The most common and most likely answer to this crossword clue is the 7 letter word ATOMISM
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More clues leading to the result ATOMISM
Buddy explains!

The straight part
We know that "Ancient Greek philosophy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ancient greek philosophy = atomism.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 ATOMISM mean?
ATOMISM noun- The ancient Greek theory that all matter is composed of very small indestructible and indivisible particles.
- The doctrine that society arises from individuals and that larger structures are unimportant.