The most common and most likely answer to this crossword clue is the 13 letter word CONCEPTUALISM
I've seen this crossword clue in The Guardian
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Buddy explains!
The straight part
We know that "Philosophical theory" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case philosophical theory = conceptualism.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 CONCEPTUALISM mean?
CONCEPTUALISM noun- The art movement towards conceptual art.
- A theory, intermediate between realism and nominalism, that the mind has the power of forming for itself general conceptions of individual or single objects; the doctrine that universals have an existence in the mind apart from any concrete embodiment.