Matrix representation of Husserl's part-whole-foundation theory.
1990; Duke University Press; Volume: 32; Issue: 1 Linguagem: Inglês
10.1305/ndjfl/1093635670
ISSN1939-0726
AutoresRichard Blecksmith, Gilbert T. Null,
Tópico(s)Psychotherapy Techniques and Applications
ResumoThis paper pursues two aims, a general one and a more specific one.The general aim is to introduce and illustrate the use of Boolean matrices in representing the logical properties of one-and (mainly) two-place predicates over small finite universes, and hence of providing matrix characterizations of finite models for sets of axioms containing such predicates.This method is treated only to the extent required to pursue the more specific aim, which is to consider axiomatic systems involving the part-whole relation together with a relation of foundation employed by Husserl. / Husserl structuresWe present an axiom system which is a first-order formalization of the theory of part-whole-foundation relations suggested by Husserl ([11], [12]: Third Investigation).Our axiom system employs two primitive predicates '<' and 'ϊ' which denote the part and foundation relations.Subsequent to HusserΓs own work, the part, but not the foundation relation, was studied independently by Stanislaw Lesniewski ([16]; [17]; [18]; [19]) and his student Alfred Tarski ([28], pp.24-29; [29], pp.161-172), and later by Henry Leonard and Nelson Goodman ([14]; [15]; [7]; [8]).Quine has also contributed to this development [24], and the whole topic has been studied extensively by Rolf Eberle [5].Several part-whole concepts developed within the Lesniewski-Tarski-Leonard-Goodman tradition 1 are involved in the present study.*We would like to thank Dr. Curtis Herink, Department of Mathematics, Mercer University, Macon, Georgia, for help in coming up with Example 2 and Axioms A12, A13, and A14.Thanks to Robert McFadden
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