Object's details: Whitehead's pointfree geometry and diametric posets

Provider:Akademicka Platforma Czasopism

Description

Title:
Whitehead's pointfree geometry and diametric posets
Creator:
Gerla, Giangiacomo;
Paolillo, Bonaventura
Description:
This note is motivated by Whitehead’s researches in inclusion-based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead’s definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to avoid such a drawback. Moreover, since such a notion enables us to define a metric in the set of points, our proposal looks to be a good starting point for a foundation of the geometry metrical in nature (as proposed, for example, by L.M. Blumenthal).
Object availability:
free access
Rights:
Prawa autorskie (c) 2017 Logic and Logical Philosophy
Date:
2010.12.30
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion
Language:
English
Source:
Logic and Logical Philosophy; Vol. 19 No. 4 (2010); 289-308;
Logic and Logical Philosophy; Tom 19 Nr 4 (2010); 289-308;
2300-9802;
1425-3305
Format:
application/pdf
Publisher:
Uniwersytet Mikołaja Kopernika w Toruniu
Relation: https://apcz.umk.pl/LLP/article/view/LLP.2010.010/980
Subject:
Whitehead;
pointfree geometry;
lattices;
diameters
Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2010.010
Data provider:
Akademicka Platforma Czasopism

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