Saturday


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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Saturday


In the venerable Jowett translation of Plato’s Sophist dialogue, the complete text of which can be found online at Project Gutenberg (and can also be found at Google Books, p. 379), we find the following exchange between Theaetetus and the Eleatic Stranger:

STRANGER: Let us push the question; for if they will admit that any, even the smallest particle of being, is incorporeal, it is enough; they must then say what that nature is which is common to both the corporeal and incorporeal, and which they have in their mind’s eye when they say of both of them that they ‘are.’ Perhaps they may be in a difficulty; and if this is the case, there is a possibility that they may accept a notion of ours respecting the nature of being, having nothing of their own to offer.

THEAETETUS: What is the notion? Tell me, and we shall soon see.

STRANGER: My notion would be, that anything which possesses any sort of power to affect another, or to be affected by another, if only for a single moment, however trifling the cause and however slight the effect, has real existence; and I hold that the definition of being is simply power.

The Greek text of the Eleatic Stranger’s crucial formulation is as follows:

Ξένος: λέγω δὴ τὸ καὶ ὁποιανου̂ν [τινα] κεκτημένον δύναμιν [247e] εἴτ’ εἰς τὸ ποιει̂ν ἕτερον ὁτιου̂ν πεφυκὸς εἴτ’ εἰς τὸ παθει̂ν καὶ σμικρότατον ὑπὸ του̂ φαυλοτάτου, κἂν εἰ μόνον εἰς ἅπαξ, πα̂ν του̂το ὄντως εἰ̂ναι: τίθεμαι γὰρ ὅρον [ὁρίζειν] τὰ ὄντα ὡς ἔστιν οὐκ ἄλλο τι πλὴν δύναμις.

This I shall simply call Plato’s definition of being.

Nicola Abbagnano, 15 July 1901 - 09 September 1990

Nicola Abbagnano, 15 July 1901 - 09 September 1990

This memorable definition of being in Plato — the power to affect or be affected (Sophist, 247e) — has been construed by Abbagnano in terms of possibility: being is the possibility to affect or be affected. The Greek term that Jowett translated as “power” — “δύναμις” — Abbagnano translated as “possibility.” While this isn’t quite as creative as some Heideggerian “translations” of Greek, it is an unusual translation. Despite this, I count the transformation from power to possibility as justified, since the Platonic account of being does not demand acting or suffering in actuality, but only the possibility of acting or suffering. Abbagnano, to my mind, has retained the essence of Plato’s meaning. And the Platonic definition, such as it is, seems reasonable to me, as we can scarcely credit anything with being if it has no relation whatsoever to us (or to the world). Thus the Platonic definition of being so construed also provides us with a definition of non-being.

critical existentialism

This Platonic conception of being immediately suggests a tripartite division among beings:

1) those which both act and suffer,

2) those which act only but do not suffer, and

3) those which suffer only but do not act.

There remains, obviously, a fourth possibility, but I noted above that the schematization of the Platonic definition of being introduces a tripartite division among beings, while the fourth possibility excludes all beings:

4) those which neither suffer nor act.

This fourth possibility — those which neither act nor suffer — represents, by definition, non-being and may be considered the null permutation (analogous to the empty set). There is an implicit paradox here, since we seem to be referring to beings that neither act nor suffer, which of course are impossible. Does non-being consist of impossible beings? And there is, as well, the ontologically interesting question of the possibility of the individuation of non-beings. Nothingness has always been a philosophical puzzle, and the above approach allows us a novel perspective on nothingness. It is difficult if not impossible to imagine the utter oblivion of non-being. Even the sinners trapped in the ice of the frozen Cocytus are able to converse with Dante (or, at least, are merely seen encased in ice), and therefore seem possess being to some degree in virtue of this interaction.

Dore's illustration of the damned frozen in the river Cocytus.

It is difficult to resist observing that the ontological “inertness” which has of late been ascribed to mathematics by Jody Azzouni (and we may generally suppose this to hold for all beings, if such they be, which constitute the formal sciences) would seem to indicate that mathematics is concerned not with beings but with non-being: we do not affect the objects of the formal sciences, and they do not affect us. But this is ultimately much too simplistic: the objects of the formal sciences — numbers, propositions, etc. — affect us in so far as we conceive them, and, depending upon the philosophy of mathematics that one advocates, there remains the possibility that might affect the objects of the formal sciences, for example, by creating and conceiving them (as in a constructivist philosophy of mathematics).

Azzouni's book on the philosophy of mathematics opens with a discussion of metaphysical inertness.

Azzouni's book on the philosophy of mathematics opens with a discussion of metaphysical inertness.

If man is the measure of all things, as according to Protagoras, then mathematics has no measure since mathematics is resolutely anti-anthropocentric. If, as Russell held, mathematics is the study in which we never know what we are talking about nor whether what we are saying is true, this is entirely justified, because we are, as it were, talking about nothing, and what we are saying is neither true nor false. But Russell’s philosophy of mathematics exemplified a classically anti-anthropocentric position, and Russell himself was willing to formulate some of his positions in terms of non-being (as in, for example, his “no classes” theory of classes), so in this particular context Russell’s modern formulation is a re-statement of traditional view, and in his thought no suggestion of a constructivist alternative is ever made. Nevertheless, Azzouni’s account of ontological inertness does closely correspond to the definition of non-being in terms of neither suffering nor acting, and it would be worthwhile to follow up on this correspondence in a systematic way. But another time.

An imaginary illustration of Protagoras teaching.

An imaginary illustration of Protagoras teaching.

And there is more. Within each ontological division outlined above we may adopt a hierarchy of being, securely based upon quantification of the number of beings which a given being affects or by which it is affected. The measure of ontological power — ontological potency, as it were — is a being’s scope of acting and suffering. Now, we may assume that those beings that both act and suffer possess a greater scope of being than those one-sided beings which act only or suffer only. Whether either one of these two inferior forms of being — viz. acting only or suffering only — ought to be superior to the other is a greater problem, and we will not address it here.

We can go further than this by defining acting and suffering within regional ontologies (to invoke a formulation of Husserl). Regional ontologies themselves admit a scope of possible acting and suffering. They overlap and intersect (to invoke a formulation of Wittgenstein).

The idea of regional ontologies is due to Husserl (left) while the idea of family resemblances overlapping and intersecting is due to Wittgenstein (right).

The idea of regional ontologies is due to Husserl (left) while the idea of family resemblances overlapping and intersecting is due to Wittgenstein (right).

A further note: construing the Platonic definition of being in terms of the possibility of affecting or being affected, as Abbagnano does, suggests a distinction between so construing Plato and, in contrast, interpreting the Platonic definition of being in terms of actually affecting or being affected. This latter interpretation would require specifying a scope of time during which a putative existent’s affecting or being affected would be relevant, for not everything affects or is affected by everything else at any one moment. But this too suggests a further division (perhaps the narrowest formulation of being) in terms of which only that which affects or is affected by a given being at a given instant contributes to its reality: call it, if you will, being at an instant. More of this at another time.

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It all goes back to Plato, here shown in an imaginary medieval portrait.

It all goes back to Plato, here shown in an imaginary medieval portrait.

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Ontological Ruminations

18 April 2009


Six Protagorean Propositions on

moerman-de-cleyn-werelt

the Nature of Man and the World


1. The history of ontology reveals that our perception of the structure of the world has changed dramatically over time.

2. The scope of human action and activity has changed with this change in perception of the structure of the world.

3. Human beings, at least in part, constitute the world (i.e., they contribute, in part, to the constitution of the world).

4. Human beings, in turn, are constituted at least in part by the scope of our activities.

5. Our self-constitution after the image of what we believe the world to be has in fact made the world what it is, if only in part.

6. The world is, again, in part, self-constituting.


microcosm

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