A conjecture has a propositional attitude while a hypothesis does not. A conjecture may depend on a system, but it may be true outside of the scope of that syst

A conjecture has a propositional attitude while a hypothesis does not. A conjecture may depend on a system, but it may be true outside of the scope of that system — think "true but unproved". (Not unprovable like a Gödel sentence!) Once its proof is discovered (made), it becomes a valid hypothesis of the system by its proof which augments that system's domain of truth. A conjecture is someone's conjecture while a hypothesis is derived from a system itself ("my system has a valid hypothesis"). We don't "derive conjectures" from brains, they're made by persons. When someone says "my hypothesis is", there is an implicit system they are strictly speaking from (channeling the system? Either way, they're not saying what the believe but rather placing confidence in their understanding of the system strictly spoken from) — they're saying that this is provable within the system we know, but personally they do not have the proof on hand and it may require a little work. ("I don't know all the rules off hand!") A conjecture has an implicit system, but the speaker has a purpose to say that the system as we know it may have a derived rule we have not discovered. There is "intuition" with conjecture, and "mention" with hypothesis".