4 INTRODUCTION. 



24. The Mathematical is certain, and, by virtue of 

 this character, it stands also alone. Mathematics is the 

 only true science, and thus the primary science, the Ma- 

 thesis, or Knowledge simply, as it was called by the 

 ancients. The fundamental propositions of mathematics 

 must, therefore, be fundamental propositions for all other 

 sciences also. 



25. Physio-philosophy is only a science when it is 

 reducible to, i. e. can be placed upon an equal footing 

 with, mathematics. Mathematics is the universal science; 

 so also is Physio- philosophy, although it is only a part, 

 or rather but a condition of the universe ; both are one, 

 or mutually congruent. 



26. Mathematics is, however, a science of mere forms 

 without substance. Physio-philosophy is, therefore, Ma- 

 thematics endowed with substance. 



27. The substance of Physio-philosophy must be of 

 one kind with the form of Mathematics. 



28. The certainty of mathematical propositions de- 

 pends upon no proposition being essentially different 

 from another. Though there may be much that is diversi- 

 fied 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 propo- 

 sitions must, consequently, resemble a first proposition. 



29. Physio-philosophy must also show that all its pro- 

 positions, or that all things, resemble each other, and, 

 finally, some first proposition or thing. 



30. These natural propositions or natural things must, 

 however, resemble also mathematical propositions, and 

 depend, after all, upon fundamental mathematical pro- 

 positions. 



Now then comes the question, what is the first principle of Mathematics ? 



