Ribera painted several imaginary portraits of ancient philosophers.

Protagoras of Abdera, by Jusepe de Ribera

In the spirit of my Extrapolating Plato’s Definition of Being, in which I took a short passage from Plato and extrapolated it beyond its originally intended scope, I would like to take a famous line from Protagoras and also extrapolate this beyond its originally intended scope. The passage from Protagoras I have in mind is his most famous bon mot:

“Man is the measure of all things, of the things that are, that they are, and of the things that are not, that they are not.”

…and in the original Greek…

“πάντων χρημάτων μέτρον ἔστὶν ἄνθρωπος, τῶν δὲ μὲν οντῶν ὡς ἔστιν, τῶν δὲ οὐκ ὄντων ὠς οὐκ ἔστιν”

Presocratic scholarship has focused on the relativism of Protagoras’ μέτρον, especially in comparison to the strong realism of Plato, but I don’t take the two to be mutually exclusive. On the contrary, I think we can better understand Plato through Protagoras and Protagoras through Plato.

Firstly, the Protagorean dictum reveals at once both the inherent naturalism of Greek philosophy, which is the spirit that continues to motivate the western philosophical tradition (which Bertrand Russell once commented is all, essentially, Greek philosophy), and the ontologizing nature of Greek thought, which is another persistent theme of western philosophy, though less often noticed than the naturalistic theme. Plato, despite his otherworldly realism, is part of this inherent naturalism of Greek philosophy, which in our own day has become explicitly naturalistic. Indeed, Greek philosophy since ancient Greece might be characterized as the convergence upon a fully naturalistic conception of the world, though this has been a long and bumpy road.

The naturalism of Greek thought, in turn, points to the proto-scientific character of Greek philosophy. The closest approximation to modern scientific thought prior to the scientific revolution is to be found in works such as Archimedes’ Statics and Eratosthenes of Cyrene’s estimate of the diameter of the earth. If these examples are not already fully scientific inquiries, they are at least proto-science, from which a fully scientific method might have emerged under different historical conditions.

Plato and Protagoras were both guilty of a certain degree of mysticism, but strong traces of the scientific naturalism of Greek thought is expressed in their work. Protagoras’ μέτρον in particular can be understood as an early step in the direction of quantificational concepts. Quantification is central to scientific thought (in my podcast The Cosmic Archipelago, Part II, I offered a variation on the familiar Cartesian theme of cogito, ergo sum, suggesting that, from the perspective of science, we could say I measure, therefore I am), and when we think of quantification we think of measurement in the sense of gradations on a standard scale. However, the most fundamental form of quantification is revealed by counting, and counting is essentially the determination whether something exists or not. Thus the Protagorean μέτρον — specifically, the things that are, that they are, and the things that are not, that they are not — is a quantificational schema for determining existence relative to a human observer. Protagoras’ μέτρον is a postulate of counting, and without counting there would be no mathematicized natural science.

All scientific knowledge as we know it is human scientific knowledge, and all of it is therefore anthropocentric in a way that is not necessarily a distortion. For human beings to have knowledge of the world in which they find themselves, they must have knowledge that the human mind can assimilate. Our epistemic concepts are the framework we have erected in order to make sense of the world, and these concepts are human creations. That does not mean that they are wrong, even if they have been frequently misleading. The pyrrhonian skeptic exploits this human, all-too-human weakness in our knowledge, claiming that because our concepts are imperfect, no knowledge whatsoever is possible. This is a strawman argument. Knowledge is possible, but it is human knowledge. Protagoras made this explicit. (This is one of the themes of my Cosmic Archipelago series.)

Taking Plato and Protagoras together — that is, taking Plato’s definition of being and Protagoras’ doctrine of measure — we probably come closer to the originally intended meaning of both Plato and Protagoras than if we treat them in isolation, a fortiori if we treat them as antagonists. Plato’s definition of being — the power to affect or be affected — and Protagoras’ dictum — that man is the measure of all things, which we can take to mean that quantification begins with a human observer — naturally coincide when the power to affect or be affected is understood relative to the human power to affect or be affected.

Since human knowledge begins with a human observer and human experience, knowledge necessarily also follows from that which affects a human being or that which a human being can effect. The role of experimentation in science since the scientific revolution takes this ontological interaction of affecting and being affected, makes it systematic, and derives all natural knowledge from this principle. Human beings formulate scientific experiments, and in so doing affect the world in building an experimental apparatus and running the experiment. The experiment, in turn, affects human beings as the scientist observes the experiment running and records how it affects him, i.e., what he observers in the world as a result of his intervention in the course of events.

Plato and Protagoras taken together as establishing an initial ontological basis for quantification lay the metaphysical groundwork for scientific naturalism, even if neither philosopher was a scientific naturalist in the strict sense.

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I have previously discussed Protagoras’ μέτρον in Ontological Ruminations: Six Protagorean Propositions on the Nature of Man and the World and A Non-Constructive World.

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