Fundamental mathematical theories. (English) Zbl 0863.03005

Temple, George

Philos. Trans. R. Soc. Lond., Ser. A 354, No. 1714, 1941-1967 (1996).

In this posthumously published paper, G. Temple sketches a new attempt to found mathematics based on a symmetric relation between pairs of terms or objects. The basic objects are “taxa” (instead of sets) characterized by their mutual relations of association and dissociation, and forming “taxonomic systems”. The author discusses taxonomic algebra, gives hints for a generalization of the concept of a neighbourhood, compares taxonomic systems with set theory, discusses basic problems of propositional logic in terms of taxonomic theory, relates taxonomic theory to abstract arithmetic and to type theory. The paper is accompanied by a note by Martin Hyland.

Reviewer: V.Peckhaus (Erlangen)

MSC:

03A05	Philosophical and critical aspects of logic and foundations
00A30	Philosophy of mathematics
03B30	Foundations of classical theories (including reverse mathematics)

Keywords:

foundations of mathematics; symmetric relation between pairs of terms or objects; taxonomic algebra; neighbourhood; taxonomic systems; set theory; propositional logic; abstract arithmetic; type theory