Counter Example and Dilemma

Counter Example

In my analysis I gave the notational differences between Leibniz and Newton as sufficient evidence for Leibniz as the founder of mathematics. However this is only one argument that is given to legitimize this claim that Leibniz is the soul founder, other arguments include dates of publication, type of publication, and general acceptability of the men’s theories. For example while Leibniz published papers on the Calculus, Newton published the Principia Mathematica which laid out Newton’s Calculus as well has Classical Mechanics. These other arguments do, in fact, follow a common idea, one of intellectual ownership. What does it mean for a person to own an idea? This question in the ground work for a counter example that if true would make the claim that Newton is the father of Calculus regardless of how we think about the Calculus today or what Leibniz’ contributions to the advancement of mathematics were.

Consider for a moment then that Newton and Leibniz did not formulate independent views of the Calculus. In particular that Leibniz based his Calculus off of Newton’s but did so in a way that was much more metaphysical, meaning that while Newton could only describe his new mathematics in terms of English by referring to terms like velocity, Leibniz would then be able to talk about this new mathematics in terms of mathematics. That is to say that the first derivative is dy/dx. If Leibniz’ Calculus is simply a translation of Newton’s Calculus into mathematical notions then Leibniz is not the founder of the Calculus merely the man who made it understandable in mathematics.



Dilemma

Assuming my counter example that Leibniz based his Calculus not independently of Newton’s creates a dilemma in that Leibniz may then only as a developer of the Calculus. The implication then is that he did not have the background knowledge the lead to Newton’s Calculus nor Newton understanding. All that Leibniz would be able to claim, is that Leibniz simply generalized Newton’s Calculus, which is also a very notable place to be in the history of mathematics. The notion of Leibniz’ work being dependent on the work of Newton would then imply that Leibniz’ first had an understanding of the scientific and applied notion of the Calculus to which he then build the theoretical and generalized notions. Which adds to a grander dilemma that is Leibniz educational background; if Leibniz started out with the Newtonian Calculus Leibniz would have been a natural philosopher. These dilemmas lead to contradictions about Leibniz and his academic work.