Whitehead's pointfree geometry and diametric posets

• Authors: Gerla Giangiacomo , Paolillo Bonaventura
• Languages of publication: EN

Abstracts

EN

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).

Keywords

EN

Whitehead; pointfree geometry; lattices; diameters

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2010
• Volume: 19
• Issue: 4
• Pages: 289–308

Dates

published

2010-12-01

Contributors

author

Gerla Giangiacomo

• Dipartimento di Matematica, Università di Salerno, Via Ponte don Melillo 84084 Fisciano, (SA) Italy

author

Paolillo Bonaventura

• Dipartimento di Matematica, Università di Salerno, Via Ponte don Melillo 84084 Fisciano, (SA) Italy

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Identifiers

DOI

10.12775/LLP.2010.010