Attempt to Introduce the Concept of Negative Quantities into World Wisdom

by Immanuel Kant, Tim Newcomb (translator)

A new 2024 translation of "Attempt to Introduce the Concept of Negative Quantities into World Wisdom" from the original German manuscript first published in 1763. The original German title is "Versuch den Begriff der negativen Größen in die Weltweisheit einzuführen". This new edition contains an afterword by the translator, a timeline of Kant's life and works, and a helpful index of Kant's key concepts and intellectual rivals. This translation is designed for readability, rendering Kant's enigmatic German into the simplest equivalent possible, and removing the academic footnotes to make this critically important historical text as accessible as possible to the modern reader.The early sections of the treatise discuss the utility of mathematical methods in philosophical reasoning, emphasizing the potential of mathematical concepts, such as negative quantities, to enhance metaphysical understanding. Kant critically evaluates existing philosophical methods and proposes the integration of mathematical precision into philosophical discourse.Kant delves into the mathematical understanding of negative numbers and explores their philosophical implications, arguing for their relevance beyond mere mathematical operations. Kant weaves a detailed exploration of how negative quantities, understood mathematically, can contribute to a more nuanced understanding of metaphysical concepts.The paper also discusses the opposition between logical and real oppositions, drawing parallels and distinctions between mathematical and philosophical reasoning. Kant emphasizes the importance of considering both types of opposition in understanding philosophical problems, and argues that the concept of negative quantities offers a novel way of approaching these problems.

90 pages, Paperback

Published January 21, 2024

About the author

Immanuel Kant was an 18th-century philosopher from Königsberg, Prussia (now Kaliningrad, Russia). He's regarded as one of the most influential thinkers of modern Europe & of the late Enlightenment. His most important work is The Critique of Pure Reason, an investigation of reason itself. It encompasses an attack on traditional metaphysics & epistemology, & highlights his own contribution to these areas. Other main works of his maturity are The Critique of Practical Reason, which is about ethics, & The Critique of Judgment, about esthetics & teleology.

Pursuing metaphysics involves asking questions about the ultimate nature of reality. Kant suggested that metaphysics can be reformed thru epistemology. He suggested that by understanding the sources & limits of human knowledge we can ask fruitful metaphysical questions. He asked if an object can be known to have certain properties prior to the experience of that object. He concluded that all objects that the mind can think about must conform to its manner of thought. Therefore if the mind can think only in terms of causality–which he concluded that it does–then we can know prior to experiencing them that all objects we experience must either be a cause or an effect. However, it follows from this that it's possible that there are objects of such a nature that the mind cannot think of them, & so the principle of causality, for instance, cannot be applied outside experience: hence we cannot know, for example, whether the world always existed or if it had a cause. So the grand questions of speculative metaphysics are off limits, but the sciences are firmly grounded in laws of the mind. Kant believed himself to be creating a compromise between the empiricists & the rationalists. The empiricists believed that knowledge is acquired thru experience alone, but the rationalists maintained that such knowledge is open to Cartesian doubt and that reason alone provides us with knowledge. Kant argues, however, that using reason without applying it to experience will only lead to illusions, while experience will be purely subjective without first being subsumed under pure reason. Kant’s thought was very influential in Germany during his lifetime, moving philosophy beyond the debate between the rationalists & empiricists. The philosophers Fichte, Schelling, Hegel and Schopenhauer saw themselves as correcting and expanding Kant's system, thus bringing about various forms of German Idealism. Kant continues to be a major influence on philosophy to this day, influencing both Analytic and Continental philosophy.