Aristotle: Logic and Philosophy of Language

For the second edition, the translation has been completely rewritten and the commentary has been thoroughly revised in the light of recent scholarship.

Book 1 of Euclid's Elements opens with a set of unproved assumptions: definitions , postulates, and ‘common notions’ . The common notions are general rules validating deductions that involve the relations of equality and congruence. The attested postulates are five in number, even if a part of the manuscript tradition adds a sixth, almost surely spurious , that in some manuscripts features as the ninth, and last, common notion. The postulates are called αἰτήματα both in the manuscripts of the Elements (...) and in the ancient exegetic tradition. It is not said, however, that this denomination is original, as it coincides with the nomen rei actae associated with the verbal form introducing the postulates themselves. Since antiquity it has been recognized that the postulates naturally split into two groups of quite different character: the first three are rules licensing basic constructions, the fourth and the fifth are assertions stating properties of particular geometric objects . I transcribe postulates 1–3 in the text established by Heiberg : ᾐτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράϕεσθαι. (shrink)

A lógica, considerada como uma disciplina técnica iniciada por Aristóteles e tipicamente representada pela variedade de cálculos lógicos modernos, constitui um esclarecimento e refinamento de uma convicção e prática presentes no senso comum, ou seja, o fato de que os seres humanos crêem que a verdade pode ser adquirida não apenas por evidência imediata, mas também por meio de argumentos. Como uma primeira aproximação, a lógica pode ser vista como um registro “descritivo” das principais formas de argumento presentes no senso (...) comum, mas o fato de que alguns desses padrões possam realmente permitir a derivação de consequências falsas a partir de premissas verdadeiras impõe a tarefa de tornar explícitos que padrões correspondem a um “raciocínio correto” e quais não. Nesse ponto, a lógica (que contém a apresentação de tais padrões) parece ser dotada de uma característica “normativa”. Isso equivale a dizer se pretende que os cálculos lógicos espelhem adequadamente a noção intuitiva de “consequência lógica” e que nesse sentido eles não podem ser totalmente arbitrários ou convencionais, mas devem satisfazer certos requisitos básicos tais como as condições de correção e (tanto quanto possível) de completude semântica. Em tal forma eles são “julgados” de acordo com os requisitos fundamentais presentes no nível do senso comum e aparecem como “idealizações” das espécies de raciocínio praticadas no senso comum. Por essa razão também vários tipos de cálculos lógicos são inteiramente justificados uma vez que tornam explícitos, de uma forma idealizada, os modos concretos de raciocinar que são impostos pelo particular domínio de referência da disciplina na qual são usados e que são basicamente reconhecidos no senso comum. DOI: 10.5007/1808-1711.2011v15n1p15. (shrink)

This paper intends to explain key differences between Aristotle’s understanding of the relationships between nous, epistêmê, and the art of syllogistic reasoning(both analytic and dialectical) and the corresponding modern conceptions of intuition, knowledge, and reason. By uncovering paradoxa that Aristotle’s understanding of syllogistic reasoning presents in relation to modern philosophical conceptions of logic and science, I highlight problems of a shift in modern philosophy—a shift that occurs most dramatically in the seventeenth century—toward a project of construction, a pervasive desire for (...) rational certainty, and a general insistence on the reducibility of the sciences. The major motivation of this analysis is my intention to show that modern attempts to reduce science/epistêmê to a single science/method of inquiry occlude dialectical and ethico-political dimensions of “reason” and, hence, also impoverish philosophy’s critical capacities. (shrink)

The drive of this book, without ever quite saying so, is to recommend Aristotle’s teaching on truth for contemporary thought. The book is more about concepts and arguments around truth than about truth per se. The explanation of the famous definition of truth, as saying of what is that it is, occupies a few pages. The rest of the book elucidates the vast subtext of this limpid passage. What must intellect be, what must speech be, what must beings be, for (...) this saying of what is? The “correspondence theory of truth,” which textbooks routinely attribute to Aristotle, is repudiated. Correctness and accuracy are not the fundamental values of truth. They are byproducts of a more fundamental responsiveness to the way .. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

In the Posterior Analytics, Aristotle takes up the position of those who hold that all knowledge is demonstrable, and, hence, scientific. Such people are said to base their arguments on the fact that some demonstrations are circular or reciprocal (72b251). As Aristotle makes clear in the text, a circular demonstration consists of an argument (form) in which the conclusion is equivalent to one of the premises. But as Aristotle hastens to point out, demonstrations cannot be circular, for the essence of (...) demonstration is to proceed from what is prior to what is posterior, and the same things cannot be both prior and posterior. A circular demonstration has the form ‘if A is, then B must be;’ and ‘if B is, then A must be’: “consequently, the upholders of circular demonstration are in the position of saying that if A is, A must be—a simple way of proving anything” (73a5). (shrink)

WE must first state the subject of our inquiry and the faculty to which it belongs: its subject is demonstration and the faculty that carries it out demonstrative science.