Prior Analytics - Book II   

proved through the thesis proposed, and demonstrate it through them,

e.g. if A should be proved through B, and B through C, though it was

natural that C should be proved through A: for it turns out that those

who reason thus are proving A by means of itself. This is what those

persons do who suppose that they are constructing parallel straight

lines: for they fail to see that they are assuming facts which it is

impossible to demonstrate unless the parallels exist. So it turns

out that those who reason thus merely say a particular thing is, if it

is: in this way everything will be self-evident. But that is

impossible.

If then it is uncertain whether A belongs to C, and also whether A

belongs to B, and if one should assume that A does belong to B, it

is not yet clear whether he begs the original question, but it is

evident that he is not demonstrating: for what is as uncertain as

the question to be answered cannot be a principle of a

demonstration. If however B is so related to C that they are

identical, or if they are plainly convertible, or the one belongs to

the other, the original question is begged. For one might equally well

prove that A belongs to B through those terms if they are convertible.

But if they are not convertible, it is the fact that they are not that

prevents such a demonstration, not the method of demonstrating. But if

one were to make the conversion, then he would be doing what we have

described and effecting a reciprocal proof with three propositions.

Similarly if he should assume that B belongs to C, this being as

uncertain as the question whether A belongs to C, the question is

not yet begged, but no demonstration is made. If however A and B are

identical either because they are convertible or because A follows

B, then the question is begged for the same reason as before. For we

have explained the meaning of begging the question, viz. proving

that which is not self-evident by means of itself.

If then begging the question is proving what is not self-evident

by means of itself, in other words failing to prove when the failure