Page:Symbolical Methods of Study.djvu/21

xii forms without substance. Physio-philosophy " (i.e., what we should call the philosophy of physical Nature) "is, therefore, mathematics endowed with substance.

"The certainty of mathematical propositions depends upon no proposition being essentially different from another. Though there may be much that is diversified or heterogeneous, there is nothing new in mathematics.

"For to prove a mathematical proposition is to show (or demonstrate) that it is equivalent, i.e. of the same kind with another proposition. All mathematical propositions must consequently resemble a first proposition.

"Physio-philosophy must also show that all its propositions, or that all things, resemble each other, and, finally, some first proposition or thing.

"These natural propositions, or natural things, must, however, resemble also mathematical propositions, and depend, after all, upon fundamental mathematical propositions.

"Now, then, comes the question—What is the first principle of mathematics ?

"The highest mathematical idea, or the fundamental principle of all mathematics, is the zero = o.

"Mathematics is thus in possession of an eternal principle.