""Lambda theory: Introduction of a constant for" nothing" into set theory, a model of consistency and most noticeable conclusions

Logique Et Analyse 56 (222):165-181 (2013)
Download Edit this record How to cite View on PhilPapers
The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class
(categorize this paper)
PhilPapers/Archive ID
Upload history
Archival date: 2013-12-24
View other versions
Added to PP index

Total views
256 ( #22,950 of 2,432,203 )

Recent downloads (6 months)
15 ( #40,426 of 2,432,203 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.