“Primary relations” in a new foundational axiomatic framework

Journal of Philosophical Logic 36 (6):641 - 657 (2007)
Abstract
The new system of axioms we propose is based on the foundational theory of De Giorgi et al. Scuola Normale Superiore di Pisa, Preprints di Matematica 26: 1 (1996) slightly modified. In that paper (which is dedicated to a new axiomatic framework for mathematics, informatics and logic) the authors use two kinds of primitive notions: relations and qualities. Since their system is based on the distribution paradigm, they start from distinction. We propose to shift the perspective and to start from unity and then from within unity to pass to distinction; to this end we apply ideas of Lesniewski, Nijhoff International Philosophy Series 44 (1992). We introduce only one kind of entity as a primitive notion, namely relations, and treat qualities as articulations of relations. The new concept of "primary relation" permits the introduction of a dynamic, non-standard form of identity, which we hope will find application in various fields where self-referential structures are required
Keywords distribution paradigm  dynamic oneness  primary relations
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