Leibniz on The Elimination of Infinitesimals

My aim in this paper is to consider Leibniz’s response to concerns raised about the foundations of his differential calculus, and specifically with his doctrine that infinitesimals are “fictions,” albeit fictions so well-founded that their use will never lead to error. I begin with a very brief sketch of the traditional conception of rigorous demonstration and the methodological disputes engendered by the advent of the Leibnizian calculus differentialis. I then examine Leibniz’s claim that infinitesimal magnitudes are fictions, and consider two strategies he employed in the attempt to show that such fictions are acceptable.