This philosophy gives patriarchal extremists a boost (8)

I believe the answer is:

platonic

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'this philosophy' is the definition.
The definition and answer are not the same part of speech.

'patriarchal extremists a boost' is the wordplay.
'extremists' means to remove the middle letters (letters on the extreme ends of the word).
'boost' becomes 'tonic' (tonic can mean a stimulant or booster).
'patriarchal' with its centre removed is 'pl'.
'pl'+'a'+'tonic'='PLATONIC'

'gives' acts as a link.

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(Other definitions for platonic that I've seen before include "(Of love) without sexual desire" , "Purely spiritual (love)" , "Chastely intimate" , "Excluding congress" , "(Of love) intimate but not sexual" .)

I've seen this clue in The Guardian.

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