Negative Numbers and Immanuel Kant's Pre-Critical Understanding of Mathematics

In the early history of mathematics, we can find at least three different types of interpretations of negative numbers: (1) the rejecting type, which considers negative numbers as indicators of errors in reasoning; (2) the computational type, which considers negative numbers only as useful computational tools; and (3) physicalist type, which gives realist interpretations of negative numbers such as opposed physical forces. By comparing these types with Immanuel Kant's (1724-1804) ideas found in his pre-critical text Attempt to Introduce the Concept of Negative Magnitudes into Philosophy (1763), we conclude that Kant espoused the physicalist interpretation of negative numbers. This insight enables us to conclude that pre-critical Kant followed not only Newton's understanding of the natural world but his understanding of mathematics as well.