how properly to interpret Aristotle's statements regarding these inferences, but find some plausibility in the views of Manley Thompson and A.N.Prior that Aristotle had in mind a particular arrangement of existential import unfamiliar to most contemporary logicians. (shrink)

It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist of (...) an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations. (shrink)

Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to non-empty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.

An unconventional formalization of the canonical square of opposition in the notation of classical symbolic logic secures all but one of the canonical square’s grid of logical interrelations between four A-E-I-O categorical sentence types. The canonical square is first formalized in the functional calculus in Frege’s Begriffsschrift, from which it can be directly transcribed into the syntax of contemporary symbolic logic. Difficulties in received formalizations of the canonical square motivate translating I categoricals, ‘Some S is P’, into symbolic logical notation, (...) not conjunctively as \, but unconventionally instead in an ontically neutral conditional logical symbolization, as \. The virtues and drawbacks of the proposal are compared at length on twelve grounds with the explicit existence expansion of A and E categoricals as the default strategy for symbolizing the canonical square preserving all original logical interrelations. (shrink)

This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" (...) and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together. (shrink)

In this article, I discuss Robert Kilwardby’s theory of judgement and consider its implications for his view of truth and falsity. I start by considering Kilwardby’s claim that truth and falsity are primarily found in composite thought, i.e. judgement. I then examine his distinction between two different kinds of being, namely real and conceptual, arguing that different kinds of true judgement, according to Kilwardby, have different kinds of existential import, either real or merely conceptual. Since Kilwardby develops his position by (...) commenting on Aristotle’s logical treatises, an important aim of the article is that of showing how he addresses exegetical issues in those sources and offers solutions that go beyond Aristotle’s alleged intentions. The focus of the paper is on negative judgement because that is where Kilwardby diverges from Aristotle most conspicuously. (shrink)

In this article, I discuss Robert Kilwardby’s theory of judgement and consider its implications for his view of truth and falsity. I start by considering Kilwardby’s claim that truth and falsity are primarily found in composite thought, i.e. judgement. I then examine his distinction between two different kinds of being, namely real and conceptual, arguing that different kinds of true judgement, according to Kilwardby, have different kinds of existential import, either real or merely conceptual. Since Kilwardby develops his position by (...) commenting on Aristotle’s logical treatises, an important aim of the article is that of showing how he addresses exegetical issues in those sources and offers solutions that go beyond Aristotle’s alleged intentions. The focus of the paper is on negative judgement because that is where Kilwardby diverges from Aristotle most conspicuously. (shrink)

This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of (...) the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. (shrink)