"McCarthy's Folly," as the owner of the property in 2009 called it, stands about 25 feet tall. Constructed of local limestone blocks, it's decorated with porcelain tiles and copper medalions and a lot of small gargoyles that don't spout water. There were also four bronze plaques which somebody took long ago.
In 1982, just after Ian bought the property for his industrial refractory-services business, somebody slipped a sheet of paper handwritten on one side underneath his door. Ian said that the text in this document is all that he knows about the structure although he did mention some details that were not in the document (which he photocopied for me.)
I spoke with an elderly man who said he had lived in the neighborhood for 52 years. He told me a few more possible origin-stories about the McCarthy Monument.
Between the two of them, I heard six hypotheses. I can only remember five:
Commemoration of the victims of a disaster at the "amethyst mine" which was really the nearby limestone quarry that contained some amethyst, for which the area's known as Diamond Hill.
In honor of the erector Alexander McCarthy's brother, the Lord Mayor of the Ballintemple district (where the monument stands.)
Commemoration of William Penn, (of Pennsylvania fame,) who spent some time in Cork.
Commemoration of (again) a dog but in this case by several families.