Overview
The natural part of the IFF consists of an infinite number of levels: ‘obj’ = ‘0’, ‘sml’ = ‘1’, ‘lrg’ = ‘2’, ‘vlrg’ = ‘3’, … n, …. It is partitioned into two aspects, pure and applied. In the pure aspect, the finite metalevels are populated by generic and parametric meta-ontologies. Generic means that the terminology and axiomatization for any two metalevels is identical. Parametric means that the metalevel index is a parameter. Hence, only one copy of a meta-ontology with a level parameter is needed for all finite levels. The pure aspect is partitioned into a core component and a structure component. The natural part includes meta-ontologies for both set theory and category theory, with set theory in the core component and category theory in the structural component. The single meta-ontology in the core component is the very large-sized generic IFF set theory meta-ontology (IFF-SET). This incorporates the specialization of the ‘meta’ namespace (IFF-META) in the metashell.