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“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.” ― Niels Bohr

Introduction

Paradox, ambiguity, uncertainty; these are the sort of concepts which, if you think about them for long enough, will probably start to make you feel a little giddy, a little uncomfortable, perhaps even a little queasy. Almost by definition they are confusing, contradictory, non-logical ideas; portals to the fathomless realms of the unknown. And, as H.P. Lovecraft observed in the introduction to his 1927 essay, Supernatural Horror, “the oldest and strongest emotion of mankind is fear, and the oldest and strongest kind of fear is fear of the unknown.” [^1]

In a 2016 psychology review and research synthesis about fundamental fears, R. Nicholas Carleton supports Lovecraft by positing that fear of the unknown, or ‘FOTU’ is quite possibly the fundamental fear. He notes that, ‘FOTU tautologically does not require a priori learning; indeed, the first thing that could be feared would be “the perceived absence of information at any level of consciousness.”’ [^2]

From the abyss of the unknown out of the very fabric of our fears, we conjure demons, fiends and nameless horrors; they are legion. We learned this as children when, without conscious effort, we materialised monsters under our beds, in our cupboards, in the darkened doorways of our rooms. Of course as we grew up we learned to dispel such childish fears with reason. Relax. There’s nothing to be afraid of. Ah yes sweet logic is the light which banishes the darkness of the unknown. And so when ideas like paradox pop up, ideas which defy coherent rationale, it’s no wonder we almost always pull ourselves away with a slightly unsettled shudder.

So settle in, if you’re game, while we explore that uncomfortable little idea that is paradox. Paradox which seems to characterize so many of the big problems at the forefront of modern science; paradox which has fascinated and confounded philosophers for millennia; paradox, without which mathematics could not have solved the problems on which all modern technology relies.