One grain of sand is not a heap of sand; two grains of sand are not a heap of sand; …. ; adding one more grain of sand to some sand is not enough to make a heap of sand; yet, at some point, we agree we have a heap of sand.
So, where are the boundaries?
Part of what is interesting to me is that while we might have problems to provide a formal, systematic analysis, we seem to have strong intuitions that are (more or less, and in fact more, where all things are otherwise equal) in agreement with the intuitions of others.
In law, such issues about vagueness also arise, and they lead to legal contention, so are important to decide. In this radio broadcast, there is a fun discussion of the sorities paradoxes and some mention of how legislators address them; in particular, just how can legislators ‘define’ nudity?
Analysis Extra: The Philosopher’s Arms: Sorites’ Heap 10 Sep 2012
The program is about 30 minutes long and should play in your browser. The broadcast content is copyright the BBC. Radio 4 is great!