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<c1> The dialogue is between Socrates (c.470–399 BC), and Theaetetus (c.417–369 BC), who was later to become one of the greatest Greek mathematicians. Theaetetus would have been a teenager at the time.

Socrates has been explaining the philosophical position of Protagoras of Abdera (c.485–c.410 BC), who was the first and greatest of the so-called Sophists. In particular, he held that nothing can be real if it is subject to change.

Socrates attributes the theory of perception which follows to Protagoras and other ‘famous men’. Plato doesn’t actually state that he and/or Socrates believed it to be true; but I think it’s likely that they did, and it was certainly accepted as the Platonic theory of perception at least until very recent times.

<c2> Socrates is only half-joking here. The point he is making is that you need to be initiated into the true philosophy, if you are to understand that things can be real without being tangible or visible. Indeed, the purpose of his theory of perception is to establish that the things we touch and see are not fully real, and that the only realities are unchanging entities which cannot be perceived by the senses.

Although he might have held that ordinary folk assume that only tangible and visible things are real, it immediately becomes clear that he is thinking of materialist philosophers such as the atomists — in particular, the followers of Democritus, also of Abdera (c.460–c.370).

The Greek word I have translated as ‘reality’ is ousia, which is conventionally translated as ‘substance’ when used by Aristotle. Here Plato is clearly saying that, for the materialists, actions etc. are not merely ‘insubstantial’, but unreal and illusory.

<c3> This is a clever pun. Theaetetus describes the atomists in the same terms as they described their atoms: hard, and resistant to penetration by other bodies.

<c4> The Greek word which I have translated as ‘fundamental principle’ is arche (literally ‘beginning’), which the earliest Greek philosophers used for the ultimate constituent or constituents of reality, from which all the phenomena of nature are derived. Different philosophers championed different ‘principles’, such as water, air, fire, or earth; or all four together; or all four with additional principles such as ‘love’ and ‘strife’; or atoms of different shapes colliding by chance — and so on.

The bold theory which Plato puts forward here (and which he undoubtedly believed in) is that only motion is real. It is interesting to speculate how difficult it was for the Greeks to conceive of motion without there being material objects which moved; but it probably wasn’t as difficult as it was for 19th-century philosophers and scientists to conceive of waves without anything that waved, since the Greeks had not acquired the mind-set of Aristotelian metaphysics and mechanistic science. In any case, for Plato the world as revealed in experience was less fully real than the world of ideas revealed to the intellect.

As for his ascribing the theory to earlier philosophers, this may have been a rhetorical device to lend more authority to what he was saying. But from what little we know, at least some aspects of the theory are present in earlier philosophers. In particular, Heracleitus of Ephesus (c.540–c.480 BC) held that the senses cannot yield knowledge since everything is perpetually changing; and Pythagoras of Samos (c.580–c.500 BC) held that the ultimate realities are not material objects, but numbers.

<c5> Passive motions are what constitute the nature of physical objects, and active motions are the forces they exert. Plato doesn’t say so here, but he (in common with many other primite theorists) believed that the eye emitted a visual stream which went out towards the objects of perception.

<c6> Note that Plato uses a sexual metaphor for explaining how the interaction between the observer and the observed gives rise to a perception. Sexual reproduction is part of the familiar world of experience, whereas scientific theories about perception are difficult to conceptualise, and in need of models drawn from experience.

Note also that only beings of the same kind can reproduce, and what they give birth to is also of the same kind. This is why he stresses that the observer, the observed, and the resulting perception are all motions. It would be much more difficult to understand how a hunk of inert matter could give rise to a motion.

Significantly, Plato says that the interaction always gives rise to twins — the sensation in the observer, and the quality in the object of sensation. In other words, just as we have sensations only when we are sensing an object, so the object has sensory qualities only as long as it is being observed; and what qualities it has will depend on the observer with whom it is interacting. An unobserved object has no colour, sound, smell, temperature, etc.

<c7> Plato now comes back to the two kinds of motion, and says that one is quick, and one is slow. It seems obvious that it is the active motion which is quick, and the passive motion which is slow. An object consisting in slow motion changes only gradually, and tends to stay put (or if it does move, it moves very slowly in comparison with the speed of light or sound). The fastesr motions he is talking about here are sensations and sensory qualities.

<c8> Plato’s image is of the eye sending out motions (the visual stream) in search of an object, and the object sending out motions (in modern terms, reflected light) in search of an observer. To pursue his sexual analogy, it is like two people of the opposite sex looking for partners at a party. There won’t be any sex, let alone the birth of twins, if one of them fancies someone else.

However, he also makes it clear that, although he has talked as though there were things waiting to be observed, the things themselves don’t really come into being until they are observed.

<c9> Plato takes the strong line that things exist only in so far as they are interacting with each other. The world of experience is a holistic system, in which everything is connected with everything else, and nothing has any reality as an isolated entity. In particular, our existence as perceivers depends on our having something to perceive, and the existence of what we perceive depends on its being perceived.

He also makes the point that what is passive in one relationship may be active in another. For example, the eye can both see and be seen.

This is not the whole story, since, for Plato, we are not merely perceivers. We also have an immaterial, rational soul, which is independent of the material world of experience, and has direct access to a separate, unchanging realm of eternal truths.

<c10> Finally, Plato makes the very modern-looking point that it is our language which makes us conceive things in the world of experience as unchanging and existing objectively. However difficult, we should reform the way we describe the world, so as to reflect its every-changing nature.