I recently discovered the philosophy of Gottfried Wilhelm Leibniz, the polymath and philosopher. Some believe that he developed Calculus independent of Sir Isaac Newton, as a mathematician. We have been using Leibniz’s notation, in the infinitesimal calculus. He also contributed to what we know today as modern logic, binary system etc. It is his infinitesimal calculus and its relation with his philosophy that I find fascinating. The way he thought about the world can be seen in his math work, especially his calculus.
“Monadology” is his seminal philosophy work. Monad, the idea and the word itself, has existed in philosophy for centuries. Pythagoreans are attribute for its origin. According to Wikipedia —
Monad refers in cosmogony (creation theories) to the first being, divinity, or the totality of all beings. The concept was reportedly conceived by the Pythagoreans and may refer variously to a single source acting alone and/or an indivisible origin.
Monad as a concept was taken and enhanced by Leibniz where he referred to Monad as an elementary particle. He calls Monads as the “real atoms of nature”. According to Leibniz, Monads —
- are indivisible
- can neither be made, nor destroyed
- do not have parts
- do not occupy space
- may possess qualities
- can cause changes to one another
- come into being by creation
- destroyed by annihilation
Leibniz considered these infinite number of Monads made up the space. It means that the space is not empty, as Newton had suggested, but has Monads and since they indivisible, but do not take space, they are the basis for all the other ‘stuff’ somehow by interacting with each other. The part of Monads being indivisible is the key. That makes them infinitesimal, that cannot be detected by any apparatus we can build. Thus, we can see how the above is similar to his calculus work which deals with
Sum of infinite number of infinitesimals equate a finite amount.
As Ruth Lydia Saw writes in the best way possible —
If we consider his own discoveries in mathematics, we shall see how marvellously it must have seemed to Leibniz that everything pointed to and reinforced his metaphysical account of universe. For him, the universe is constituted by an infinite number of non-spatial beings presenting the appearance of large bodies moving in space. At the same time, the invention of the microscope shows minute differences which are lost in large perception and leads to possibility of ever more minute differences to be revealed by more powerful instruments. Then Leibniz himself invents the infinitesimal calculus which is based on the possibility and the usefulness of treating a finite amount as equivalent to the sum of an infinite number of infinitesimal amounts.