Axioms of Parmenides

In Plato’s analogy of the divided line we’re told that we can only ever have opinions or doxa about the physical world.  What is fascinating here is his reasoning.  The reason that we can only have knowledge of the physical world, according to Plato, is not because everyone perceives or interprets things differently.  The issue here isn’t about some subjectivism or relativism at the heart of how minds relate to reality.  Rather, it is built into the very fabric of physical reality, not the mind that regards to that reality, that it can only be a domain of opinion.  Because everything in physical reality is doomed to change or becoming, what is true of a physical being now becomes false later.

I say “the rose is red”.  This can only ever be an opinion, according to Plato, not because someone else might see or interpret it differently or because I might be color blind, but because the rose is condemned to turn brown and die.  Truth, for Plato, must preserve itself.  If the truth value of a proposition changes with time, then it is not genuinely knowledge, but opinion.  Consequently, the entire world of physical beings will be reduced to appearances, a sort of veil of maya that we must pierce to get to true reality.  There is no truth to be found in this world of appearances, of physical objects, because this world that we dwell in, this world that is the world of our embodiment, is a world of change that fails to preserve truth.

Lurking in the background here is the imperative of Parmenides.  Parmenides’s declaration is not simply that being is and non-being is not, but also that being is knowable.  The great and disturbing poem of the Eleatic Stranger does not merely observe that being is, but also seeks to establish that being is identical to thought.  Thought in being must be identical for being to be knowable.  Otherwise we are left with nothing but a skepticism.  If we make the claim that being is identical, we are also implicitly claiming that being must be rational.  But what does it mean to say that being is rational?  It means that it obeys the following two principles:

The principle of identity or A = A

and

The principle of non-contradiction or ~(A & ~A)

The structure of reality must mirror the structure of thought and the structure of thought must mirror the structure of reality.  Anything less and we fall into a skepticism, says this tradition.  If, then, we must reject the thesis that physical objects have being, says Plato, then this is because they fail to meet the requirements of the principle of identity and non-contradiction.  In changing, physical beings are non-identical to themselves and contradict themselves.  Henceforth, Plato will say that the number 17 is more real than a rose, because the number 17 is always the number 17 and never becomes anything else.  The entire world of becoming will be demoted and treated as unreality.  And do we not witness echoes of this initial philosophical decision in both Badiou’s mathematization of ontology that effectively reduces, again, appearance to a sort of surface-effect or in object-oriented philosophy’s doctrine of withdrawal that “rescues” entity from change?

So much of Plato falls into place in this moment.  Plato’s strange denunciation of writing, so profoundly explored by Derrida, will be seen to arise from how the written is always non-identical to itself both in the differentiality of the signifier, but also in its difference from what it signifies.  Writing will everywhere harbor violations of the principles of identity and non-contradiction, and above all, will create the possibility of rendering formal paradoxes material or embodied.  “If the Barber of Seville cuts everyone’s hair except those who cut their own hair, who cuts the Barber’s hair?”  Clearly the real barber never has trouble getting a haircut.  This is a paradox that is only capable of existing in the symbolic, in a signifying system.  It will mark Plato’s hostility to art and the simulacrum as something that competes with the self-identical real.  It is the underlying rationale for Plato’s denigration of the body and the senses.

Much of the history of philosophy will be an attempt to reconcile being with these two principles of thought, which is why it is led to such strange places.  Everywhere philosophy will seek a sort of parallelism of thought and being that arises as a demand that being obey the principles of non-contradiction and identity.  Again and again this requirement will lead to denunciations of the body, materiality, difference, the physical world, and appearance or phenomenality.  Lurking behind all of this will be a will to power and a denial of death, for where thought is identical with the thing, where the concept can replace the thing, we have escaped the constraints of embodiment and materiality.  Given the deep price we must pay to formulate a theory of knowledge and reality consonant with these principles, we must raise the question of whether we don’t get further with difference than identity.