Assumptions: In logic, statements that are explicitly supposed as true in arguments.
There are three things to be noted about assumptions:
1. One needs a term like this, whether premiss, presupposition, supposition or - like here - assumption, simply because one does make assumptions, and especially in the course of arguments.
2. Assumptions are supposed to be true, but need not be believed to be true. One reason is that one may make an assumption in order to refute it by a reductio ad absurdum; another reason is that one may need to make an assumption to explain something, without knowing that the assumption is true; a third reason is that one may for the moment simply make assumptions to see where the argument leads.
3. There is a general problem of assumptions, which may be stated as follows: What assumptions does one really make to explain something? (See: Presupposition) This sort of question is especially important in philosophy, logic, and epistemology, and it is often not at all easy to recognize and state clearly what it is that one in fact assumes as a matter of course. An example outside the fields mentioned is the grammar of one's natural language.