ANTINOMY

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VERSE

∃☉

∃☉ ⊃ ∃P [ P ( ☉ ) = ☉ ]

∀P [ P ( ☉ ) ≠ ☉ ]

∃P [ P ( ☉ ) = ☉ ] · ¬∃P [ P ( ☉ ) = ☉ ]

∃☉

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TRIAL

Featured in the film Antinomy, the above is not a logical argument; it is a visual poem written in the form of a logical argument. A ludicrous combination of symbolic logic systems – that is neither strictly valid nor sound – it surely would make any respectable philosopher shudder. The 20th century intellectual Bertrand Russell would have surely charged whoever responsible with crimes against logic and reasoning – but Russell was a philosopher, not an artist.

Sometimes an inquiry is so prodigious that there must be cross pollination not only between fields but between entire systems of thought. The artist and philosopher both inquire into the same dimensions of being, but their modalities differ entirely. They speak different languages, so how are they meant to speak with each other?

The verse above attempts to dissolve that tension by writing in the form of one mode of thought using the language of another: the form of a poem in the language of first-order predicate logic. This means that while it guarantees to displease both the poet and the logician, it is also engaging with both simultaneously; two sides of the same coin, they must determine how to speak with each other.

∃ // existential quantifier: “there exists…”

Given the form and language of the poem, the logician would be able to translate the symbolic system back into natural language, but she would not be able to make sense of it. It says nothing logically. Given the form and language of the poem, the poet might not be able to interpret the symbols, but she would certainly be able to grapple with the apparent push and pull, tension and release, of the verse’s structure and presentation.

☉ // Sol: “Sun”

The poet Rita Mestokosho says that her task as a poet is to “come into the world to witness life.” To witness life, to feel it and engage with it – that is the imperative of the poet in the waking life: perception. The logician, living the same life on the same planet at the same time, also witnesses the world, but she does not feel it in the same way. She rationalizes it. Her mode is entirely different. The logician is after the pursuit of explanation and formalization; she seeks the capital-t Truth by distilling language down to its atoms – investigating objects and their relations. She seeks to model the world to find the gaps in her explanation.

⊃ // supset: “implies; if…then”

The archetypes of the poet and the logician point to a dualism baked into our inquiry: we who witness life chose between apparently exclusive modes. The poet and the logician, through their two distinct modes of inquiry, cannot make sense of the world in its entirety.

There is no perception nor model of the world which can capture the world as it is completely. Even if the poet and the logician were to work together to create a more complete perception of the world as we experience it, it would still miss out on the near-infinite set of withheld and inaccessible perspectives. You can’t look at both sides of the coin at once.

P // function: “perception”

This is the ultimate chasm that exists between what the 18th century philosopher Immanuel Kant referred to as the phenomenal and the noumenal – i.e., things as we experience them versus “things-in-themselves”.

There is clearly a causal relationship between the phenomenal and the noumenal, but it is asymmetric. The latter influences the former, but the former can never be a complete representation of the latter. The world as we experience it grasps but never touches the world-in-itself. No perception or model is complete, and often, our models and perceptions contradict each other.

This is what Kant referred to as antinomies: contradictions between incompatible principles that appear to be equally valid on their own. This concept is fueled by the dualism at the heart of our Western inquiry. At its very foundation, it relies on the assumption of either/or – negating the possibility of both/and.

= // equivalence: “equals”

If you try to formalize an antinomy using classical logic, interesting things happen. A conjunction between two opposite propositions is not acceptable in first-order logic – but that is precisely what an antinomy is. You have “x” and you have “not x”; both are provable, so they are put in a conjunction: “x and not x”.

∀ // universal quantifier: “for all…”

In our Western logical systems, this results in what is called an explosion: ex contradictione quodlibet – from contradiction, anything follows. The proof is less important than the result, but effectively, through what is called a disjunctive syllogism, anything follows from a contradiction. The system collapses. It proves everything and in so doing, says nothing.

≠ // un-equivalence: “does not equal”

These contradictions don’t exist in the world; they emerge from the rules we apply to our reasoning and our attempt to explain. To Kant, antinomies – and the explosive contradictions that follow – are a diagnostic alert that we have overstepped our reasoning and explanation.

We’ve reached a thesis and an antithesis that are both provable but that are incompatible with each other; however, the system need not collapse. The point of friction between these two dualities – effectively, the Hegelian dialectic – is where:

the phenomenological sparks make a starry night out of the epistemological void…

· // conjunction: “and”

The poem and film play with this dualism, contraction, and explosion using the same form in different structures. They perceive; they grasp; they miss; and they collapse to where they started. They show many sides of the coin, our Sun: 15 different wavelengths, sonifications of that data, and dozens of terrestrial aural perspectives. But they can never come together to create a complete multidimensional mosaic of the Sun-in-itself.

¬ // negation: “it’s not the case that…”

This is why the 20th century philosopher Ludwig Wittgenstein ended his Tractatus Logico-Philosophicus with the closing line, “Whereof one cannot speak, thereof one must remain silent.”

Antinomy is, thus, a silent investigation of itself.