ARISTOTLE'S PROGRAM Aristotle says outright that the law of non-contradiction cannot be demonstrated: you can't prove everything, and among the things you ...

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.

Aristotle shares with Plato the attitude that the world, ‘the all,’ is a kosmos, a well-ordered and beautiful whole which, as such, can be rendered intelligible, or understood, by the intellect. One understands things, generally speaking, by tracing them back to their sources, origins or principles and causes or explanatory factors, and seeing in what manner they are related to these principles. We know, or understand, a thing when we grasp ‘the why’ or cause. Consequently, understanding is systematic. Some things (...) we understand through themselves - these are the first principles and as such are not understood by tracing them back to causes. We understand other things by systematically relating them in appropriate ways to what is known through itself. These other things are known through, or by means of, their causes and principles. (shrink)

RECENT attempts to explain and justify Aristotle's principle of non-contradiction have focused to a great extent on the dialectical dimension of Aristotle's account. For example, T. Irwin maintains that Aristotle justifies the PNC by arguing that there is a sub-set of dialectical opinions which no one can rationally give up. J. Lear supports the importance of the dialectical dimension by summarizing Aristotle's defense of the PNC as follows: The opponent of the PNC tries to argue dialectically that one should not (...) accept it. "Aristotle's point is that there is no conceptual space in which such a rational discussion can occur." By appealing to the limits of rationally, externally, expressible discourse as the basis of the PNC, Irwin and Lear fail to take seriously the more explicitly psychological and metaphysical bases of the PNC. C. Kirwan, and most recently, R. Smith also either argue against or ignore the role of the psychological and metaphysical bases. Smith goes so far as to argue that common axioms like the PNC are simply empty statement schemata of universal validity, i.e., general verbal forms or patterns which no one can deny with intelligibility. (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)

In Metaphysics III, Chapter 4, Aristotle sets out and defends the Law of Non-Contradiction. The arguments are, however, rather less satisfactory than one might have expected, given the enormous historical influence the text has had. His major argument is a particularly tangled one, and the others are often little more than throw-away remarks. This essay is a commentary on the chapter, but its aim is less to interpret the text , than to see whether there is anything that Aristotle could (...) have meant that would have served his purpose. Whilst other commentators have sometimes attempted this, they have always taken his conclusion to be correct, even if his arguments were not; I do not. The commentary is therefore a confrontation between Aristotle and modern dialetheism. (shrink)

Aristotle's treatise De Interpretatione is one of his central works; it continues to be the focus of much attention and debate. C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system, basing this view upon a detailed chapter-by-chapter analysis.By treating the work systematically, rather than concentrating on certain selected passages, Whitaker is able to show that, contrary to traditional opinion, it forms (...) an organized and coherent whole. He argues that the De Interpretatione is intended to provide the underpinning for dialectic, the system of argument by question and answer set out in Aristotle's Topics; and he rejects the traditional view that the De Interpretatione concerns the assertion and is oriented towards the formal logic of the Prior Analytics. In doing so, he sheds valuable new light on some of Aristotle's most famous texts. (shrink)

In what follows I will say little if anything about the animadversions vis-à-vis Irwin and Lukasiewicz and Owen, because there is so much of such greater interest in what Code has told us about Aristotle, the great preponderance of which, in my opinion, is true. I will review some of this truth, specify one place where I have trouble reconciling his account with the evidence, and then try to give a better account that I think is entirely compatible with the (...) rest of what he has given us. (shrink)

Aristotle was the first and one of the greatest logicians. He not only devised the first system of formal logic, but also raised many fundamental problems in the philosophy of logic. In this book, Dr Lear shows how Aristotle's discussion of logical consequence, validity and proof can contribute to contemporary debates in the philosophy of logic. No background knowledge of Aristotle is assumed.

Critical discussion of Alan Code's paper "Aristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principle of Non-Contradiction?".

The purpose of this dissertation is to provide a defence of Aristotle's principle of contradiction against the critique made on it by Jan Lukasiewicz in an article he wrote in 1910 which was translated and published in the March 1971 number of The Review of Metaphysics. Lukasiewicz maintains in general that the law of contradiction has no logical worth. Specifically, he charges Aristotle with having several laws of contradiction instead of one as Aristotle claims; with attempting to prove the law (...) despite his claim that this is impossible and finally with failing in the very attempt to prove the law, or at least one of its formulations. In 20 chapters, each dealing with a respective section of Lukasiewicz's article, I attempt to show that all of Lukasiewicz's allegations are unfounded. My methodology is simply to follow Lukasiewicz through his 20 sections and compare what he says with what Aristotle actually wrote. If successful, this dissertation will show, in basic agreement with Professor Joseph Owens, that the best way to read Aristotle is on his own terms and not, as in the case of Lukasiewicz, via the latest developments in symbolic logic. I reiterate, with Aristotle, that the law of contradiction is the basic principle of being qua being and has logical worth precisely because of that fact. (shrink)