Like a lazy, indolent slacker, say, given no slack over branch of philosophy (10)
I believe the answer is:
tautologic
'like a lazy indolent slacker say given no slack' is the definition.
I can't judge whether this definition defines the answer.
'branch of philosophy' is the wordplay.
'branch' becomes 'taut' (I can't justify this - if you can you should give a lot more credence to this answer).
'of' becomes 'o''.
'philosophy' becomes 'logic' (logic is a kind of philosophy).
'taut'+'o'+'logic'='TAUTOLOGIC'
'over' acts as a link.
Can you help me to learn more?
I've seen this clue in The Independent.
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