maxims themselves without proof, if he cannot know the truth of others without proof, which are as self-evident as these.  Upon this ground it is that intuitive knowledge neither requires nor admits any proof, one part of it more than another.  He that will suppose it does, takes away the foundation of all knowledge and certainty; and he that needs any proof to make him certain, and give his assent to this proposition, that two are equal to two, will also have need of a proof to make him admit, that what is, is.  He that needs a probation to convince him that two are not three, that white is not black, that a triangle is not a circle, &c., or any other two [determined] distinct ideas are not one and the same, will need also a demonstration to convince him that it is impossible for the same thing to be and not to be.

20.  Their Use dangerous where our Ideas are not determined

And as these maxims are of little use where we have determined ideas, so they are, as I have showed, of dangerous use where [our ideas are not determined; and where] we use words that are not annexed to determined ideas, but such as are of a loose and wandering signification, sometimes standing for one, and sometimes for another idea:  from which follow mistake and error, which these maxims (brought as proofs to establish propositions, wherein the terms stand for undetermined ideas) do by their authority confirm and rivet.

CHAPTER VIII.  OF TRIFLING PROPOSITIONS.

1.  Some Propositions bring no Increase to our Knowledge.

Whether the maxims treated of in the foregoing chapter be of that use to real knowledge as is generally supposed, I leave to be considered.  This, I think, may confidently be affirmed, That there are universal propositions, which, though they be certainly true, yet they add no light to our understanding; bring no increase to our knowledge.  Such are—­

2.  As, First, identical Propositions.

First, All purely identical propositions.  These obviously and at first blush appear to contain no instruction in them; for when we affirm the said term of itself, whether it be barely verbal, or whether it contains any clear and real idea, it shows us nothing but what we must certainly know before, whether such a proposition be either made by, or proposed to us.  Indeed, that most general one, what is, is, may serve sometimes to show a man the absurdity he is guilty of, when, by circumlocution or equivocal terms, he would in particular instances deny the same thing of itself; because nobody will so openly bid defiance to common sense, as to affirm visible and direct contradictions in plain words; or, if he does, a man is excused if he breaks off any further discourse with him.  But yet I think I may say, that neither