Ehrlich, Philip (2021) Are Points (Necessarily) Unextended? [Preprint]

Preview

Text Are Points (Necessarily) Unextended_ (Final).pdf Download (338kB) | Preview

Abstract

Since Euclid defined a point as "that which has no part" it has been widely assumed that points are necessarily unextended. It has also been assumed that this is equivalent to saying that points or, more properly speaking, degenerate segments, have length zero. We challenge these assumptions by providing models of Euclidean geometry where the points are extended despite the fact that the degenerate segments have null lengths, and observe that whereas the extended natures of the points are not recognizable in the given models, they can be recognized and characterized by structures that are suitable expansions of the models.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Ehrlich, Philip ehrlich@ohio.edu
Additional Information:	To appear in Philosophy of Science
Keywords:	Points, Euclidean Geometry
Subjects:	Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic Specific Sciences > Physics
Depositing User:	Professor Philip Ehrlich
Date Deposited:	30 Jul 2021 16:21
Last Modified:	30 Jul 2021 16:21
Item ID:	19389
Subjects:	Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic Specific Sciences > Physics
Date:	29 July 2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19389

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item