Chunk and Permeate: The Infinitesimals of Isaac Newton

In the paper of Brown and Priest 2004, the authors developed the chunk and permeate method, which they described as a 'paraconsistent reasoning strategy'. There it is suggested that the method of chunk and permeate could apply to the historical infinitesimal calculus. However, no attempt was made to look at actual historical examples. In this paper, I show that the method of chunk and permeate can indeed apply, as a rational reconstruction, to certain of Isaac Newton's arguments that use infinitesimals. This rational reconstruction maintains and uses, rather than sidesteps, the apparent contradictions in Newton's arguments. The applicability of chunk and permeate to other historical arguments, e.g. of Leibniz/L'Hospital and Fermat, has also been investigated and will be communicated in future publications.