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Not set against song bloke skipped? Fine (8)

Ross

I believe the answer is:

variable

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'not set' is the definition.
The definition and answer can be both related to thinking as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'against song bloke skipped? fine' is the wordplay.
I cannot really understand how this works, but
'against' could be 'v' (abbreviation for 'versus') and 'v' is present in the answer.
'song' could be 'aria' (piece of music in an opera) and 'aria' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for variable that I've seen before include "can be changed" , "Fickle" , "Unsteady" , "Changeable or inconstant" , "Prone to change" .)

I've seen this clue in the Sydney Morning Herald.
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