Supposition, n.
Etymology: [F. supposition, L. suppositio a placing under, a substitution, fr. supponere, suppositium, to put under, to substitute. The word has the meaning corresponding to suppose. See Sub-, and Position.]
1. The act of supposing, laying down, imagining, or considering as true or existing, what is known not to be true, or what is not proved.
2. That which is supposed; hypothesis; conjecture; surmise; opinion or belief without sufficient evidence. This is only an infallibility upon supposition that if a thing be true, it is imposible to be false. Tillotson. He means are in supposition. Shak.
Shades of meaning
Fernald has no entry of its own for supposition; he lists it under fancy, hypothesis, idea.
Where he writes about it:
A conjecture is more methodical than a guess, while a supposition is still slower and more settled; a conjecture, like a guess, is preliminary and tentative; a supposition is more nearly final; a surmise is more floating and visionary, and often sinister; as, a surmise that a stranger may be a pickpocket. — from hypothesis