I am attracted to the philosopher Avrum Stroll's book Surfaces' because it offers the possibility of seeing surface as both a physical entity and an abstraction, and makes no claims about the primacy of one surface above another. It is a discussion that is played out on many levels and continuously returns to the topographic language of ordinary speech and the mathematics of geometry. Indeed the opening discussion uses ordinary things to pose extraordinary thoughts. For example, if a dice has six contiguous surfaces without gaps or openings, and it also has 12 edges, where are the edges? Can an edge be a surface? If a solid glass marble has a chip, is the chip in or on the surface? Does the chip have its own surface? These and many other everyday examples are used to pose the philosophical problem of perception through a discussion of how we define and perceive surfaces. Stroll then examines the geometry of ordinary speech, including words like margins, limits, boundaries and edges, to draw similarities and differences between this topological language and the mathematics of geometry. In the same breath he manages to discuss surfaces as both abstractions and physical entities. At times I find the plausibility of arguments for surface as a theoretical abstraction neatly countered by equally powerful conceptions of surface based on everyday speech in the physical world.
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