A Preface to Logic

A Preface to Logic

A Preface to Logic

A Preface to Logic

Excerpt

In the history of ideas the past century is one marked by an extraordinary development of logic. A discipline, which had remained for more than twenty centuries in approximately the state to which the mind of Aristotle reduced it, suddenly entered upon a period of rapid growth and systematic development. While the essential elements of the Aristotelian logic have not been overthrown or shaken, the labours of Boole, Peirce, Schröder. Frege, Russell, Whitehead, and a host of fellow workers have produced a calculus of classes and a calculus of propositions in which the Aristotelian theory of the syllogism is seen to occupy only a tiny corner. The potentialities of the new logic as a scientific instrument have already been indicated in the illumination which the application of modern logic has brought to the foundations of mathematics. There is reason to hope that parallel results may soon be achieved in other fields.

Unfortunately, however, periods of rapid and extensive development of a science are frequently periods of loose thinking about the foundations of the science itself. Such was the case with mathematics in the eighteenth century and with biology in the nineteenth. So it is today that the philosophic significance of the new logic, the character of its presuppositions, and the directions of its possible application are problems which have attracted relatively little reflective thought. Indeed, with a sort of perverse professional modesty, many of our most brilliant contemporary logicians have insisted that the subject of their study is simply marks on paper, or symbols generally, without relevance to the objective realities that are explored by the natural and social sciences.

It may be that this attitude represents a healthy reaction away from the excessive claims of an absolustic rationalism which . . .

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