A note on flux and constancy

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Heraclitus of Ephesus was among the early proponents of a theory of universal flux. His claim was that the world is in a state of incessant change, where no two objects are identical among and in themselves. A reference to his cosmology is made in Plato’s Cratylus: we are informed that Heraclitus postulated the impossibility of stepping twice into the same river, since other waters are continuously flowing in. The metaphor is intended to encapsulate the view that the world is in constant motion and nothing is at rest.

Heraclitus referred to this constant change as the universal logos. His is a metaphysical theory, though it does have far-reaching epistemological ramifications. With regard to metaphysics, it propounds an ontology where no ontic identity is possible: an object cannot be identical to itself for it always changes. By the same token, said object cannot be the same as any other object, for that too is not identical to itself. The absence of identity implies the lack of constancy in objects and their properties.

With everything in a state of flux, there is no constant feature which can be held as a benchmark with which to comprehend and categorise objects, thus rendering nonsensical epistemic claims on the world: no object can be known for no object exists as an identity/constant and so what is purportedly known about something can, at the very best, concern only an instance in an infinite stream thereof and, hence, be inadequate in furnishing genuine knowledge.

To assess at some further depth the value of the proposition that “one cannot step into the same river twice, because new waters continuously flow in”, we will conduct a thought experiment where there indeed exists a universal law of differentiation, so that no two quanta of matter are identical. We shall take Heraclitus’ logos as true.

The Heraclitean logos as a universal truth about the world

Let us accept that by studying the world that environs us, we find that each object differs from others in its own class and even in itself over the passage of time. We do, for instance, recognise that no two human beings are identical as far as their material constitution is concerned, since their DNA strands do exhibit certain unique sequences. Similar for plants, other animals and inanimate matter, such as a grain of sand. Along those lines, we posit the operation of a universal law of differentiation, overriding and determining each and every aspect of the world and, for argument’s sake, we take that to be a universal truth about the world: indeed no identity exists, other than the law of differentiation — logos — itself.

Does that provide universal necessity to the claim of Heraclitus? Is there no identity other than logos being constant?

To challenge that perception we shall proceed with considering reality as having two magnitudes: (i) the realm of sensible objects and (ii) that of intelligible ones. Predicated on this hypothesis, we can suggest the presence of an intelligible object, say “River“, R, as independent from the instance of the world it names — the thought of a thing not being the thing itself unless it only is an object of thought.

R, therefore, is an abstraction from the world, not an ontic presence in it. An abstraction encapsulates the common in the multitude _of inputs received from the sensible instances concerned. The abstraction does not signify enumeratively each and every quantum of matter that manifests in certain [inter]operations to produce the sensible object — or illusion — of a “river as a stream of water”, but rather refers to the formulated object of thought — the _idea — applicable to all possible instances of the world partaking of the attributes and states of affairs germane to R.

Additionally, we may take note of the relation between the general and particular abstractions, such as by placing R in a certain taxonomy that would denote its relation to other intelligible objects. For example, we can have an array encompassing the extensions of the abstraction — the lower order abstractions belonging to it — taking the form of River(Amazon, Danube, Nile), or else R(A, D, N). This array denotes a hierarchical relation between the abstraction R and its extensions A, D, N. The extensions which are more particular than the general abstraction, are not necessarily instances of the [ever-changing] world, but abstractions in their own accord, even if we follow the rationale of Heraclitus, since each and every one of them is subject to inter- and intra- differentiation, courtesy of the ever-flowing masses of water that [re-]constitute them.

To that end, abstractions are names of instances in the world, objects that are comprehensible beyond its spatiotemporal categories. They are intelligible, existent only as presences in the thinkable. The fact that new masses of water always [re]form a river, so that its constitution is never the same, and hence “the river” doesn’t persist in the world, is irrelevant to the possible constancy of the idea made out of it, be it a general or particular one. We may thus suggest that what is in the world has change — or the lack thereof — in itself, regardless of the idea attached to it; while what partakes of the thinkable has change — or the lack thereof — because of and _in the manner _that it is thought.

Such metaphysical bifurcation between the world and the thinkable enables us to circumvent the subsequent epistemological tensions of the Heracletean theory. By arguing that there can be an identity, albeit only as an intelligible object, we effectively make the ontological claim that ideas exist, though not substantially as instances of the world, but as presences in the thinkable.

That the intelligible object R can be meaningfully discerned from the intelligible objects A, D, N and that those also are discernible from one another, is an indication of certain knowledge of the features/properties that make R equal to R or R unequal to A, D, N etc. Indeed, that we can intelligibly tell whether there is a certain difference between, say, River and Dog, implies that we may, at least to a degree, identify what is or is not constitutive of — and constant in — each. The higher the precision and clarity of such discernibility, the better grounded the knowledge derived therefrom.

This granted, it would be erroneous to consider a claim on the multiplicity of appearances as having no epistemic value, for such recognition per se still is an intelligible comprehension of the world: some commonalities among a given set of multitudes of appearances are traced and abstracted from the totality of the world to deliver an epistemic judgement on the multiplicity of phenomena that is constant in itself.

Concluding remarks

The underlying theme thus far, is that there is no necessary mutual causation between the world and the thinkable, so that one can be independent from the other. Heraclitus’ worldview even if it were truthful about the world it would still not be necessarily or always true about the thinkable, for even if all objects of sense are constantly changing, such as the river in which one may not step twice, objects of intelligence can be held constant, even when they refer to the instances of the world.

To put forward such counter-claim we resorted to a bi-magnitudinal conception of reality encompassing both sensible and intelligible objects. The metaphysical features of that approach are to be found in the treatment of intelligible objects as ontologically existent, though not substantially as instances of the world, but as presences in the thinkable. Such is a two-fold approach to ontology, where reason and experience operating in tandem do reveal aspects of reality that otherwise remain obscure to any one of them.

The continuation of such metaphysics is an epistemology that can deliver epistemic judgements about things and states of affairs in themselves. It can deliver certain knowledge of an intelligible object even if it does not necessarily have a sensible equivalent, such as discerning an abstraction River from another one Dog. In a nutshell, it is an epistemology which evaluates the degree of correspondence between the intelligible object and its properties to the common in the multitude of the case under examination, assessing the equivalence of the idea to the pattern it names.

In contradistinction, Heraclitus’ metaphysics effectively render obsolete any epistemological claim other than logos being true. They do so by denying any identity, any constancy whatsoever beyond that of the universal law of differentiation. For while there may still be patterns to be identified in an ever-changing world, these will have to be recognised as instances of an ever-flowing stream of reality and, hence, as limited to that instance from which they were drawn, not being generalisable to all possible occurrences of the same situation. “Sameness” is definitively not a feature of that world.

It would be futile to produce a description about that which is always and necessarily elusive by virtue of its incessant flux. If a description were made about anything other than logos, and it were held as meaningful and verifiable — such as a “river” being understood as “river” or “stepping twice” as “stepping twice” — the Heraclitean system would be exposed to a tension it could not address with internal consistency. If what is described can be truthful beyond a given instance in the ever-changing world, if it is constant in some way, then the claim about the absence of identity is not universally true, for constancy is an identity of a sort.

Conclusively, what is intriguing is that we can intelligibly refer to ever-changing objects or to change as such in a manner that can be constant in itself. This might be suggestive of the need to draw delineations between objects of sense and intelligence and, moreover, to concede the possibility of each magnitude of our reality having features exclusive to it.

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