This fascinating letter by William Hamilton, one of the leading mathematicians and thinkers of the Victorian era, offers a critique of Augustus De Morgan's seminal work on symbolic logic, A Budget of Paradoxes. Hamilton argues that De Morgan's work is flawed, and offers a series of counter-arguments that shed new light on this important area of mathematics. This letter is a valuable resource for anyone interested in the history of mathematics or the development of logic. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.