This is one of the biggest challenges in genealogy; finding the parents of people who were born before 1850. I suggest that you find the will of James Pierson and see if it mentions a son, William. Look for the will and probate in the county where he died.
Sometimes parents' names are in a person's obituary.
If the Informant knew that info at time of death, they are on the death certificate but William died before Indiana was issuing death certificates.
The genealogical or historical society in the county where he died might be able to provide you more information.
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