The most common and most likely answer to this crossword clue is the 8 letter word HUMANISM
H
U
M
A
N
I
S
M
Buddy explains!

The straight part
We know that "philosophical system" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case philosophical system = humanism.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 HUMANISM mean?
HUMANISM noun- The study of the humanities or the liberal arts; literary (especially classical) scholarship.
- (often capitalized) Specifically, a cultural and intellectual movement in 14th-16th century Europe characterised by attention to classical culture and a promotion of vernacular texts, notably during the Renaissance.
- An ethical system that centers on humans and their values, needs, interests, abilities, dignity and freedom; especially used for a secular one which rejects theistic religion and superstition.
- Humanitarianism, philanthropy.