In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises (contrary (...) and contradictory) studied by the Stagerian in the Analytica Priora (B15). According to him, the following syllogisms are valid from opposite premises, in which small Latin letters stand for terms such as subject and predicate, and capital Latin letters stand for the categorical propositions such as in the traditional notation: (i) in the second figure, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), and Aba,Oba ` Oaa (Baroco); (ii) in the third one, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) and Eab, Iab ` Oaa (Ferison). Finally, we discuss the passage from the Analytica Posteriora (A11) in which Aristotle states that the Principle of Non-Contradiction is not generally presupposed in all demonstrations (scientific syllogisms), but only in those in which the conclusion must be proved from the Principle; the Stagerian states that if a syllogism of the first figure has the major term consistent, the other terms of the demonstration can be each one separately inconsistent. These results allow us to propose an interpretation of his deductive theory as a broad sense paraconsistent theory. Firstly, we proceed to a hermeneutical analysis, evaluating its logical significance and the interplay of the results with some other points of Aristotle’s philosophy. Secondly, we point to a logical interpretation of the Aristotelian syllogisms from opposite premises in the antilogisms method proposed by Christine Ladd-Franklin in 1883, and we also present a logical treatment of the Aristotelian demonstration with inconsistent material in the paraconsistent logics Cn, 1 _ n _!, introduced by da Costa in 1963. These two issues seem having not yet been analysed in detail in the literature. (shrink)

No Órganon Aristóteles descreve alguns esquemas dedutivos nos quais a presença de inconsistências não acarreta a trivialização da teoria lógica envolvida. Esta tese é corroborada por três diferentes situações teóricas estudadas por ele, as quais são apresentadas neste trabalho. Analizamos o esquema de inferência utilizado por Aristóteles no Protrepticus e o método de demonstração indireta para os silogismos categóricos. Ambos os métodos exemplificam como Aristóteles emprega estratégias de redução ao absurdo logicamente clássicas. Na sequência, discutimos os silogismos válidos a partir (...) de premissas opostas (contrárias e contraditórias) estudadas pelo Estagirita no Analytica Priora (B15). De acordo com o autor, os seguintes silogismos são válidos a partir de premissas opostas, nos quais letras latinas minúsculas denotam termos como sujeito e predicado, enquanto que letras latinas maiúsculas denotam proposições categóricas tal como na notação tradicional: (i) na segunda figura, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), e Aba,Oba ` Oaa (Baroco); (ii) na terceira, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) e Eab, Iab ` Oaa (Ferison). Por fim, discutimos a passagem do Analytica Posteriora (A11) no qual Aristóteles enuncia que o Princípio de Não-Contradição não é, em geral, pressuposto de toda demonstração (silogismo científico), mas apenas daquelas nas quais a conclusão deve ser provada a partir do Princípio; o Estagirita enuncia que se um silogismo da primeira figura tiver o termo maior consistente, os outros termos da demonstração podem ser separadamente inconsistentes. Estes resultados permitem-nos propor uma interpretação de sua teoria dedutiva como uma teoria paraconsistente lato sensu. Primeiramente, efetuamos uma análise hermenêutica, avaliando seu significado lógico e a correlação desses resultados com outros aspectos da filosofia de Aristóteles. Em segundo lugar, consignamos uma interpretação dos silogismos aristotélicos a partir de premissas opostas à luz dos antilogismos propostos por Christine Ladd-Franklin em 1883, e da demonstração aristotélica com termos inconsistentes nas lógicas paraconsistentes Cn, 1 n !, introduzidas por da Costa em 1963. Esses dois aspectos não parecem ter sido ainda detalhadamente analisados na literatura. DOI:10.5007/1808-1711.2010v14n1p71. (shrink)

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper (...) we present some conservative translations involving classical logic, Lukasiewicz three-valued system L₃, the intuitionistic system Iⁱ and several para-consistent logics, as for instance Sette's system Pⁱ, the D'Ottaviano and da Costa system J₃ and da Costa's systems $\text{C}_{n}$ , 1 ≤ n ≤ ω. (shrink)

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper (...) we present some conservative translations involving classical logic, Lukasiewicz three-valued system L3, the intuitionistic system I1 and several paraconsistent logics, as for instance Sette's system P1, the D'Ottaviano and da Costa system J3 and da Costa's systems Cn, 1≤ n≤ω. (shrink)

Arthur Madigan presents a clear, accurate new translation of the third book of Aristotle's Metaphysics, together with two related chapters from the eleventh book. Madigan's accompanying introduction and commentary give detailed guidance to these texts, in which Aristotle sets out what he takes to be the main problems of metaphysics or 'first philosophy' and assesses possible solutions to them; he takes his starting-point from the work of earlier philosophers, especially Plato and some of the Presocratics. These texts serve (...) as a useful introduction both to Aristotle's own work on metaphysics and to classical metaphysics in general; they are also a good example of Aristotle's dialectical method, which reasons not from known truths but from reputable opinions. (shrink)

The Joint Non-Trivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J 3-theories. These theories are three-valued with more than one distinguished truth-value, reflect certain aspects of model type logics and can. be paraconsistent. J 3-theories were introduced in the author's doctoral dissertation.

Aristotle was the first philosopher in the Western tradition to address politics systematically and empirically, and he remains a central figure in political theory. This essential volume presents Aristotle's complete political writings—including his Politics, Economics, and Constitution of Athens—in their most authoritative translations, taken from the complete works that is universally recognized as the standard English edition. Edited by Jonathan Barnes, one of the world’s leading scholars of ancient philosophy, and with an illuminating introduction by Melissa Lane, an (...) authority on ancient political philosophy, this compact but comprehensive volume will be invaluable for all students of politics, philosophy, classics, or Western thought. (shrink)

In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n (...) and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤nshrink)

Aristotle is without question the founder of the science of biology. In his treatise On the Parts of Animals, he develops his systematic principles for biological investigation, and explanation, and applies those principles to explain why the different animal kinds have the different parts that they do. It is one of the greatest achievements in the history of science. This new translation from the Greek aims to reflect the subtlety and detail of Aristotle's reasoning. The commentary provides help (...) in understanding each argument as well as an integrated account of the goals and methods of the work taken as a whole. (shrink)

Joe Sachs has followed up his brilliant translation of Aristotle's Physics with a new translation of Metaphysics. Sachs's translations bring distinguished new light onto Aristotle's works, which are foundational to history of science. Sachs translates Aristotle with an authenticity that was lost when Aristotle was translated into Latin and abstract Latin words came to stand for concepts Aristotle expressed with phrases in everyday Greek language. When the works began being translated into English, those abstract Latin (...) words or their cognates were used, thus suggesting a level of jargon and abstraction, and in some cases misleading interpretation, which was not Aristotle's language or style. These important new translations open up Aristotle's original thought to readers. (shrink)

This article examines the main aspects of Husserl's phenomenology, which are analyzed in "Appearance and Sense" by Gustav Shpet: the relation between sense and comprehension and between noesis and noema. Shpet emphasizes the hermeneutical theme of "comprehension" as a resolutive dimension to solve aspects not clarified by Husserl. Shpet's critical enquiry, in the course of his subsequent observation, converge into an hermeneutical logic. Shpet identifies the centrality of language as a form of thinking, through the recovery of Humbodt's meaning of (...) the "inner form". (shrink)

The foundation of ancient, invented writing systems lies in the predominant iconicity of their sign shapes. However, these shapes are often used not for their referential meaning but in a metaphorical way, whereby one entity stands for another. Metaphor, including its subcategories pars pro toto and metonymy, plays a crucial role in the formation of the earliest pristine invented scripts, yet this mechanism has been understudied from a cognitive, contextual, and comparative perspective. This article aims to address issues pertaining to (...) the definition, development, and application of these mechanisms in the formation of the Mesopotamian, Egyptian, and Chinese scripts. We analyze the local cases of metaphor-in-action in primary inventions, focusing first on visual metaphors and, second, on the typical or idiosyncratic uses of metonyms. (shrink)

In a recent contribution to this journal, D. Kovacs addresses the following passage from the fourth Eclogue :o mihi tum longae maneat pars ultima uitae,spiritus et quantum sat erit tua dicere facta!Kovacs takes it for granted that the meaning of l. 54 should correspond to the Loeb translation, ‘and inspiration enough to hymn your deeds!’. Starting from this assumption, he rejects the reading spiritus, arguing that a genitive is required ; the possible solution he suggests is pectoris, used metaphorically in (...) the sense of ‘poetical ability’. That seems a clever conjecture, restoring excellent style. Nevertheless, we have to assume that spiritus replaced pectoris as a gloss, but I cannot see any reason why somebody would have wanted to explain obscurum per obscurius: other words would have been far more appropriate. On the other hand, Virgil most likely chose the word spiritus, whose basic meaning is not ‘inspiration’ but ‘breath’, in order to amplify line 53. (shrink)

Edited by Richard McKeon, with an introduction by C.D.C. Reeve Preserved by Arabic mathematicians and canonized by Christian scholars, Aristotle’s works have shaped Western thought, science, and religion for nearly two thousand years. Richard McKeon’s The Basic Works of Aristotle—constituted out of the definitive Oxford translation and in print as a Random House hardcover for sixty years—has long been considered the best available one-volume Aristotle. Appearing in paperback at long last, this edition includes selections from the Organon, (...) On the Heavens, The Short Physical Treatises, Rhetoric, among others, and On the Soul, On Generation and Corruption, Physics, Metaphysics, Nicomachean Ethics, Politics, and Poetics in their entirety. (shrink)

This reissue of Richard Robinson's classic volume on Aristotle's Politics contains his clear and accurate translation of, and commentary on, books III and IV, brought up to date by a supplementary essay and new bibliography by David Keyt. This is the ideal companion to study these important books of a classic text in the history of political philosophy.

The eighth book of Aristotle's Physics is the culmination of his theory of nature. He discusses not just physics, but the origins of the universe and the metaphysical foundations of cosmology and physical science. He moves from the discussion of motion in the cosmos to the identification of a single source and regulating principle of all motion, and so argues for the existence of a first `unmoved mover'. Daniel Graham offers a clear, accurate new translation of this key text (...) in the history of Western thought, and accompanies the translation with a careful philosophical commentary to guide the reader towards an understanding of the wealth of important and influential arguments and ideas that Aristotle puts forward. (shrink)

Eudemian ethics -- Nicomachean ethics -- Magna moralia -- Virtues and vices.