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Friday, 19 April 2013

Topologies, chronologies and lexicologies

Much as there is a danger of loosing the specific dimensions of time by making it spacial (as Bergsonians keep pointing out), I always wonder how far can we stretch analogies that go from time to space. I believe there is a McTaggartian element to space where locations are relative to indexicality and distances play the role of events. I was wondering that the multiplicity of spaces - when we move from an image of geometry filled with physics to an image of a plurality of topologies where multiple spaces intertwine with no space in particular playing the part of the purely formal - could be transfered to time. A multiplicity of temporalities, of chronologies as opposed to a fixed calendar providing the merely formal element for other events in time. The calendar is not fixed once and for all but rather is relative to other chronologies by providing a fixity that is needed for time to have a sense of future - the repeated. The repeated is not something independent of any other process but rather a chronology that sponsors the future. It could be the calendar, connected to repetition in the movements of the stars, but this is no fixed choice. Now for the analogy with space: I think space also needs a dimension of the far (or the far away) and this is provided by some sort of fixed space - like a map - that is built out of repetitions - or rather of regular folds. The geometrical space (which is the map of all maps) is the spatial calendar. There we have a complete isotropy - all places are the same, none is occupied. It is a mere tic-tacking of space. Mere projection of what has been seen of the space. Still, there is nothing special about geometry but rather any space (as any time can be used as a calendar) can be used as a geometry. Of the multiple spaces, one is picked up to provide fixity, to sponsor a measurement. It is only because there is a fixed topology (and a fixed chronology) that we can talk about the far away (and the future). The far away and the future are products of the Dopplerian nature of whatever is in space or in time - they are located in relation to something else equally located. Time passes because there is an underlying rhythm of repetitions - there is space because there is an underlying regularity of distances (the geometrical space). In both cases, fixity is required but not always fully established . In a sense, it is given, but as a task (to use Kant's phrase that makes evident how much process philosophy has a Kantian origin).

In fact, this Dopplerian nature of space and time - and the idea that nothing is fixed but something needs to be made fix - has a lot to do with the Quinean rejection of analyticity. The rejection of the distinctions between calendars and events (or of the distinction between geometry and topologies) is of the same kind as the rejection of the distinction between truths grounded on meaning alone and truths grounded on the world also. In all cases, what is at stake is a fixed measure, a fixed formal structure established once and for all. There isn't a fixed formality in space, in time or in meaning - and there isn't a structure ready to be filled by picking up a conventional geometry (or calendar, or meaning postulate). The distinction between facts and conventions is in any case not given (but maybe given as a task). Feeding back, one could think of language without analyticity as having different lexicologies, different maps of meaning that intertwine while one is taken to be fixed so that language can work (words have provisional, passing meaning). Maybe there is a plurality of Quinean spheres (the sphere image that appear in the end of the Two Dogmas) intersecting with each other. They are like topological spaces and different agents act based on different spheres.

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