I speak of all, whether they do or do not exist.
But a perpendicular cannot be drawn in a triangle which does not exist. What does not exist is nothing.
But perhaps that which does not exist may exist; and I see with perfect clearness how every thing said would be verified, supposing it to exist. Thus we can and do speak of all existences and non-existences without any exception.
We leave it to the reader to judge if we have not, while thus rudely troubling our good mathematician with our importunate questions, made him reply as would have replied every one not at all acquainted with metaphysics. It is evident that these replies ought to be accepted as reasonable, as satisfactory, and as the only ones in this case that all the mathematicians in the world could give.
This being so, all that we have advanced is found in these replies and explications. All science is founded on the postulate of existence; every argument, to demonstrate even the most essential properties and relations of things, must start with the supposition of their existence.
[CHAPTER VIII.]
THE FOUNDATION OF PURE POSSIBILITY, AND THE CONDITION OF ITS EXISTENCE.
53. We have said that the foundation of the pure possibility of things, and of their properties and relations, is founded in the essence of God, wherein is the reason of every thing.[22] And it may at first sight seem that science needs only this foundation, and does not require to rest upon the condition of the existence of things; because, if essences are represented in God, the object of science is found in the Divine essence; and consequently, the argument founded upon the impossibility of asserting any thing of nothing, is not conclusive. Supposing there to be such a representation, science is not occupied with a pure nothing, but with a real thing; and it has consequently in view a positive object, even when it abstracts the reality of the thing considered.