My sympathies lie strongly with the Platonistic view that mathematical truth is absolute, external, and eternal, and not based on man-made criteria; and that mathematical objects have a timeless existence of their own, not dependent on human society nor on particular physical objects.
Plato’s ideas do not belong to space-time but they exist independently of the human mind and are the cause of phenomena. This is why, when we talk of Plato, we sometimes talk of the realism of essences. In this sense (a distant independent reality, probably not situated in time and space-time), it is difficult for the philosophical realism of a physicist to avoid being a little bit Platonist. Bohm himself, previously a standard bearer of the “materialist” physicists, even says now that perceived objects are only projections of what exists (4).
I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.
However, it seems to me that nevertheless one ingredient of this wrong theory of mathematical truth is perfectly correct and really discloses the true nature of mathematics. Namely, it is correct that a mathematical proposition says nothing about the physical or psychical reality existing in space and time, because it is true already owing to the meaning of terms occuring in it, irrespectively of the world of real things. What is wrong, however, is that the meaning of terms (that is, the concepts they denote) is asserted to be something man-made and consisting merely in semantic conventions. The truth, I believe, is that these concepts form an objective reality of their own, which we cannot create or change, but only perceive and describe.
Science and mathematics were to be removed from the hands of the merchants and the artisans. This tendency found its most effective advocate in a follower of Pythagoras named Plato" and "He (Plato) believed that ideas were far more real than the natural world. He advised the astronomers not to waste their time observing the stars and planets. It was better, he believed, just to think about them. Plato expressed hostility to observation and experiment. He taught contempt for the real world and disdain for the practical application of scientific knowledge. Plato's followers succeeded in extinguishing the light of science and experiment that had been kindled by Democritus and the other Ionians."
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our “creations,” are simply the notes of our observations.
The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.
I am aware that the great Plato himself, and after him, a man posterior to him in date, though not in mind, I mean Iamblichus of Chalcis (who initiated us into other branches of philosophy, and also into this by means of his discourses), did both of them as far as hypothesis goes, take for granted the fact of a Creation and assumed the universe to have been, in a certain sense, the Work of Time, in order that the most important of the effects produced by this Power, may be reduced into a shape for examination.
The Chaldaeans distinguished between two fiery bodies: one possessed of a noetic nature and the visible sun. The former was said to conduct the latter. According to Proclus, the Chaldaeans call the "solar world" situated in the supramundane region "entire light." In another passage, this philosopher states that the supramundane sun was known to them as "time of time...."
On this account, it appears to me that Plato delivers a twofold generation of the Sun; one indeed, in conjunction with the seven governors of the world, when he fashions the bodies of them, and inserts them in circulations; but the other according to the enkindling of light, through which he imparts to the Sun supermundane power. For it is one thing to generate the bulk of the Sun itself by itself, and another in conjunction with a ruling characteristic, through which the Sun is called the king of every visible nature, and is established analogous to the one fountain of good. For as this fountain, being better than the intelligible essence, illuminates both intellect and the intelligible, thus also the sun being better than a visible nature, illuminate both that which is visible and sight. But if the Sun is beyond a visible essence, it will have a supermundane nature. For the world is visible and tangible, and has a body. Hence, we must survey the Sun in a twofold respect; viz. as one of the seven planets, and as the leader of wholes; and as mundane and supermundane, according to the latter of which he splendidly emits a divine light. For in the same manner as The Good luminously emits truth which deifies the intelligible and intellectual order; as Phanes in Orpheus sends forth intelligible light which fills with intelligence all the intellectual Gods; and as Jupiter enkindles an intellectual and demiurgic light in all the supermundane Gods; thus also the Sun illuminates every thing visible through this undefiled light. The illuminating cause too is always in an order superior to the illuminated natures. For neither is The Good intelligible, nor Phanes intellectual, nor Jupiter supermundane. In consequence of this reasoning therefore, the Sun being supermundane emits the fountains of light. And according to the most mystic doctrines, the wholeness of the Sun is in the supermundane orders; for in them there is a solar world, and a total light, as the Chaldean Oracles assert, and which I am persuaded is true. And thus much concerning these things.