Which means, that the true infinite is more than a mere world beyond the finite, and that we, in order to become conscious of it, must renounce that _progressus in infinitum._ (3) Pythagoras, as is well known, philosophised in numbers, and conceived number as the fundamental principle of things. To the ordinary mind this view must at first glance seem an utter paradox, perhaps a mere craze. What, then, are we to think of it? To answer this question, we must, in the first place, remember that the problem of philosophy consists in tracing back things to thoughts, and, of course, to definite thoughts. Now, number is undoubtedly a thought: it is the thought nearest the sensible, or, more precisely expressed, it is the thought of the sensible itself, if we take the sensible to mean what is many, and in reciprocal exclusion. The attempt to apprehend the universe as number is therefore the first step to metaphysics. In the history of philosophy, Pythagoras, as we know, stands between the Ionian philosophers and the Eleatics. While the former, as Aristotle says, never get beyond viewing the essence of things as material (ὕλη), and the latter, especially Parmenides, advanced as far as pure thought, in the shape of Being, the principle of the Pythagorean philosophy forms, as it were, the bridge from the sensible to the super-sensible. We may gather from this, what is to be said of those who suppose that Pythagoras undoubtedly went too far, when he conceived the essence of things as mere number. It is true, they admit, that we can number things; but, they contend, things are far more than mere numbers. But in what respect are they more? The ordinary sensuous consciousness, from its own point of view, would not hesitate to answer the question by handing us over to sensuous perception, and remarking, that things are not merely numerable, but also visible, odorous, palpable, &c. In the phrase of modern times, the fault of Pythagoras would be described as an excess of idealism. As may be gathered from what has been said on the historical position of the Pythagorean school, the real state of the case is quite the reverse. Let it be conceded that things are more than numbers; but the meaning of that admission must be that the bare thought of number is still insufficient to enunciate the definite notion or essence of things. Instead, then, of saying that Pythagoras went too far with his philosophy of number, it would be nearer the truth to say that he did not go far enough; and in fact the Eleatics were the first to take the further step to pure thought.