TWIL #013 - The Sorites Paradox
If removing one grain of sand never turns a heap into a non-heap, how does a heap ever stop being one? The paradox of vagueness has no clean answer.
- #philosophy
- #logic
- #language
The Sorites Paradox (from the Greek soros, meaning heap) is ancient - attributed to Eubulides of Miletus in the 4th century BC - and still doesn't have a universally agreed resolution.
The argument goes like this:
- 1,000,000 grains of sand is a heap.
- If you have a heap, removing one grain still leaves a heap.
- Therefore, 1 grain of sand is a heap. (By applying rule 2 repeatedly.)
The conclusion is obviously false. But which premise fails? Rule 2 seems undeniable - one grain can't be the thing that makes the difference. And yet following it to its conclusion produces nonsense.
The paradox exposes something real about language: many of our most useful words - heap, tall, bald, hot, rich - are vague in a precise sense. They don't have a sharp boundary, and that's not a flaw in language or a gap in our knowledge. The vagueness is the whole point. We need words that can be applied flexibly across a spectrum.
Proposed solutions range from "just pick an arbitrary threshold" (unsatisfying but pragmatic), to formal logics that allow degrees of truth rather than just true/false, to accepting that some questions simply don't have answers - not because we don't know, but because reality doesn't carve at those joints.