No, a utility function is a perfectly well-defined mathematical object. The question is what it means for a human to "have" such an object; so "have" is the word we should be tabooing.

Does Abraham Lincoln have a six-dimensional vector space? Does Spain have an abelian group? The question "do humans have a bounded utility function" is kind of like that.

Does Abraham Lincoln have a six-dimensional vector space? Does Spain have an abelian group? The question "do humans have a bounded utility function" is kind of like that.

"Does Abraham Lincoln have a personality?" would be somewhat analogous. (By somewhat I mean 'more'.)

No, a utility function is a perfectly well-defined mathematical object. The question is what it means for a human to "have" such an object; so "have" is the word we should be tabooing.

Does Abraham Lincoln have a six-dimensional vector space? Does Spain have an abelian group? The question "do humans have a bounded utility function" is kind of like that.

"Does Abraham Lincoln have a personality?" would be somewhat analogous. (By somewhat I mean 'more'.)