Leibniz vs. Newton: Mathematics and Metaphysics

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The Calculus War

My first calculus teacher was a huge fan of Isaac Newton, so early in the school year, he decided to assign his students the homework of writing an essay on the the controversial “Calculus War” between Newton and Leibniz. While, ironically, I didn’t learn much about mathematics in doing this project, researching these two individuals taught me a good deal about an important division in metaphysics. However, before I get into their metaphysical arguments, I should start with some context.

Sir Isaac Newton and Gottfried Wilhelm Leibniz were incredibly important figures within several different fields, but their most famous conflict was in the field of mathematics. The so-called “Calculus War” was a dispute over which of the two mathematicians had first come up with the theory of calculus.

Newton and Leibniz had acknowledged each other to quite a significant degree long before this conflict became a true war. The two had worked together on parts of their development of Calculus, such as the development of the power series, and Newton had written in one of his letters that Leibniz had developed a method which was novel to him. Despite this cooperation, the title of “the inventor of calculus” became a point of great conflict.

In 1704, Leibniz anonymously published a review on Newton’s writing of quadrature, heavily suggesting that Newton had borrowed many of the ideas of fluxional calculus from Leibniz. Moreover, Newton was involved in the publishing of the Commercium Epistolicum which made a case against Leibniz.

Today, many high school students know of Newton as the father of calculus, and there are a few reasons Newton seems to come out of this conflict on top. First, Leibniz stopped contributing to the controversy in its later years. He believed that the events which this conflict had surrounded were effectively irrelevant after many years. Second, the Royal Society, the organization which created the committee in charge of investigating and resolving this dispute, was biased toward Newton.

Modern consensus holds that Newton and Leibniz developed Calculus independently. Newton is considered the father of infinitesimal calculus, while Leibniz is considered the father of differential and integral calculus.
This is the most famous conflict between Leibniz and Newton; however, there is another dispute of perhaps even greater importance than credit for the creation of calculus. The war between these two incredibly intelligent individuals spans from the realm of the mathematical to the world of the metaphysical.

Rationalism and Empiricism

Although they were conceptually united in mathematics, Leibniz and Newton were deeply divided in their metaphysical views. Leibniz was a rationalist, and Newton was an empiricist.

Rationalism, in the context of philosophy, is the view that human reason is the only true basis of knowledge. By reason, rationalists more specifically mean a priori reason, which is purely logical and not based in experience. The empiricists were quite the opposite. To them, the only true knowledge is that which is derived a posteriori from experience and the senses .

Leibniz and Newton never directly debated these issues; however, Samuel Clarke, a supporter of Newton, furthered this indirectly. Leibniz and Clarke had an ongoing correspondence debating these issues, and these letters were eventually published. Leibniz, as a rationalist, attempted to start from general concepts and use pure reason and the principle of sufficient reason to deduce the nature of the world. Clarke, and by extension Newton, used empirical observations regarding natural phenomenon to figure out governing principles of the world. With different methods of describing the same things, Leibniz and Newton disagreed on conceptions of space, time, and other issues regarding the nature of the world. Newton believed space was absolute, which means that it could also be empty. Leibniz had a more relational theory of space. Explaining that theory requires going into depth regarding Leibniz’s ideas about monads and other such concepts, so that’s a topic for another time. Long story short, they argued over mathematics because their ideas were too similar, but they indirectly debated over metaphysics because their ideas were seemingly incompatible.

So, while I didn’t learn much about mathematics writing this essay, my calculus teacher somehow managed to introduce me to a very important division within the history of metaphysics. Leibniz and Newton, the inventors of calculus, were also representatives of two incredibly important (and diametrically opposed) schools of thought.