Is this puzzle legitimate?

Question

I've been browsing through Puzzling SE's most downvoted questions, when I stumbled upon one of those "bad communication I will xkcd cut your arm off" questions. I've heard similar questions with the same premise. The premise goes something along the lines of this:

Two sons and two fathers were standing under the sun. There were only three shadows. Why?

Please spend no more than two seconds pondering such a bad question, with the bad answer of:

The two sons and two fathers consist of a man, his father, and his son. The man then counts as both a son and a father.

I question the legitimacy of this question, as I probably should. Can those people really count as "Two sons, AND, two fathers"? I guess the question can be worded as, "Given a set of two sons and a set of two fathers, how can their union have three elements?" Does this rewording make an ounce of sense? If so, the answer would be correct.

I thought about it for awhile. I figured that two people of the past can be considered as two sons, two fathers, two grandfathers, and two grandchildren by the logic of the premise. However, we can also say that "There are two sons in the kitchen. There are two fathers in the kitchen. There are two mathematicians in the kitchen. There are two Spaniards in the kitchen. Altogether there are two people in the kitchen." In that sense, it seems perfectly legitimate? How do we interpret "and"?

Tagged "lateral thinking", but I don't know what better tag there is.

Answer 1

A more rigorously correct way of phrasing it would be:

Two sons were standing under the sun, and two fathers were standing under the sun. There were only three shadows. How can this be?

But the whole point of these lateral thinking puzzles is that they're supposed to cue you into making an assumption that shouldn't be made. The text does suggest there are two sons AND two fathers, being separate pairs of people - deliberately so. In order to solve the puzzle, you need to use a different and less natural interpretation of the phrase. This is a reasonable thing to do because the more natural interpretation is already known to be incorrect, and "once you have eliminated the impossible, whatever remains, however improbable, must be the truth".

The same is true with other lateral-thinking puzzles, such as the famous one-half, one-third, one-ninth of seventeen puzzle: the wording is deliberately set up so as to mislead you into assuming one interpretation, but if you twist your head a bit, you can just about make it fit a different interpretation which is the required one to solve the puzzle. The 'right' interpretation is less natural than the 'wrong' one, because if it were any other way, the puzzle would be trivial.