We can sense Perceptions (physical world), intuitions (not open to introspection) and reason (open to introspection)

1 – Physical (Senses)

2 – Intuitionistic (Emotions and Intuitions)

3 – Intellectual (reason)

Reality consists of the following actionable and conceivable dimensions:

1 – point, (identity, or correspondence)

2 – line (unit, quantity, set, or scale defined by relation between points)

3 – area (defined by constant relations)

4 – geometry (existence, defied by existentially possible spatial relations)

5 – change (time (memory), defined by state relations)

6 – pure, constant, relations. (forces (ideas))

7 – externality (lie groups etc) (external consequences of constant relations)

7 – reality (or totality) (full causal density)

We can speak in descriptions including (at least):

1 – operational (true) names

2 – mathematics (ratios)

3 – logic (sets)

4 – physics (operations)

5 – Law (reciprocity)

6 – History (memory)

7 – Literature (allegory (possible))

8 – Literature of pure relations ( impossible )

8a – Mythology (supernormal allegory)

8b – Moral Literature (philosophy – super rational allegory)

8c – Pseudoscientific Literature (super-scientific / pseudoscience literature)

8c – Religious Literature (conflationary super natural allegory)

8d – Occult Literature (post -rational experiential allegory )

We can testify to the truth of our speech only when we have performed due diligence to remove:

1 – ignorance,

2 – error,

3 – bias,

4 – wishful thinking,

5 – suggestion,

6 – obscurantism,

7 – fictionalism, and

8 – deceit.

So of the tests:

1 – categorical consistency (equivalent of point)

2 – internal consistency (equivalent of line)

3 – external correspondence (equivalent shape/object)

4 – operational possibility (what you just described) (equivalent of change [operations])

6 – limits, parsimony, and full accounting. (equivalent of proof)

Those operations existed or can exist.

You can imagine a something with the properties of a unicorn, you can speak of the same, draw the same, sculpt the same … but until you can breed one (and even then we must question), and we can test it, the unicorn does not exist ***in any condition that we can test in all dimensions necessary for you to testify it exists***

This is just one of the differences between TRUTH (dimensional consistency (constant relations)), and some subset of the properties of reality (DIMENSIONAL CONSISTENCY).

Mathematics allows us to describe constant relations between constant categories (correspondence) by means of self-reference we call ‘ratios’ to some constant unit (one). The more deterministic (constant) the relations the more descriptive mathematics, the higher causal density that influences changes in state, the more information and calculation is necessary for the description of candidate consequences, and eventually we must move from the description of end states to the description of intermediary states that because of causal density place limits on the ranges of possible end states.

In other words, in oder to construct theories (descriptions) of general rules of constant relations, we SUBTRACT properties of reality from our descriptions until we include nothing but identity(category), quantity, and ratio, and constrain ourselves to operations that maintain the ratios between the subject (identity).

Mathematics has evolved but retained (since the greeks at least) the ‘magical’ (fictional, supernormal fiction, we call platonism) as a means of obscuring a mathematician’s lack of understanding of just why ‘this magic works’. When in reality, mathematics is trivially simple, because it rests on nothing more than correspondence (identity), quantity, ratio, and operations that maintain those ratios, and incrementally adding or removing dimensions, to describe relations across the spectrum between points(identities, objects, categories) and pure relations at scales we do not yet possess the instrumentation or memory or ability to calculate at such vast scales – except through intermediary phenomenon.

As such, operationally speaking, the discipline of mathematics consists (Truthfully) of the science (theories of), general rules of constant relations at scale independence, in arbitrarily selected dimensions. In other words. Mathematics consists of the study of measurement.

it is understandable why we do not grasp the first principles of the universe – they are unobservable directly except at great cost. It is not understandable why we do not grasp the first principles of mathematics: because measurement is a very simple thing, and dimensions are very simple things.

That mathematicians still speak in fictional language, just as do theists and just as do the majority of philosophers (pseudo science, pseudo-rationalism, pseudo-mythology)

Ergo, infinities are a fictionalism. Multiple infinities are a fictionalism. Both fictionalism describe conditions where time and actions (operations) have been removed as is common in the discipline of measurement (mathematics). Operationally, numbers (operationally constructed positional names, must be existentially produced as are changes in gears. And as such certain sets of numbers (outputs) are produced faster (like seconds or minutes vs hours) than other sets of numbers (outputs).