Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

cognition of structure 47Fig. 2.2.are those picked out in conceiving the configurations as structured sets.) So,seeing two dissimilar configurations, conceived as structured sets, as instances ofthe same structure may involve visualizing an appropriate spatial transformation.But I doubt that it is necessary to visualize a spatial transformation. Wemay instead be able to see, quite directly, diverse configurations as instancesof the same structure. How is this possible? We can directly recognize objectsof different shapes, sizes, colours, surface textures, etc. as members of a singleclass, such as the category of hand. We sometimes think of all hands, or at leastall left hands, as having the same shape. But the actual shape of a hand varieswith degree of openness and positions of the fingers, as well as their relativethickness. What we actually mean by ‘the shape’ of a hand is something moreabstract, a spatial property that is preserved not only under shape-preservingtransformations, but also under transformations involved in normal changes ofpalm shape and finger positions. Yet we can visually recognize something as ahand directly, regardless of palm shape and finger positions. We certainly donot deduce that something we see is a hand from other perceptible properties;rather, the visual system has acquired a category representation for hand;and when visual inputs from seeing a hand strongly activate this categoryrepresentation, one visually recognizes what one is seeing as a hand. In thesame way, the visual system can acquire a representation for a category of visualconfigurations of marks that provide instances of a common structure. Let uscall these representations category specifications.⁵ My suggestion is that a visualcategory specification gives us a visual means of grasping structure that is moreflexible than a visual template.⁵ This is what is called a ‘category pattern’ in Kosslyn (1994).