The classic example is that of Theseus' ship, regarding the concept of identity:
There is an ancient puzzle concerning the ship of Theseus, a sacred wooden vessel of the Athenians. As the years passed, repairs saw more and more of the ship replaced by new components: one year half a dozen planks, the year before that a mast, and so on. Eventually a time was reached when the ship contained none of the original components. These originals, the tale goes, had been assiduously collected over the years, and as soon as the collection was complete the parts were reassembled into a (leaky) ship.
Which of the two, if either, is the original ship?
Suppose that when the ship was launched, she was granted free mooring rights at her home port in perpetuity: to which of the two vessels would this concession apply?
There is no absolute "right answer" - we can know all the facts, and still be at a loss as to which ship deserves the identity "Theseus' old ship". Ultimately, we (the linguistic community) simply need to decide for ourselves which definition would be most useful to us.
Prof. Jack Copeland discusses this in his book on Artifical Intelligence:
Our decision must not be arbitrary... in the case of the ship, the decision must take account of whether the purposes for which we need the concept same ship (eg for long-term contracts) are best served by taking the reconstructed ship, the repaired ship, or neither, to be the same ship as the one originally launched.
He goes on to observe that the question Can a machine think? poses a similar problem. The concept of 'intelligence' is as man-made, artificial and relative as the concept of identity, so we simply need to decide for ourselves what definition of 'intelligence' is most useful for our purposes.
This now raises the question: For what purposes do we need moral concepts?