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Higher Values and Non‐Archimedean Additivity
Author(s) -
CARLSON ERIK
Publication year - 2007
Publication title -
theoria
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 16
eISSN - 1755-2567
pISSN - 0040-5825
DOI - 10.1111/j.1755-2567.2007.tb01185.x
Subject(s) - additive function , simple (philosophy) , mathematics , value (mathematics) , real number , additive model , pure mathematics , statistics , discrete mathematics , mathematical analysis , epistemology , philosophy
Many philosophers have claimed that extensive or additive measurement is incompatiblewith the existence of “higher values”, any amount of which is better than any amount of some other value. In this paper, it is shown that higher values can be incorporated in a non‐standard model of extensive measurement, with values represented by sets of ordered pairs of real numbers, rather than by single reals. The suggested model is mathematically fairly simple, and it applies to structures including negative as well as positive values.