Let's suppose that I want to write or say a statement to which I want to add meaning. Also let's suppose that this statement is only true if we say so or we deduce it from axioms. Also let's suppose that no implicit premises count in a deduction. Everything has to be explicit. Now.. how do we call a collection of axioms necessary for a statement which has a meaning to be true? In the real life people say things without explicitly saying on which grounds they argue a particular statement. What part of philosophy deals with the thinking about what is necessary to be true in order for a particular statement with added meaning to be true?
To give a example: if I say that 2+2=4, I would have to write explicitly everything that I suppose is true in order for this statement to be true. I would have to say for example that I suppose that it is true that I can be true and that knowledge is possible. In plain english, I want to have absolutely no room for a speculation in this statement. It seems to me that even in mathematics we don't explicitly say everything that we have to assume to be true in order for a statement to be true.