Reason, Empiricism, Self-Reference

I just picked up Kant's "The Critique of Pure Reason". The blurb says, “This thory [sic] as an attempt to bridge the gap between rationalism and empiricism and, in particular, to counter the radical empiricism of David Hume." I suspect that in its 836 pages it will attempt to bridge the gap between reason and empiricism, a divide noted in "Philosophy in Minutes" as:

“Reacting against the rationalism of Descartes, Spinoza and Leibniz, British philosophers dismissed the idea that reason is our only reliable source of knowledge and developed the opposing movement known as empiricism. While not denying that reasoning is important to assessing information, the empiricists believed that the source of that information is the outside world, accessed through our senses.”

Certainly, it would be nice to be able to explain the value of the
fine-structure constant by reason and not by measurement. As Feynman observed:

“There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!"

See also,
Parameters of Nature, which asks the question:

“Can all fundamental dimensionless continuous parameters of Nature be calculated from theoretical principles, without any input from experiments?"

Consider these two self-referential statements:

    “This sentence is true"
    “This sentence is false"

These two sentences are axioms -- things declared true by fiat -- and axioms are the basis of reason, which is simply mechanical logical operations on true statements.

As an aside, we know that mechanical operations on self-referential systems can produce "infinite loops":

    “The next sentence is true"
    “This sentence is false"

Self-referential systems of this form are "undecidable".

But consider these two self-referential statements:

    “This sentence has five words"
    “This sentence has no words"

The truth or falsity of those statements cannot be ascertained except empirically.

Is Nature self-referential? I suspect that it is (cf. "
Searle's Chinese Room Argument". We are self-referential and we are part of Nature. But that raises the question if our self-reference is emergent or fundamental.) Does Nature make statements that can only be decided empirically? Does Nature even speak (i.e. make statements about itself)? That depends on your worldview...