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Added by: Viviane FairbankAbstract:
This book is intended for the newcomer to formal logic and is designed to provide an introduction for the intelligent general reader as well as for the student in the classroom. Its primary purpose is to present in a clear, natural, and orderly fashion the fundamentals of a subject that has now acquired the status of an exact science... Chapters I through VII are devoted to the exposition of material necessary to the construction of the deductive system of truth-functions... Thanks to the special notation that has come to be characteristic of symbolic logic, it is possible to express the logical material with clarity and exactness and to organize it, as in Chapter VIII, into a deductive system. Chapters IX through XI are given over to the study of general propositions and of forms of inference involving them... Care has been taken to show how Aristotelian logic is accommodated within the framework of the extended, present-day subject: by introducing the reader to quantification theory and to the current notation for expressing forms of general propositions, and finally, by presenting, in Chapter XII, the calculus of classes.Comment: This introductory textbook to formal logic was widely used in America in the mid-20th Century. Although some of the methods and notations are now outdated, it still provides a useful introduction to central ideas in formal and informal logic, and could be used as a reference for those preparing an introductory logic course (or for those interested in the history of logic education).
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Added by: Clotilde Torregrossa, Contributed by: Benedict EastaughAbstract:
Aristotle is generally credited with the invention of logic. More than two thousand years ago, he noticed that good, persuasive arguments have certain kinds of shapes, or structures. Logic was born when he began to study those structures, which he called syllogisms, identifying underlying patterns of ordinary human reasoning and then devising simple methods which can be used to determine whether someone is reasoning correctly. Aristotle was aware that this was a momentous discovery, and he himself thought that all scientific reasoning could be reduced to syllogistic arguments. There are hints that Aristotle saw his syllogistic logic as providing useful practice for participants in ancient debating contests, contests which he himself would have encountered as a student in Plato’s Academy. There are also hints that Aristotle might have envisioned his syllogistic logic as providing a way to catalogue facts about science. But Aristotle never fleshes out any such details. His Prior Analytics, the text in which he presents his syllogistic, focuses on the mechanics of the syllogistic far more than on its interpretation, and in fact the comparative lack of interpretive detail has sometimes led scholars to suppose that what we have today of Aristotle’s logic is his own sometimes scrappy lecture notes or his students’ notes, and not a polished, finished work. But in the end these are of course only guesses. In modern times, the main scholarly interest in Aristotle’s ancient logic has focused increasingly on the proper interpretation of the mechanical methods which Aristotle invented and on their relation to his wider philosophy.
Comment: This chapter can be used as a first introduction to Aristotle's logic. It could be set in a course on history of logic, for example by pointing to the limits of Aristotle's system in order to set up later developments (e.g. Frege). It could also be used in an introductory logic course, with students set exercises such as working out whether syllogisms represent valid derivations in classical first-order logic.