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Written 08/30/26

Published 08/30/26

∀x, x ∈ 𝒱

For all x, x belongs to the universe of sets.

y(X) = Hom𝒞(−, X)

For any object X, X can be represented by all the ways other objects relate to X.

∀x ∈ 𝓜, x : Thing

For all mathematical objects x, x is a Thing.

There exists sufficient consensus among observers for (x) to admit a common reference. Namely, “x”.

There exists some observation, experience, or representation through which (x) is accessible/operable. Namely, “x”.

There exists some set of possible states under which (x) may be observed or represented.

There exists sufficient continuity across these states for them to be identified as expressions of a unified object (x).

Together, these conditions are conditionally sufficient to warrant the notation

x : Thing

The above statement is not yet axiomatically defined, however it does not appear to be incorrect. The pertinent inquiry is: why?