Tautological Recursion

The first few layers of an infinite geometric sequence of self-negation in Menger’s Sponge – this object (under full expansion/compression) has infinite surface area and zero volume.

Bertrand Russell once remarked that all of mathematics consists of tautologies. In this sense, we are considering as logically foundational a vast, complex panoply of equivalences, equations, symmetries and relationships asserting unproblematic definitions, references, ontologies. It may be true that from within any system of reference, any conceptual schema whatsoever only acquires and maintains aspirational consistency as a function of relatively arbitrary equivalences; all definitions being made in terms of other definitions and thus leading us indirectly, circularly back to finding ourselves inhabiting the interior surface of a vast and hyper-inflating tautological referential space. If Gödel’s work on incompleteness has any lasting consequences in such a self-enclosed referential cartography, it is that the metaphysical “beyond” is indistinguishable from the discontinuous within and that, right there, is a tautology of non-trivial existential and cosmological consequence.

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