One of the positive aspects of these yearly essay competition is the possibility of learning something new. I have you to thank for bringing Sorites paradox to the table. Very interesting and I am learning about it for the first time. I will therefore have to give it some more thought.
But for starters it appears to do with 'definition'. Among questions running through my mind are:
- what is a heap?
- what is a grain of sand?
- is a grain of sand, a heap, i.e. a tiny heap?
- is a heap, a big grain of sand?
- is a heap made of grains of sand alone, or along with something else, e.g. air?
- when a grain is removed, is it removed along with any other thing?
- what does 'remove' mean? Can things be separated, and if so by what? If by nothing, then it means they have not been separated or 'removed'. If by something, from whence did that something come? Or was the something always there?
Following the issue of structural definition, is a question of functional definition. That is, has any change being made when a grain of sand is removed from a heap? If a heap remains a heap, then for the hour-glass example, time has not changed. If another grain is removed still time has not changed. But then a sum of zero changes of time must equal zero, yet when the hour glass is emptied a duration of time has definitely passed. It therefore appears inevitable that removal of a grain of sand from a heap has changed that heap. If you like changed to 'Heap - 1'. Removing another grain can be represented as ('Heap - 1') - 1, etc.
I therefore agree, that the paradox suggests that there must be a limit to the addition or subtraction from a heap without changing the definition of heap. In this way Sorites paradox must admit of events.
Your essay and the paradox is one deserving of being read again and again. A "heap" of value to gain.
Wishing you the best in the competition also,