Logic underpins knowledge – but what if logic itself is flawed?

We use logic to weave facts into our thought systems, but paradoxes make us question what we think we know. It can be even worse, because logic alone may not make sense of reality.

To Abigail Beale

I’m not bald. At least not as I write this. But if an unscrupulous philosopher were to pluck hairs from my head, hair by hair, I would be bald. ? Hard if not impossible to say.? And if I can’t identify the transition to bald, am I actually bald?

This is the philosopher’s favorite version of the thought experiment, first described in relation to grains of sand in a heap called the Sorites paradox (Greek for “heap”). This is often used as evidence that classical logic may be insufficient to explain the world around us.

We don’t pay much attention to it, but this is troubling because logic runs through human knowledge like a stick of rock. We assume that a set of facts can be constructed into a thought system. But where does that leave us if the logic itself is lacking?

A paradox begins with a premise that seems to be true, applies an inference that seems to be true, and ultimately leads to an incorrect or contradictory conclusion. As a result, many…