# The Aristotelian Continuum. A Formal Characterization

@article{Roeper2006TheAC, title={The Aristotelian Continuum. A Formal Characterization}, author={P. Roeper}, journal={Notre Dame J. Formal Log.}, year={2006}, volume={47}, pages={211-232} }

While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.

#### Topics from this paper

#### 14 Citations

THE CLASSICAL CONTINUUM WITHOUT POINTS

- Computer Science, Mathematics
- The Review of Symbolic Logic
- 2013

A point-free construction of the classical one-dimensional continuum, with an interval structure based on mereology and either a weak set theory or a logic of plural quantification, demonstrating the independence of “indecomposability” from a nonpunctiform conception is developed. Expand

The Classical Continuum without Points Geo ¤ rey Hellman and

- 2012

We develop a point-free construction of the classical onedimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quanti
cation. In some… Expand

The logic of Kant’s temporal continuum

- Mathematics
- 2017

In this thesis I provide an account of the philosophical foundations and mathematical structure of Kant's temporal continuum. I mainly focus on the development of a formalization of Kant's temporal… Expand

THE LOGIC AND TOPOLOGY OF KANT’S TEMPORAL CONTINUUM

- Mathematics, Computer Science
- The Review of Symbolic Logic
- 2018

A mathematical model of Kant's temporal continuum is provided that satisfies Kant’s synthetic a priori principles for time and illuminates what “faculties and functions” must be in place, as “conditions for the possibility of experience”, for time to satisfy such principles. Expand

Continuity of Motion in Whitehead’s Geometrical Space

- Mathematics
- 2014

The paper explores a neglected conception in the foundations of spacetime theories, namely the conception of gunk, point-free spaces inaugurated by De Laguna and Whitehead. Despite the… Expand

Brentanian continua and their boundaries

- 2020

Brentanian continua and their boundaries Arthur Heller Britto This dissertation focuses on how a specific conceptual thread of the history of mathematics unfolded throughout the centuries from its… Expand

Leibniz on the Continuity of Space

- Philosophy
- 2019

The present essay describes Leibniz’s foundational studies on continuity in geometry. In particular, the paper addresses the long-debated problem of grounding a theory of intersections in elementary… Expand

An Lω 1 ω 1 axiomatization of the linear Archimedean continua as merely relational structures

- Mathematics
- 2007

We have chosen the language Lω1ω1 in which to formulate the axioms of two systems of the linear Archimedean continua - the point-based system, SP, and the stretch-based system, SI - for the following… Expand

Continuum as a primitive type (version 2)

- Computer Science, Mathematics
- ArXiv
- 2015

The paper is the revision and extended version of the Section 6 of the paper {\em Types and operations} arXiv:1501.03043. Here, primitive types (corresponding to the intuitive concept of Continuum)… Expand

"The whole is greater than the part": Mereology in Euclid's elements

- Mathematics
- 2016

The present article provides a mereological analysis of Euclid’s planar geometry as presented in the first two books of his Elements . As a standard of comparison, a brief survey of the basic… Expand

#### References

SHOWING 1-10 OF 14 REFERENCES

First- and Second-Order Logic of Mass Terms

- Mathematics, Computer Science
- J. Philos. Log.
- 2004

An account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Expand

An Essay on the Foundations of Geometry

- Computer Science, Physics
- 1897

This text is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA and consists of four chapters, which explore the various concepts of geometry and their philosophical implications, including an historical overview of the development of geometrical theory. Expand

Region-Based Topology

- Mathematics, Computer Science
- J. Philos. Log.
- 1997

A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of… Expand

Some points in formal topology (Topology in Computer Science, Schloß Dagstuhl, 2000)

- Theoretical Computer Science, vol. 305 (2003), pp. 347–408. http://www.math.unipd.it/ sambin/publications.html. MR 2013578. 230 232 Peter Roeper School of Humanities A D Hope Building G46 The Australian National University Canberra ACT 0200 AUSTRALIA Peter.Roeper@anu.edu.au
- 2003

Some points in formal topology ( Topology in Computer Science , Schloß Dagstuhl ,

- Theoretical Computer Science
- 2000

Topological representations of mereological systems,”, in Things, Facts and Events, edited by J. Faye

- Rodopi, Atlanta,
- 2000

Generalisation of First-Order Logic to Nonatomic Domains

- Mathematics, Computer Science
- J. Symb. Log.
- 1985

Grundlagen der Geometrie, 12th edition, B. G. Teubner, Stuttgart, 1977, with supplements by Paul Bernays, Teubner Studienbücher: Mathematik

- MR 0474006
- 1977