'Unless,' said I [Socrates], either philosophers become kings in our states or those whom we now call our kings:. and rulers take to the pursuit of' philosophy seriously and adequately, and there is a conjunction of these two things, political power and philosophic intelligence, while the motley horde of the natures who at present pursue either apart from the other are compulsorily excluded, there can be no cessation of troubles, dear Glaucon, for our states, nor, I fancy for the human race either. Nor, until this happens, will this constitution which we have been expounding in theory ever be put into practice within the limits of possibility and see the light of the sun.

'Yes,' he said. 'But these things (the solutions to problems in solid geometry such as the duplication of the cube) do not seem to have been discovered yet.' 'There are two reasons for this,' I said. 'Because no city holds these things in honour, they are investigated in a feeble way, since they are difficult; and the investigators need an overseer, since they will not find the solutions without one. First, it is hard to get such an overseer, and second, even if one did, as things are now those who investigate these things would not obey him, because of their arrogance. If however a whole city, which did hold these things in honour, were to oversee them communally, the investigators would be obedient, and when these problems were investigated continually and with eagerness, their solutions would become apparent.'

For it is obvious to everybody, I think, that this study [of astronomy] compels the soul to look upward and leads it away from things here to higher things.

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

I have hardly known a mathematician who was capable of reasoning.

If in a discussion of many matters … we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability.

If someone separated the art of counting and measuring and weighing from all the other arts, what was left of each (of the others) would be, so to speak, insignificant.

It was Plato, according to Sosigenes, who set this as a problem for those concerned with these things, through what suppositions of uniform and ordered movements the appearances concerning the movements of the wandering heavenly bodies could be preserved.

Let no-one ignorant of geometry enter. Said to have been inscribed above the door of Plato's Academy.

No physician, in so far as he is a physician, considers his own good in what he prescribes, but the good of his patient; for the true physician is also a ruler having the human body as a subject, and is not a mere money-maker.

The excessive increase of anything causes a reaction in the opposite direction.

The qualities of number appear to lead to the apprehension of truth.

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.
[Often seen condensed to: 'Geometry is knowledge of the eternally existent'.]

They assembled together and dedicated these as the first-fruits of their love to Apollo in his Delphic temple, inscribing there those maxims which are on every tongue- 'know thyselP and 'Nothing overmuch.'

Trees and fields tell me nothing: men are my teachers.

Wherefore also these Kinds [elements] occupied different places even before the universe was organised and generated out of them. Before that time, in truth, all these were in a state devoid of reason or measure, but when the work of setting in order this Universe was being undertaken, fire and water and earth and air, although possessing some traces of their known nature, were yet disposed as everything is likely to be in the absence of God; and inasmuch as this was then their natural condition, God began by first marking them out into shapes by means of forms and numbers.

Wisdom alone is a science of other sciences, and of itself.

The beauty of life is, therefore, geometrical beauty of a type that Plato would have much appreciated.

Every theory of love, from Plato down, teaches that each individual loves in the other sex what he lacks in himself.

[Plato] was the first to envisage the idea of timeless existence and to emphasize it—against reason—as a reality, more [real] than our actual experience…

Amicus Plato amicus Aristoteles magis amica verita.
Plato is my friend, Aristotle is my friend, but my greatest friend is truth.

The thoughts of Plato and Machiavelli... don't seem quite enough armor for a world beset with splitting the atoms, urban guerrillas, nineteen varieties of psychotherapists, amplified guitars, napalm, computers, astronauts, and an atmosphere polluted simultaneously with auto exhaust and TV commercials.

This missing science of heredity, this unworked mine of knowledge on the borderland of biology and anthropology, which for all practical purposes is as unworked now as it was in the days of Plato, is, in simple truth, ten times more important to humanity than all the chemistry and physics, all the technical and indsutrial science that ever has been or ever will be discovered.

But, indeed, the science of logic and the whole framework of philosophical thought men have kept since the days of Plato and Aristotle, has no more essential permanence as a final expression of the human mind, than the Scottish Longer Catechism.

For the philosopher, order is the entirety of repetitions manifested, in the form of types or of laws, by perceived objects. Order is an intelligible relation. For the biologist, order is a sequence in space and time. However, according to Plato, all things arise out of their opposites. Order was born of the original disorder, and the long evolution responsible for the present biological order necessarily had to engender disorder.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.

The smallest particles of matter were said [by Plato] to be right-angled triangles which, after combining in pairs, ... joined together into the regular bodies of solid geometry; cubes, tetrahedrons, octahedrons and icosahedrons. These four bodies were said to be the building blocks of the four elements, earth, fire, air and water ... [The] whole thing seemed to be wild speculation. ... Even so, I was enthralled by the idea that the smallest particles of matter must reduce to some mathematical form ... The most important result of it all, perhaps, was the conviction that, in order to interpret the material world we need to know something about its smallest parts.
[Recalling how as a teenager at school, he found Plato's Timaeus to be a memorable poetic and beautiful view of atoms.]

The influence (for good or ill) of Plato's work is immeasurable. Western thought, one might say, has been Platonic or anti-Platonic, but hardly ever non-Platonic.