Mereology and Infinity

• Authors: Niebergall Karl-Georg
• Languages of publication: EN

Abstracts

EN

This paper deals with the treatment of infinity and finiteness in mereology. After an overview of some first-order mereological theories, finiteness axioms are introduced along with a mereological definition of “x is finite” in terms of which the axioms themselves are derivable in each of those theories. The finiteness axioms also provide the background for definitions of “(mereological theory) T makes an assumption of infinity”. In addition, extensions of mereological theories by the axioms are investigated for their own sake. In the final part, a definition of “x is finite” stated in a second-order language is also presented, followed by some concluding remarks on the motivation for the study of the (first-order) extensions of mereological theories dealt with in the paper.

Keywords

EN

mereology; infinity; axioms of finiteness; relative interpretability second-order language

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2016
• Volume: 25
• Issue: 3 Mereology and Beyond (II)
• Pages: 309-350

Dates

online

2016-08-08

Contributors

author

Niebergall Karl-Georg

• Department of Philosophy, Humboldt-Universität zu Berlin, Germany

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Identifiers

DOI

10.12775/LLP.2016.023