The most common and most likely answer to this crossword clue is the 10 letter word PHRENOLOGY
I've seen this crossword clue in Financial Times
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More clues leading to the result PHRENOLOGY
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The straight part
We know that "Fanciful science" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fanciful science = phrenology.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PHRENOLOGY mean?
PHRENOLOGY noun- The science, now generally discredited, which studies the relationships between a person's character and the morphology (structure) of the skull.