"It depends on what the meaning of is is." - Bill Clinton

If we say "a = b and b = a" - what does that mean? Can we build a reliable comprehensive system based on those concepts - when it might not be clear 1) what "a" and "b" actually are, and 2) what it means to say they are equal.

We know it works - but we don't really know why. Asking this question is just another open thread for exploration as the moment emerges, and the energy to approach this topic carefully has begun to coalesce.

Mon, May 10, 2021

In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems.

An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication.

A formal proof is a complete rendition of a mathematical proof within a formal system.

https://en.wikipedia.org/wiki/Axiomatic_system

Other major Wikipedia references

https://en.wikipedia.org/wiki/Conceptions_of_God

Conceptions of God in monotheist, pantheist, and panentheist religions – or of the supreme deity in henotheistic religions – can extend to various levels of abstraction:

as a powerful, human-like, supernatural being, or as the deification of an esoteric, mystical or philosophical entity or category; as the "Ultimate", the summum bonum, the "Absolute Infinite", the "Transcendent", or Existence or Being itself; as the ground of being, the monistic substrate, that which we cannot understand; and so on. The first recordings that survive of monotheistic conceptions of God, borne out of henotheism and (mostly in Eastern religions) monism, are from the Hellenistic period. Of the many objects and entities that religions and other belief systems across the ages have labeled as divine, the one criterion they share is their acknowledgment as divine by a group or groups of human beings.

https://en.wikipedia.org/wiki/Conceptions_of_God