A better word choice, and I submit the correct word choice, is "speculation." One speculates about the future, and assumes about the past or present.
Some synonyms ... assumption, axiom, premise, presumption
All that said, either word works in common usage - I understood exactly what you meant. Just that people are judged in part by their vocabulary and usage.
Seems like there is a lot of speculation about the past ...
"If this is the boots being mentioned, the interesting thing is his pants legs. Why would they have been pulled up like that? Perhaps to get something out of his boot?"