knowledge reaches as far as our ideas.  And we are capable of making as many self-evident propositions, as we have names for distinct ideas.  And I appeal to every one’s own mind, whether this proposition, ‘a circle is a circle,’ be not as self-evident a proposition as that consisting of more general terms, ‘whatsoever is, is’; and again, whether this proposition, ’blue is not red,’ be not a proposition that the mind can no more doubt of, as soon as it understands the words, than it does of that axiom, ’it is impossible for the same thing to be and not to be?’ And so of all the like.

5.  In Co-existance we have few self-evident Propositions.

II.  Secondly, as to co-existance, or such a necessary connexion between two ideas that, in the subject where one of them is supposed, there the other must necessarily be also:  of such agreement or disagreement as this, the mind has an immediate perception but in very few of them.  And therefore in this sort we have but very little intuitive knowledge:  nor are there to be found very many propositions that are self-evident, though some there are:  v.g. the idea of filling a place equal to the contents of its superficies, being annexed to our idea of body, I think it is a self-evident proposition, that two bodies cannot be in the same place.

6.  III.  In other Relations we may have many.

Thirdly, As to the relations of modes, mathematicians have framed many axioms concerning that one relation of equality.  As, ’equals taken from equals, the remainder will be equal’; which, with the rest of that kind, however they are received for maxims by the mathematicians, and are unquestionable truths, yet, I think, that any one who considers them will not find that they have a clearer self-evidence than these,—­that ‘one and one are equal to two’, that ’if you take from the five fingers of one hand two, and from the five fingers of the other hand two, the remaining numbers will be equal.’  These and a thousand other such propositions may be found in numbers, which, at the very first hearing, force the assent, and carry with them an equal if not greater clearness, than those mathematical axioms.

7.  IV.  Concerning real Existence, we have none.

Fourthly, as to real existance, since that has no connexion with any other of our ideas, but that of ourselves, and of a First Being, we have in that, concerning the real existence of all other beings, not so much as demonstrative, much less a self-evident knowledge:  and, therefore, concerning those, there are no maxims.

8.  These Axioms do not much influence our other Knowledge.

In the next place let us consider, what influence these received maxims have upon the other parts of our knowledge.  The rules established in the schools, that all reasonings are ex praecognitis et praeconcessis, seem to lay the foundation of all other knowledge in these maxims, and to suppose them to be PRAECOGNITA.  Whereby, I think, are meant these two things:  first, that these axioms are those truths that are first known to the mind; and, secondly, that upon them the other parts of our knowledge depend.