There are obvious benefits to be gained from the study of logic: heightened ability to express ideas clearly and concisely, increased skill in defining one's terms, enlarged capacity to formulate arguments rigorously and to analyze them critically. But the greatest benefit, in my judgment, is the recognition that reason can be applied in every aspect of human affairs.

For more than six decades, and for thousands of students, Introduction to Logic has been the gold standard in introductory logic texts. In this 15th Edition, Carl Cohen and Victor Rodych update Irving M. Copi's classic text, improving on its many strengths and introducing new and helpful material that will greatly assist both students and instructors.

The year 1897 saw the publication of the first of the modern logical paradoxes. It was published by Cesare Burali-Forti, the Italian mathematician whose name it has come to bear. Burali-Forti's own formulation of the paradox was not altogether satisfactory, as he had confused well-ordered sets as defined by Cantor with what he himself called “perfectly ordered sets”. However, he soon realized his mistake, and published a note admitting the error and making the correction. He concluded the note with the (...) observation that his result could be established on the basis of the correct definition of well-ordered set as easily as for the “perfectly ordered sets” for which it had first been obtained. We shall reproduce his results in their corrected form. (shrink)

The purpose of the article is to explain two curious doctrines maintained by frege and rejected by wittgenstein in the 'tractatus logico-philosophicus'. that a special assertion sign is necessary was maintained by frege because he wanted to apply his concept-writing to ordinary language, and it was rejected by wittgenstein because his concern in the 'tractatus' was with scientific assertions only. frege's paradoxical notion that 'the concept horse is not a concept' was a consequence of his symbolizing functions by 'unsaturated' expressions. (...) wittgenstein's picture theory eliminated expressions for relations and thereby avoided the fregean paradox. (shrink)

This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.