This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

Equality1 gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift I assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = (...) b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names ‘a’ and ‘b’ designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign ‘a’ is distinguished from the sign ‘b’ only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true.. (shrink)

The establishment of South Africa's Truth and Reconciliation Commission was a pioneering international event. Never had any country sought to move forward from despotism to democracy both by exposing the atrocities committed in the past and achieving reconciliation with its former oppressors. At the center of this unprecedented attempt at healing a nation has been Archbishop Desmond Tutu, whom President Nelson Mandela named as Chairman of the Truth and Reconciliation Commission. With the final report of the Commission just published, Archbishop (...) Tutu offers his reflections on the profound wisdom he has gained by helping usher South Africa through this painful experience. In No Future Without Forgiveness, Tutu argues that true reconciliation cannot be achieved by denying the past. But nor is it easy to reconcile when a nation "looks the beast in the eye." Rather than repeat platitudes about forgiveness, he presents a bold spirituality that recognizes the horrors people can inflict upon one another, and yet retains a sense of idealism about reconciliation. With a clarity of pitch born out of decades of experience, Tutu shows readers how to move forward with honesty and compassion to build a newer and more humane world. (shrink)

In the course of the discussion, Professor Quine pinpoints the difficulties involved in translation, brings to light the anomalies and conflicts implicit in our ...

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

_Reading Science_ looks at the distinctive language of science and technology and the role it plays in building up scientific understandings of the world. It brings together discourse analysis and critical theory for the first time in a single volume. This edited collection examines science discourse from a number of perspectives, drawing on new rhetoric, functional linguistics and critical theory. It explores this language in research and industrial contexts as well as in educational settings and in popular science writing and (...) science fiction. The papers also include consideration of the role of images in science writing and the importance of reading science discourse as multi-modal text. The internationally renowned contributors include M. A. K. Halliday, Charles Bazerman and Jay Lemke. (shrink)