perceived particular things through which we conceive and deduce them: Man is more permanent than Tom, or Dick, or Harry; this circle is born with the movement of my pencil and dies under the attrition of my eraser, but the conception Circle goes on forever. This tree stands, and that tree falls; but the laws which determine what bodies shall fall, and when, and how, were without beginning, are now, and ever shall be, without end. There is, as the gentle Spinoza would say, a world of things perceived by sense, and a world of laws in- ferred by thought; we do not see the law of inverse squares but it is there, and everywhere; it was before anything began, and will survive when all the world of things is a finished talc. Here is a bridge: the sense perceives concrete and iron to a hundred million tons; but the mathematician sees, with the mind's eye, the daring and delicate adjustment of all this mass of material to the laws of mechanics and mathematics and en- gineering, those laws according to which all good bridges that are made must be made; if the mathematician be also a poet, he will see these laws upholding the bridge; if the laws were violated the bridge would collapse into the stream beneath; the laws are the God that holds up the bridge in the hollow of his hand. Aristotle hints something of this when he says that by Ideas Plato meant what Pythagoras meant by "num- ber" when he taught that this is a world of numbers (meaning presumably that the world is ruled by mathematical con- stancies and regularities). Plutarch tells us that according to Plato "God always geometrizes"; or, as Spinoza puts the same thought, God and the universal laws of structure and operation are one and the same reality. To Plato, as to Bertrand Russell, mathematics is therefore the indispensable prelude to philosophy, and its highest form; over the doors of his Academy Plato placed, Dantesquely, these words, "Let no man ignorant of geometry enter here."[1]
- ↑ The details of the argument for the interpretation here given of the doctrine of Ideas may be followed in D. G. Ritchie's Plato, Edinburgh, 1902, especially pp. 49 and 85.
