Kant: Debt and Nothing. “Less than Zero (Nothing)”

Abstract

It is well known that since their inception as equation solving algorithms, negative magnitudes have achieved legitimacy through their interpretation as debt. The transformation of mathematics into a natural science has rendered this view unsatisfactory. Kant’s 1763 essay on negative magnitudes is an attempt to follow Euler’s indispensability argument from Reflexions sur l’espace et le temps, to show the reality (in the physical sense) of negative magnitudes starting from Newton’s third law of motion. Kant’s term real opposition (a breakthrough from Aristotle: “quantity has no concrete opposition,” Cat. 5b 11) seeks to reconcile the old interpretation – debt – with the new one – force. What interests us in this text is the difficulty emerging from this endeavour: the repression of the paradox of negative magnitudes (“less than nothing”), which is only properly elucidated when interpreted as debt. That is to say, the paradoxical quality of negative magnitudes (that they are “weniger wie Nichts” – “less than nothing”), which only debt as a social object could render real, becomes the main obstacle to their physical interpretation.