Daniel E. Sutherland

Kant's Philosophy of Mathematics and the Greek Mathematical Tradition

Kant made two intimately related claims that greatly influenced the philosophy of mathematics: first, mathematical cognition is synthetic a priori; second, mathematical cognition requires intuition for the content and the justification of mathematical concepts and propositions. Kant held that intuitions, like concepts, are a fundamental kind of representation. Intuitions belong (at least for humans) to the faculty of sensibility and represent spatial and temporal properties; concepts belong to the faculty of understanding. Kant contrasts intuitions and concepts by claiming that intuitions are singular representations that relate to objects immediately, while concepts are general representations that relate to objects mediately, that is, mediated by intuitions (A320/B376-77, A68/B93).1 It is therefore quite natural that some recent accounts of Kants philosophy of mathematics have focused on the singularity and immediacy of intuition, and have argued that one or both play a central role in Kants philosophy of mathematics.2 While not disagreeing with this approach or its fruitfulness, I would like to propose a very different one: I would like to consider the role of intuition in representing magnitudes, and in particular, the spatially extended magnitudes of geometrical constructions. Kants theory of magnitudes has been largely overlooked; uncovering it complements recent work and gives us a more complete understanding of Kants philosophy of mathematics. I shall argue that magnitudes are at the heart of Kants theory of mathematical cognition. In particular, I shall argue that one of the aims of the theory is to explain our cognition of the mathematical properties of magnitudes, for which intuition is indispensable. Kants treatment of magnitudes is, I maintain, strongly influenced by the Greek mathematical tradition. That tradition still had currency in Kants time, allowing Kant to make allusions and tacit references to it. The best evidence for the influence of the Greek mathematical tradi-

Kant on the construction and composition of motion in the Phoronomy

This paper examines the role of Kants theory of mathematical cognition in his phoronomy, his pure doctrine of motion. I argue that Kants account of how we can construct the composition of motion rests on the construction of extended intervals of space and time, and the representation of the identity of the part–whole relations the construction of these intervals allow. Furthermore, the construction of instantaneous velocities and their composition also rests on the representation of extended intervals of space and time, reflecting the general approach to instantaneous velocity in the eighteenth century.

American Civil War Guerrillas

The irregular conflict that formed part of America’s Civil War (1861–65) became a surprisingly volatile and complex struggle. It also played a crucial role in deciding the outcome of that war. Both the Union and Confederacy used guerrillas, but rebel irregulars eventually proved to be more hindrance than help to their side. Their insistence on independent operations frustrated the Confederate government, and their ruthless attacks on both Union soldiers and pro-Union civilians drew a harsh response from the Federals. As combatants and non-combatants on both sides became trapped in a vicious cycle of retaliation and counter-retaliation, and as some guerrilla bands turned to simple outlawry, Confederate citizens lost faith in their irregular fighters and, not coincidentally, abandoned their nation’s cause.

Why Confederates Fought: Family and Nation in Civil War Virginia (review)

Combat motivation has been a hot topic in military history since at least the mid1970s, when John Keegan nudged the profession toward a deeper scholarly understanding of the “will to combat.” Marvin Cain formally accepted Keegan’s challenge on behalf of historians of the American Civil War in the early 1980s, and no one writing about Johnny Reb or Billy Yank since then has dared to ignore the issue. Indeed, the question of why men fought, broadly conceived, has become a dominant theme in the military history of the war. In both his methodology and conclusions, Aaron Sheehan-Dean has made a singular contribution to the debate. His focus is limited but precise. He asks why Virginia Confederates fought. Why did men enlist? Why did they continue to fight, even after witnessing the brutality and capriciousness of war? In seeking answers, Sheehan-Dean does not limit himself to the battlefield. Rather, much of his discussion involves general conditions of service and the political expectations of volunteer soldiers. He is especially keen, as his subtitle implies, to explore connections between military loyalty and conditions on the home front. He is more interested in why the average soldier supported the war effort than why he did not literally flee the fight. Still, much of this is of a piece, and Sheehan-Dean does an admirable job of stitching it together. His conclusions are balanced and reasonable. Sheehan-Dean emphasizes the constantly-shifting rationale for Confederate loyalties in Virginia. A few factors remained constant but acquired more importance in some seasons than in others. The sufferings wrought by invasion, occupation, and depredations on families produced additional reasons for husbands and fathers to stand fast. Some motives, old and new, also became more deeply felt as the war progressed. At the start of hostilities, for example, Sheehan-Dean finds no single issue to account for the rush of Confederate volunteers. Patriotic zeal, economic self-interest, religious conviction, honor, security, and a giant dollop of testosterone all contributed. Those elements had been much diluted by the end of the war but not the commitment of Virginians to the Confederate cause. Most important by 1865, Sheenan-Dean says, were a sense of racial superiority, the sanctity of the family, and, above all, devotion to the Confederate nation. This last factor, a product, Sheehan-Dean believes, of a “vibrant culture of nationalism” among Virginia rebels (p. 187), represents his most contentious argument. How much Sheehan-Dean’s analysis tells us about why other Southerners fought for the Confederacy remains to be seen. His conclusions seem sound for a state that acted as the seat of the Confederate nation, and whose soldiers seldom defended the borders of any other state. However, those circumstances may well prove unique to Virginia, the depth of loyalties and the reasons for fighting or not fighting being markedly different in other places. Still, Sheehan-Dean cannot be held accountable for the motives of all Confederates. He has done well enough to dissect the thinking of Virginians in so sensible and engaging a manner.

James McNeill Whistler in Chile: Portrait of the Artist as Arms Dealer

The colorful and controversial life of American artist James Abbott McNeill Whistler took many twists and turns. One of the most dramatic and least explicable of the turns came in 1866, when he traveled to Valparaiso, Chile. Generations of Whistler biographers have been puzzled by the reasons for this sojourn, but a recently discovered collection of documents provides significant clues for solving the mystery. Whistler, it seems, had become involved in a scheme to provide weapons to the Chilean navy in a war against Spain. The scheme turned into a fiasco, dashing Whistler’s hopes of handsome financial profits, but his weeks in South America significantly shaped his development as an artist.

Virginia's Private War: Feeding Body and Soul in the Confederacy, 1861-1865

William Blairs Virginias Private War is a close study of the home front in the Confederacy and a significant contribution to our understanding of the Confederate defeat. Blair challenges and effectively overturns the dominant assumption that internal stresses and conflicts, particularly along lines of class and race, undermined the Confederacy. Rather, he shows that for most of the South the centripetal forces of Confederate nationalism and defence of home and hearth against an invading enemy were more powerful. Internal problems, including dissent, wracked the state of Virginia, yet these private wars actually helped prolong the conflict as they forced authorities to turn the war into more of a rich mans fight.

When the Yankees Came: Conflict and Chaos in the Occupied South, 1861-1865.@@@Seasons of War: The Ordeal of a Confederate Community.

Southerners whose communities were invaded by the Union army during the Civil War endured a profoundly painful ordeal. For most, the coming of the Yankees was a nightmare become real; for some, it was the answer to a prayer. But for all, the author argues, invasion and occupation were essential parts of the experience of defeat that helped shape the southern postwar mentality. This is a study of the occupied South, bringing to light information about the southern home front. Among the topics explored are guerrilla warfare and other forms of civilian resistance; the evolution of Union occupation policy from leniency to repression; the impact of occupation on families, churches and local government; and conflicts between southern aristocrats and poor whites. In analyzing these topics, the author examines events from the perspective not only of southerners, but also of the northern invaders and shows how the experiences of southerners differed according to their distance from a garrisoned town.

A Surgeon's Civil War: The Letters and Diary of Daniel M. Holt, M.D.

In this account of the American Civil War, Daniel M. Holt, a country doctor from upstate New York, describes camp life, army politics and the medical difficulties that he and his colleagues experienced. His reminiscences cover nearly all the major campaigns in the eastern theatre of the war.