Hi Deborah,
I have a few Arthurs including yours but no real leads. I thought that I would just give you all the records I had and see what you make of them.
There are Arthur Bradish's (no middle names listed) on the 1860 MA, 1870 VA and 1870 WV census. I've written WV but can't remember what that stands for. (I'm Australia so not familiar with all abbreviations).
Your Arthur is listed in the SS as you note, born 1874 died 1962 Ill.
There is another Arthur born the same year however he was born in the Bendigo area of Victoria Australia to parents James Bradish and Elizabeth Watson. I believe this couple to be Irish in origin not American so that can't be any connection.
Further records indicate there was another Arthur born 1892 died 1976 MA.
Arthur David Bradish 1895 - 1964 Australia Further Joseph Bradish mother Elizabeth, wfe Ruby Maud Roberts.
Arthur Jefferson Bradish born Maine, Eastport? to Walter and Frances Bradish.
Arthur Lincoln Bradish born 1875 RI, Providence to parents Addison and Mary Bradish
Arthur Melancthon Bradish born 1840 NY died sometime after 1860 and father John, mother Joanna?
Arthur Bradish an infact who died in 1934 Brentford UK.
Lastly, Arthur Oliver Bradish is listed as being born December Quarter 1897 Lambeth, Civil Registrations for England.
The above records come from Census, Social Security Death Index, Australian BDM records, Civil Registrations, the IGI and one found by Dave Kyle a fellow researcher.
Sorry I couldn't be of more help. Have you got any more leads I could try chasing?
Perhaps a fellow American Bradish may have come across them. As I say I'm Australia and my main line is in England and Ireland, although I collect every Bradish record I can find.
Good luck with your searching.
Alyshia.