The pen name The Old Whig has a couple of sources.
The first is from a reference by Friedrich Hayek regarding Edmund Burke.
The second is from The Anti-Federalist papers. An anonymous author used the name An Old Whig to sign all his correspondence to the editor of the local newspaper. The Old Whig was one of the primary proponents of the addition of a Bill of Rights to the Constitution.
His arguments were as salient then as they are today.
