The Limits of Demonstrative Science Considered in a Letter to the Rev. William Whewell

The Limits Of Demonstrative Science Considered In A Letter To The Rev. William Whewell by Henry Longueville Mansel is a polemical inquiry into what can and cannot be demonstrated in science. In a prefatory exchange with Whewell, Mansel surveys the reception of Kant in Britain, critiques sensationalist accounts of knowledge, and argues for a two-source theory: presentative intuition from the mind and representative thought derived from experience. He maintains that the mind supplies form—space, time, and other a priori conditions—without which experience would be unintelligible, and that knowledge involves both empirical content and mental form. The work contrasts mathematical certainty with physical inference, insisting that mathematical judgments are a priori in their form, while physical judgments are primarily empirical and must be tested against observed facts. It discusses the status of necessary truths in science, analyzes notions of force and magnitude, and defends a measured middle course between empiricism and rationalism. An Appendix on Geometry revisits the foundations of geometrical demonstration.