According to Lowenheim-Skolem theorem, we also have nonstandard universes of nonstandard numbers. These universes are transcendental with regards to the standard one.
Now let's look at a particular pattern visible in the standard natural numbers, i.e. Goodstein's theorem:
It is impossible to prove this pattern from anything in the standard universe:Wikipedia on "Goodstein's theorem" wrote: In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0.
However, Goodstein's theorem is still perfectly provable. Below an informal explanation of how the proof works:Wikipedia on "Goodstein's theorem" wrote: Kirby and Paris[1] showed that it is unprovable in Peano arithmetic.
Hence, the only way to explain this pattern visible in the standard universe is from logic action that originates in a transcendental universe.Mark Kim Mulgrew explaining the proof wrote: Admittedly, it is still not very clear how we would go about creating a strictly decreasing sequence that bounds the Goodstein sequence from above. Surely, we would need a sequence of very large numbers to do this. In fact, wouldn't a sequence of "decreasing infinities" (whatever that means) do the job? "Infinities" would of course be larger than any natural number, and then we might hope to be able to generalize the well-ordering principle to these "infinities" to conclude that the "decreasing sequence of infinities" terminates to zero.
We need transfinite ordinals in a nonstandard transcendental universe for this.
Hence, the transcendental universe controls the standard universe.
Is this an uncommon way of thinking?
No, it isn't.
In religion, it is even standard doctrine to believe that the transcendental controls the physical.