'Nothing exists' encapsulates the core of this mindset primarily (8)
I believe the answer is:
nihilism
'this mindset primarily' is the definition.
The definition suggests a singular noun which matches the answer.
'nothing exists encapsulates the core' is the wordplay.
'nothing' becomes 'nihil' ('nihil' can be a synonym of 'zero').
'exists' becomes 'is' ('be' can be a synonym of 'exist').
'encapsulates the core' becomes 'm' (I can't justify this - if you can you should believe this answer much more).
'nihil'+'is'+'m'='NIHILISM'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for nihilism that I've seen before include "Belief that life is meaningless" , "complete lack of principle" , "Philosophical belief that nothing in the world has a real existence" .)