Joseph Caldwell Peden is included in the book Pedens of America by E.M. Hewell. Also, Carroll Caldwell, Historian of Nazareth Presbyterian Church in Spartanburg Co., SC has co-authored a book on this Caldwell family that I have seen:
The Caldwell family of Spartanburg County, South Carolina : descendants of William and Agnes Hadden Caldwell of Ireland
(co-authored with R. Fowler).

From the Peden book:
Joseph was a son of Rev. Mitchell Peden b. 24 Aug 1809 SC and Mary Jennings.

Mitchell was a son of Andrew Peden and Jane McConnell and grandson of Thomas Peden and Elizabeth White.

I believe the last 4 all died in Spartanburg Co., SC