Link to his obit - he sounds like a character, and a man with conviction!http://www.wvgenweb.org/pleasants/aobitsc.txt
Searching the US genweb site for Pleasants County, WV was helpful - I learned that William was a native of Harrison County, and he and Adelia came to Pleasants County in 1848- bio information is not always accurate, but it gives a starting point. I also discovered that their daughter Bertha, who was married to Clemmons in 1900, remarried and became Bertha Baxter. I then looked on the WV vital records site, and found Bertha's death certificatehttp://www.wvculture.org/vrr/
It lists her parents as W.G.H. Core and Adeline C. Barrick.
The other hint I found - in the 1860 census, there is a Charlotte Core, age 22 living with William and Delia. I wonder if she was his sister? Her marriage record lists her father as David Core.