ABSTRACT
By “mathematical logic” is meant here the various attempts to renew formal and analytical logic in the spirit of mathematics and by means of mathematical terms and methods. It is a movement which assumes an increasing importance throughout the period of which we treat, Both the first suggestions for the establishment (or re-establishment) of a mathematical logic in the middle of last century and, indeed, in part earlier still, and the later development that took more explicit shape at the opening of the present century derive mainly from the work of British thinkers; and even to-day, when the movement has become an international one, the British share in it remains of the first importance. In confining ourselves to a very superficial survey in the form of a short historical review of this subject of so many ramifications, we are well aware that we are doing less than justice to its significance. The only excuse for so cursory a treatment is that we are here concerned with a very specific discipline, whose connection with the movement of philosophy as a whole is not close and whose philosophical import and relevance is even to-day a matter of much controversy. We cannot accept the claim of the over-enthusiastic devotees of mathematical logic, that this is the ground upon which philosophy as such must join issue, and upon which, indeed, its very fate must be decided. Nor can we admit that the last word has been spoken upon logic, however radically the subject has been transformed and improved by the mathematical logicians. What they have done is, rather, simply to constitute a new branch on the main trunk of logical science, a branch full of significance and extensive in its reach, but drawing nourishment far more from the soil of mathematics than from that of philosophy. That the new discipline lies closer to the heart of mathematics than to philosophy is, indeed, shown by the fact that it grew in the first instance out of mathematical interests and discussions, and was established and developed by mathematical investigators. Accordingly, if the excessive claims of mathematical logic are rejected and its philosophical relevance duly limited, this is only to endorse and affirm the more emphatically its services in its own special domain.
