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Switch to: References
Citations of:
La géométrie dans le monde sensible
Revue Philosophique de la France Et de l'Etranger 155 (3):383-383 (1965)
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Our perception of where touch occurs on our skin shapes our interactions with the world. Most accounts of cutaneous localisation emphasise spatial transformations from a skin-based reference frame into body-centred and external egocentric coordinates. We investigated another possible method of tactile localisation based on an intrinsic perception of ‘skin space’. The arrangement of cutaneous receptive fields (RFs) could allow one to track a stimulus as it moves across the skin, similarly to the way animals navigate using path integration. We applied (...) |
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This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) |
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We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory (...) |
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At present, there is a renewed interest in thoseaspects of Rudolf Carnap ''s LogischerAufbau der Welt that cannot just be reduced tothe tradition of logical positivism. There is, however,one of these aspects which seems to have beenneglected by the historical analyses of theAufbau''s background: what may be called aprogram for the mathematization of sense experience,as developed by Carnap in the most difficult partof his work, Chapter IV/A. It is the program of applying settheory and topology to the reconstruction of phenomenal (...) |
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This paper concerns a fundamental dispute in ontology between the “Foundational Ontologist”, who believes that there is only one correct way of characterizing what there is, and the ontological “Skeptic”, who believes that there are viable alternative characterizations of what there is. I examine in detail an intriguing recent proposal in Dorr (2005), which promises to yield (i) a way of interpreting the Skeptic by means of a counterfactual semantics; and (ii) a way of converting the Skeptic to a position (...) |
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This paper considers the attempts put forward by A.N. Whitehead and by Bertrand Russell to ‘construct’ points (and temporal instants) from what they regard as the more basic concept of extended ‘regions’. It is shown how what they each say themselves will not do, and how it should be filled out and amended so that the ‘construction’ may be regarded as successful. Finally there is a brief discussion of whether this ‘construction’ is worth pursuing, or whether it is better—as in (...) |
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In 1929 Tarski showed how to construct points in a region-based first-order logic for space representation. The resulting system, called the geometry of solids, is a cornerstone for region-based geometry and for the comparison of point-based and region-based geometries. We expand this study of the construction of points in region-based systems using different primitives, namely hyper-cubes and regular simplexes, and show that these primitives lead to equivalent systems in dimension n ≥ 2. The result is achieved by adopting a single (...) |
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We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of (...) |
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