Did Leibniz and Newton Discover or Create the Calculus?

摘要

The question formulated in the title only on the surface deals with the linguistical problem. In fact it concerns one of the most fundamental problems of the philosophy of mathematics: is the reality of mathematical objects given to us or is the realm of mathematics a product (a creation) of human mind? This ontological aspect of the question has also an epistemological dimension: if one answers that the mathematical reality exists independently of space, time and the human mind (such answer is usually called realism or platonism) then there arises a next question: how are we able to get the knowledge about such a reality? Similarly when the answer to the starting question is that mathematical objects are constructions and creations of the human mind (in this case one speaks about conceptualism in the broad sense) then one can ask how does this process of creating or constructing the world of mathematics look like, where are its sources and which criteria should it satisfy? In both cases the question of truth and of the decidability of mathematical statements can be given different answers.