Final answer:
The answer to the riddle is that the man in the painting is the son of the speaker, as he has no brothers or sisters and the man's father is his father's son.
Step-by-step explanation:
The riddle posed is a classic example of a brain teaser often found in the context of logic puzzles. When the man says, "that man's father is my father's son," he is referring to himself because he has no brothers or sisters. Therefore, "my father's son" would be the man himself. With this understanding, the statement implies that the man in the painting is the son of the speaker. Thus, his son is the person depicted in the painting.