A Theory of Marginal and Large Difference
Abstract We propose a new theory based on the notions of marginal and large difference which has natural models in the context of nonstandard mathematics. We introduce the notion of finite marginality and show a representation result which ensures, for finitely marginal countable models, the existen...
Saved in:
| Published in: | Erkenntnis |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
08-07-2023
|
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Abstract
We propose a new theory based on the notions of marginal and large difference which has natural models in the context of nonstandard mathematics. We introduce the notion of
finite marginality
and show a representation result which ensures, for finitely marginal countable models, the existence of a homomorphism of the structure of marginal and large difference into a nonstandard model of the natural numbers, and show the extent to which any such homomorphism is unique. Finally, we show that our theory constitutes part of the underlying abstract structure of three distinct philosophical theories of vagueness: Dean’s
neofeasibilism
, Itzhaki’s theory of
nonstandard heuristics
, and our own initial sketch of a
nonstandard primitivism
about vagueness. |
|---|---|
| ISSN: | 0165-0106 1572-8420 |
| DOI: | 10.1007/s10670-023-00709-z |