Frank A. Lewis presents a close study of book Zeta of Aristotle's Metaphysics, one of his most dense and controversial texts, commonly understood to contain his deepest thoughts on the definition of substance and related metaphysical issues. Lewis argues that Aristotle returns to the causal view of primary substance from his Posterior Analytics.
This book takes up the central themes of Aristotle's metaphysical theory and the various transformations they undergo prior to their full expression in the Metaphysics. Aristotle's metaphysics is bedevilled by classic puzzles involving such notions as form, predication, universal, and substance, which result from his attempt to adapt the various requirements on primary substance developed in his earlier works so that they fit the very different metaphysical picture in his later work. Professor Lewis argues that Aristotle is himself aware of (...) most if not all of these difficulties and in the Metaphysics works hard to ensure the coherence of his theory. He presents Aristotle's views as a formal theory complete with axioms, definitions, and theorems. (shrink)
The topic of homonymy, especially the variety of homonymy that has gone under the title, “focal meaning,” is of fundamental importance to large portions of Aristotle’s work-not to mention its central place in the ongoing controversies between Aristotle and Plato. It is quite astonishing, therefore, that the topic should have gone so long without a book-length treatment. And it is all the more gratifying that the new book on homonymy by Christopher Shields should be so comprehensive, and of such uniformly (...) high quality.’ Everyone who cares about Aristotle will be in his debt. Shields’s book falls into two parts. In the first, he is concerned to lay out the basic structure of Aristotle’s views about homonymy; in the second part, we are led through the various applications of the idea, to the analysis of friendship, for example, the homonymy of the body, the account of goodness and, not least, the homonymy of being. Shields’s book brings out well how the topic of homonymy weaves in and out of the fabric of Aristotle’s thinking in a variety of areas. I will resist the temptation to follow Shields through these various subject-matters, and instead take up essentially two topics. First, (I), the basic outline of Aristotle’s notion of homonymy, more or less independently of its different applications (here, I follow Shields’s example in the first half of his book). Thereafter, I discuss a single application: the homonymy of being (this is the subject of Shields’s last and longest chapter). Here, I will be interested (II) in how homonymy relates to the theory of the categories; and (III) in the application of homonymy to the analysis of substance in the Metaphysics. (shrink)
What in Aristotle corresponds, in whole or (more likely) in part, to our contemporary notion of predication? This paper sketches counterparts in Aristotle's text to our theories of expression and of truth, and on this basis inquires into his treatment of sentences assigning an individual to its kinds. In some recent accounts, the Metaphysics offers a fresh look at such sentences in terms of matter and form, in contrast to the simpler theory on offer in the Categories . I argue (...) that the Metaphysics initiates no change in this regard over the Categories . The point that form is (metaphysically) predicated of matter is a contribution, not to the account of statement predication, but to the analysis of compound material substances. Otherwise put, in our terms Aristotelian form is not - in particular, is not also - a propositional function, but a function from matter to compound material substances. (shrink)
In his great poem, Parmenides uses an argument by elimination to select the correct "way of inquiry" from a pool of two, the ways of is and of is not , joined later by a third, "mixed" way of is and is not . Parmenides' first two ways are soon given modal upgrades - is becomes cannot not be , and is not becomes necessarily is not (B2, 3-6) - and these are no longer contradictories of one another. And is (...) the common view right, that Parmenides rejects the "mixed" way because it is a contradiction? I argue that the modal upgrades are the product of an illicit modal shift. This same shift, built into two Exclusion Arguments, gives Parmenides a novel argument to show that the "mixed" way fails. Given the independent failure of the way of is not , Parmenides' argument by elimination is complete. (shrink)
The topic of homonymy, especially the variety of homonymy that has gone under the title, “focal meaning,” is of fundamental importance to large portions of Aristotle’s work—not to mention its central place in the ongoing controversies between Aristotle and Plato. It is quite astonishing, therefore, that the topic should have gone so long without a book-length treatment. And it is all the more gratifying that the new book on homonymy by Christopher Shields should be so comprehensive, and of such uniformly (...) high quality. Everyone who cares about Aristotle will be in his debt. (shrink)
Replying to Theaetetus’ suggestion that knowledge is true opinion at Tht. 200e, Socrates remarks that ‘a whole profession’ testifies against this definition. The orator practises the art of persuasion, not to teach people, but make them believe whatever he wants. If a robbery has taken place, for example, he cannot in a short time teach adequately the truth about what happened to people who were not on the scene.
The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more (...) free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control. (shrink)