The most common and most likely answer to this crossword clue is the 13 letter word SCHOLASTICISM
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The straight part
We know that "such philosophical method" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case such philosophical method = scholasticism.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 SCHOLASTICISM mean?
SCHOLASTICISM noun- A tradition or school of philosophy, originating in the Middle Ages, that combines classical philosophy with Catholic theology