Faulty Logic


In a juxtaposition of arguments expressed in writing and drawing, Douglas Rogerson looks at the potentialities of emotional states through the lens of a flawed mathematical equation. Is there a difference between »a« and »b«; between you and me?


a = b

a² = ab

a²-b² = ab-b²

(a+b)(a-b) = b(a-b)

(a+b) = b

a+a = a

2a = a

2 = 1


There’s a proof equating 2 as 1, often passed around grade school algebra once students are proficient enough to be perplexed by paradox. The naïve fall for a deceiving division by zero, a mathematically forbidden move since dividing by less is reciprocally multiplying by more until the infinitesimal and infinite become indistinguishable. The result is »undefined«, a limitless open-end of two bounds being the same but not one in the same, inextricably connected but not overlapping.

The integers themselves are irrelevant, standing in only to demonstrate the blurriness between. They are just as easily substituted by »a« and »b« or you and me until ultimately everything means everything, which means nothing. This consequential generalization dually admits its own logical flaw and renders its content vacuous. It is a tautology of no explanatory value as well as an assertion of nihilism. Nevertheless by contradicting everything into nothing, the resultant nothing contradictorily means everything.

It’s a circular logic like unrequited lovers: one you always have hope for and/or one you just want to forget about. Who’s who is a matter of direction, running to or away from the other, due to the same trick of reason – being both and neither at the same time. Either way they are traced produces a vicious loop with two ends untouching.

Two points determine a line, but connecting the dots collapses possible worlds into an actual reality. Closure eliminates ambiguity and thereby space for denial so instead any conclusion is left hanging on indeterminate premises and unfulfilled promises. Logical intuition entails once it happens, it happened and couldn’t be otherwise. But if nothing happens then the outcome is valid whether what happened was true or false. The only impossibility is if something happens, claiming it never had.

Inaction is an action equally to blame for inconclusiveness as refusing to move on from overcomplicating simplicities. One eliminates by maintaining sensitive words were never spoken while the other enumerates ways to say the same senseless thing. Both falter by falling for an elusory, perhaps even illusory feeling – the same undefined gap as between 1 and 2 left between »I« and »you«.