So if you don't now, how can we test this proposition?
We test things by definition=objective math or extension of definition=applied math=objective+subjective math
Anything that is not true by tautological math definition is true by probability and possibility but not certainty
However, not even math can prove itself by Godell's Theorem leading to things like Ontological Mathematics and the God Formula
No one explores the ontology of the undefined terms behind the definitions of math in of themselves leading to the Paradox of Godell's Theorem
This is because intuition in of itself is the definition behind the undefined definitions in math, the only way to know aynthing which is certainty
Certainty is belief, which is how we know and reptition of representations of his belief to gain confidence. The most successful we have of representations of belief with repetitions of success leading to success is Physics and other and fields of testable science
Proving somethig means how does it repeat compared to what we already know repeats
The best we have is intuition, defined intuition=math, and applied math= which are all assumptions with some being useful but doesn't mean THE REPRESENTATION is true
Testable only because of measurements that can be verified by the operations of the system itself
But what verifies the intuitions behind the forms we see in math?
I bet you didn't know there is metamathemics just like there is metaphysics as well as metatheory which is systems of math. Look it up and read the interesting authors and their work on
the fields of metamethatics and metatheory
Without metamathematics and methatheory imaginary ideas like the imaginary number wouldn't be possible
What happens if there is a universe where the person doesn't BELIEVE in imaginary numbers, we wouldn't have close to the math we have today
Next step is defining 0/0 and other undefined math concepts
Once we reach the ontology of that level of mathematics, with metamathematics and metatheory being beyond math, we will get back to definition being a testable variable of imagination, intuition, and how we interact and perceive reality which is determined by our DNA
Once we go beyond math and science by reconciling into a tool to test reality in of itself, even counter-intutive reality, we can find new ways to represent the same thing and therefore test the same thing by reaching metamathematics and metatheory
Hint is Euler's Formula, imaginary numbers, photons, sound being the opposite of light (postulated and demosntrated) in an experiment
It' NOT a coincidence all of a sudden you have books like the God Series or the field of Ontological Mathematics that guarantees reality=math=causility leads to God and replications(its children and their evil twins).
The constant is causility=energy=consciousnes=intuition is always required along with imagination = memory, a representation of causility real or imagined.
Even Godell's Theorem shows even mathematical thinking in of itself requires a leap of faith = intuition+imagination+ a way of verifying or at least representing what is being intuited