An overview of the problem of constructing extension combinatorially from qualities cum dispositional powers. In the model recommended here, Grassmann's algebra provides the combinatorial structure while Machian elements give the content.

According to Roy Sorensen [Philosophical Studies 100 (2000) 175–191] an object cannot differ aesthetically from its mirror image. On his view, mirror-reversing an object – changing its left/right orientation – cannot bring about any aesthetic change. However, in arguing for this thesis Sorensen assumes that aesthetic properties supervene on intrinsic properties alone. This is a highly controversial assumption and nothing is offered in its support. Moreover, a plausible weakening of the assumption does not improve the argument. Finally, Sorensen’s second argument (...) is shown to be formally flawed. As a result, the case for the aesthetic irrelevancy of orientation seems still open. (shrink)

Metaphysicians of space and time are fond of talking about objects being present at, wholly present at, or existing at certain times, or occupying certain regions of space, or even regions of space-time. Take, for example, this famous set of definitions due to Mark Johnston and David Lewis: Let us say that something persists, iff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at (...) different times, though no one part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time. (Lewis 1986, p. 202) A great deal of debate has been conducted in this terminology: debates about whether anything does endure or perdure; about the ontology of temporal parts; about whether it makes sense to apply this kind of thinking to space, as well as to time (we can ask, for example, the analogous questions whether things are extended by being entended, or pertended); about whether it can be applied to space-time, and if so, to relativistic space-time. These debates have been fruitful, but cursed with a certain amount of imprecision. People sometimes talk past each.. (shrink)

I found the following manuscript while rummaging through the papers of a Square. I believe it is the same Square the Reverend Edwin A. Abbott wrote about in Flatland, a text that was written exactly one hundred and twenty-five years ago (in 1884) but that still retains all of its charm and freshness. It tells of the adventures of a Square, a per- fectly two-dimensional being, with no depth, citizen of a world that is similarly two di- mensional and depthless, (...) who one day had the good fortune of receiving a visit from a Sphere: the three-dimensional being par excellence. What’s more, he had the even greater fortune of being given the opportunity to briefly visit the great three-dimensional world that his guest came from—our three-dimensional world. He visited and experienced this place—for him, this was a mystic experience—before falling back for all eternity into the total flatness of Flatland: the flat world, lacking depth; the world with nothing over or under it, the world in which cars and airplanes alike, so to speak, belong to the same category, and everything, literally everything, is reduced to fragile shadows on an enor- mous and eternally illuminated floor. (Which does not mean that Flatland was a per- fectly democratic world. Power was in the hands of the caste of Circles, most certainly not in the hands of the infamous Irregular Polygons.) I said that the Square’s experience was in a certain sense a mystical experience, and it is not difficult to imagine why. It is almost as if we were given the opportunity to visit a four-dimensional world, a world which we have no knowledge of, and whose shapes, beauties and dangers we could never have imagined. For us the three dimensions are eve- rything: they constitute a habitat so natural that to us it seems impossible to imagine different spaces, new and unknown dimensions, and uncommon shapes. And I am not thinking of the temporal dimension: that dimension we know far too well.. (shrink)