ABSTRACT
THE author of this remarkable treatise on the Paradoxes of the Infinite began writing it as early as 1847, during his residence in the company of the Editor at the charming country house in Liboch, near Melnik, but was interrupted by tasks of a different nature and did not complete it until the summer months of the following year, the last of his life. The work not only gave evidence that his intellectual powers (despite his advancing age of sixty-seven years and the visible decline of his bodily strength) had lost nothing of their vigour and alertness, but also furnished the learned world with fresh proofs of the uncommon insight he enjoyed into the most abstract depths of mathematics, natural science and metaphysics. Indeed, had Bolzano written and bequeathed to us nothing else than this one treatise, it is our firm belief that on its account alone he would have to be numbered among the most distinguished minds of our century. He knows how to solve with admirable ease the most interesting and complicated of the problems which are raised by the idea of the infinite and have at all times engrossed the attention of workers in these aprioristic sciences; and he can disentangle them before the very eyes of a reader with such clearness that anyone not a complete stranger to the subject, even though he may have hitherto grasped but a few of the matters in question, can still follow the author’s exposition, and find at least the majority of his propositions easy to understand. The experts on their part (if only they devote some attention to the treatise, and may we not expect this much from every scholar whatever?) are also bound to notice before long how important are the ideas which Bolzano suggests in this work and develops more circumstantially in others, especially in his Logic and in his Athanasia, and how he aims at nothing less than a complete transformation of all the modes of scientific exposition hitherto adopted.
