A Summary of the First Five Chapters - "Back Over the Road" Ch. 6 of The Evolution of Deductive Theory by Gasset
Back Over the Road
Chapter six serves as a short summary of the first five chapters to help the reader maintain the thread of the discourse. Basically, Leibnitz is the last and most extreme figure of the logical idea of truth as deduction from first principles before the revolution of the physical sciences overshadows this older (and still perfectly valid) way of knowing truth.
1) Leibnitz is considered the philosopher of "principles," and thus the purpose of this work is to set out exactly what a principle in philosophy consists of.
2) Within the logical realm a principle has to do with the uncovering of truth. It that which stands as a more fundamental foundation for the truth consequent from it. This can be either absolutely or relatively.
3) The way in which the word "truth" is understood is going to be influenced by the philosophical system the thinker/speaker has undergirded his ideas. For Leibnitz, truth is that of scientific (old sense) demonstration. It is the absolute necessity of consequences following their antecedents. 1
4) That Leibnitz is part of the Modern period of philosophy, sharing an influence from the logical deduction of the Ancients and Medievals, and a burgeoning pure mathematics which the early Rationalists were developing.
5) The latter part of the Modern period is one that went beyond pure mathematics towards the hard science of Physics, applying that use of math to the physical world around us, moving beyond the methods of Leibnitz.
"Now we will see what happens in pure mathematics when Leibnitz begins to cogitate, what innovations he, as a mathematical genius, introduces into the exact sciences, and what repercussions all this has on his philosophic way of thinking." 2
1 - Ortega y Gasset, Jose. The Idea of Principle in Leibnitz and the Evolution of Deductive Theory. (New York: W.W. Norton & Company, 1971). Pg. 44
2 - 45