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PHILOSOPHY COLLOQUIUM SERIES - Fall 2009
9/17
10/8
- Speaker: Darko Sarenac (Colorado State University)
"Fractals as a Panacea of Spatial Reasoning, or 'On Whether We Should Replace Euclid with Mandelbrot'"
Abstract: In this talk, I discuss the connection between some of my (earlier) work on the spatial modal logic for reasoning about the objects of standard metric topological spaces, and a particular class of objects in fractal geometry. Fractal geometry has been labelled "the geometry of the real world" by its proponents. The thought is that the broken, imperfect, irregular-but-self-similar objects of fractal geometry resemble real space with its complex features being a lot closer than the idealized spheres, cubes, and other perfect entities of Euclidean geometry. In doing this work, I found a strange coincidence: the logic of standard metric spaces, conceived completely independently of any fractal considerations ended up using fractals and fractal considerations in some of its deepest formal constructions. Thus, while the logic was designed to fit the products of the perfectly symmetric world of standard topological spaces and entities, it is, in the end, better suited to the real world of uneven entities that thread the fine line of Euclidean order and chaos (in its recent technical sense). While I provide no deep theoretical explanation of this phenomenon, a variety of intriguing pictures, intuitions, suggestions, and a number of theoretical puzzles are offered. The hope is that we can leave with a deeper understanding of the role of fractals in formal spatial reasoning, but more specifically and importantly, the role of fractal objects and constructions in reasoning about everyday objects.
10/22
- Speaker: Paul Teller (UC Davis)
"Two Conceptions of Truth"
(Abstract: We ordinarily think of truth as an all or nothing affair. I argue that this conception constitutes an idealization, to be sure one that most often serves us excellently. To see this conception as idealized, consider that we evaluate representations for success generally by how well they represent things the way they are. In the case of analog representations, such as maps, what counts as success is adequate, and so context relative, precision and accuracy. I suggest that on a less idealized model of truth, representational success for statements functions more like that for analog representations than we usually appreciate---even in science we never get statements that are both perfectly precise and perfectly accurate. The appearance of completely unqualified truth arises from the circumstance that we use an analog of epistemic contextualism, what I call semantic contextualism, in which we generally operate from "platforms", collections of representations that are defeasibly treated as "completely adequate".)
11/12
All colloquia held in Trinity 100 from 4:00-6:00 pm. For more information or to be added to the Colloquium Series mailing list, please contact Prof. Robert Jones.
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