William's baptism record describes him as the "second son" of John Carr. Mose's baptism record describes him as the "third son". No baptism record or any other evidence has been found for a first son. This suggests that John had an earlier son who died prior to 1797 (William's birth year) and possibly that the first son died before he could be baptised.

I think that John's father may have been called William. It was common practice in England at that time to name the first son after the father's father. This suggests that the first son (who died) was also named William and that the name was recycled for the second son,which would also have been common practice at that time [http://www.genealogy.com/35_donna.html].