Loki’s Wager and the Sorites Paradox

One paradox I keep coming across in my life is the Sorties paradox, also known as The fallacy of the Heap.
It was a gateway for me to an understanding of Buddhism. It’s a paradox that’s found in literature and art and one that shows up in philosophy of knowledge.


In Norse myths, the trickster god Loki makes a bet with a Dwarf Bok and wagers his head on the result. Upon losing, the dwarfs came to collect. Loki was willing to accept but he insisted they cut off only his head and nothing more.

A discussion ensued, with it evident that some parts were head and others neck. But neither side could agree on where one ended and the other began, so Loki kept his head (though his lips were stitched shut for being a wise-ass).

Something similar happens in Shakespeare‘s The Merchant of Venice, where Shylock demands his ‘pound of flesh’. He is thwarted by Portia, who insists that Shylock can only have flesh, not blood, and only one pound of flesh, no more or less.

Sorites – Fallacy of the Heap

In philosophy the above is covered by a thought experiment;

Imagine a ship, then start to replace the parts one by one. After each part is replaced, the question arises 'is it still the same Ship of Theseus?  If we remove grains of sand from a heap, is it still the same heap?

‘If it is supposed that the famous ship sailed by the hero Theseus in a great battle was kept in a harbour as a museum piece, and as the years went by some of the wooden parts began to rot and were replaced by new ones; then, after a century or so, every part had been replaced. The question then is if the “restored” ship is still the same object as the original.’


As the parts are changed out or added/subtracted, can still call it a ship or heap? It shows that reality doesn’t fit into our ideas and models.

There's a difference between the fuzzy reality which changes and the simple neat identities and labels we give it.

It’s a field called Mereology and is about the relationship of parts to the whole. It’s also about identity, language, and meaning.

Continuum Paradox

A related paradox is the Continuum Paradox or Fallacy. Its really the same questions.

Take a grey scale, like below. A smooth gradient from black to white through all the shades of grey. The number of greys is infinite.

Greyscale- The subtle reality

Question; where does black end and white begin? The odd insight is that at no point on the scale does black become white.

Simile of the Chariot

Another place where this paradox arises in Buddhism, it’s called The Simile of the Chariot and again it’s the the same questions and the same problems.

What is a chariot? Is it the wheels, the axles, the reins, the frame, the seat, or the driver? If the answer is no, then there is no Chariot.

It’s used to explain the doctrine of Anatta or Non-self. ‘Chariot’ is merely a name, as is our personal name, and the names of objects. There is no abiding, enduring existence of a Self.

What the Sorites and the other ideas point out is the ambiguity of language. Precise definitions may exist, but they’re the exception. When you try to define things like love, God, truth, soul or the Self, or even objects like plants, fish, table, and people, it ends up in ambiguity.

Ludwig Wittgenstein asked ‘what is a game? He couldn’t find a single feature common to all of them. We separate the world into objects and never notice it’s our language that does this.

In our everyday lives, these queries are seemingly inconsequential. But digging deeper reveals that our understanding of the world is far less certainty than we care to notice or admit.

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