'unverifiability' is formed by the negative prefix 'un-' (from Old English) attached to 'verifiability', which comes from 'verify' + the noun-forming suffix '-ability'. 'Verify' ultimately comes from Latin 'verificare', where 'verus' meant 'true' and 'facere' meant 'to make.'

'verificare' (Latin) gave rise to Old French 'verifier', which entered Middle English as 'verifien'/'verify' and developed into modern English 'verify'. From 'verify' came 'verifiable' and then 'verifiability'; adding the prefix 'un-' produced 'unverifiability'.

Originally related to making or showing something to be 'true' ('to make true'), the root evolved to mean 'to establish or confirm by evidence'; 'unverifiability' now denotes the absence of such confirmability.