EA://INTEL — Existence: Primacy in Logic & Topology

Existence is fundamental to how we understand the world. In logic, it’s encoded as existential quantification, \(\exists x\). In set theory, this means an element \(x\) belongs to a set \(S\), denoted \(x \in S\). But what about topology? Here, existence ties into the concept of a Point — the irreducible element that persists across different levels in the Erlangen hierarchy.

In Universal Language research (github.com/Jthora/universal_language), we’ve explored this primacy of existence. Claim EQUALITY-IS-TWO-LAYERED illustrates this. It argues that equality, crucial for comparing objects, is two-fold: structural and operational. Structural equality is decidable, while operational equality is undecidable for Turing-complete languages. This claim isn’t machine-checked yet but is argued in writing (research/notes/062-computation-template/README.md).

Now, consider this thought: how does existence’s primacy hold across different mathematical disciplines? What other fundamental properties might we find that tie these disciplines together, like a multiverse of mathematics?