A man looks at a picture and says this man's father is my fathers son?

Answer 1

Himself

(2) I think that the question has left out part of the original riddle which goes: "Brothers and sisters have I,none,/But this man's father is my father's son."

'My father's son' is me (or my brother or my half-brother or my stepbrother); This man's father is me = I am this man's father = his son;

This man's father is my brother = my brother is this man's father = his nephew;

This man's father is my half-brother = my half-brother is this man's father = his nephew; This man's father is my stepbrother = my stepbrother is this man's father = no blood relation.

If you include 'brothers and sisters have I, none' then the first option is the only valid one , he is looking at a portrait of his son.

If the portrait was of himself he would be saying (this man's) = (my) father is my father's son (me or my brother) = I am my own father, or my brother is my father - which would be possible given an incestuous relationship with the mother.

The comic song "I'm my own grandpa" plays with this notion and Wikipaedia cites "A proof that a man may be his own Grandfather.-There was a widow and her daughter-in-law, and a man and his son. The widow married the son, and the daughter the old man; the widow was, therefore, mother to her husband's father, consequently grandmother to her own husband. They had a son, to whom she was great-grandmother; now, as the son of a great-grandmother must be either a grandfather or great-uncle, this boy was therefore his own grandfather."