It is a sort of statement like this:—­“If on the day on which that murder was committed at Rome, I was at Athens, I could not have been present at that murder.”  Because this is manifestly true, there is no need to adduce proof of it; wherefore, it is proper at once to assume the fact, in this way:—­“But I was at Athens on that day.”  If this is not notorious, it requires proof; and when the proof is furnished the conclusion must follow:—­“Therefore I could not have been present at the murder.”  There is, therefore, a certain kind of proposition which does not require proof.  For why need one waste time in proving that there is a kind which does require proof; for that is easily visible to all men.  And if this be the case, from this fact, and from that statement which we have established, it follows that proof is something distinct from a proposition.  And if it is so, it is evidently false that argumentation is susceptible of only three divisions.

In the same manner it is plain that there is another sort of proof also which is distinct from assumption.  For if in some sort of argumentation it is sufficient to use assumption, and if it is not requisite to add proof to the assumption; and if, again, in some sort of argumentation assumption is invalid unless proof be added to it; then proof is something separate and distinct from assumption.  But there is a kind of argumentation in which assumption does not require proof; and a certain other kind in which it is of no use without proof; as we shall show.  Proof, then, is a thing distinct from assumption.  And we will demonstrate that which we have promised to in this manner.

That assumption which contains a truth evident to all men has no need of proof.  That is an assumption of this sort:—­“If it be desirable to be wise, it is proper to pay attention to philosophy.”  This proposition requires proof.  For it is not self-evident.  Nor is it notorious to all men, because many think that philosophy is of no service at all, and some think that it is even a disservice.  A self-evident assumption is such as this:—­“But it is desirable to be wise.”  And because this is of itself evident from the simple fact, and is at once perceived to be true, there is no need that it be proved.  Wherefore, the argumentation may be at once terminated:—­“Therefore it is proper to pay attention to philosophy.”  There is, therefore, a certain kind of assumption which does not stand in need of proof; for it is evident that is a kind which does.  Therefore, it is false that argumentation is susceptible of only a threefold division.