Supposition, guess (7)
I believe the answer is:
surmise
I believe this is a double definition.
'supposition' is the first definition.
(I know that supposition can be written as surmise)
'guess' is the second definition.
(I know that surmise is a more specific form of guess)
(Other definitions for surmise that I've seen before include "Presume -- rue miss (anag)" , "Suppose without evidence" , "Conjecture; Cortez's men's was wild (Keats)" , "Make a conjecture" , "suspect" .)