Laws of logic in action as glorified common-sense first principles of right reason

Clearly, such an A is part of the world W, and is distinct from the rest, ~A:

W = {A|~A}  . . . Law of [Distinct] Identity, LOI.

Now, ponder some x in W, i/l/o the partition shown by the pipe character:

No x in W can be A AND ~A, Law of Non-Contradiction [LNC].

Any x in W is A X-OR ~A, Law of the Excluded Middle [LEM].

LOI, being fundamental, needs to be expanded:

A is itself i/l/o its core characteristics (that give it distinction from whatever is ~A).

So, too, if two candidate entities x and y have no critical distinguishing characteristics, they are the same entity. The evening and the morning star are the same entity as the planet Venus. Likewise A distinct from ~A shows how two-ness is framework to any possible world, brings with it the system of numbers thus operations on them and so also the core of Mathematics. Mathematics in key part is at the core of reality. An inherently abstract system.

We must use distinct identity just to string symbols together to communicate, to think and to do Mathematics or Science. For example, as the Apostle Paul long since noted in writing to the Corinthians:

1 Cor 14:7 If even inanimate musical instruments, such as the flute or the harp, do not give distinct notes, how will anyone [listening] know or understand what is played? 8 And if the war bugle gives an uncertain (indistinct) call, who will prepare for battle?
9 Just so it is with you; if you in the [unknown] tongue speak words that are not intelligible, how will anyone understand what you are saying? For you will be talking into empty space!
10 There are, I suppose, all these many [to us unknown] tongues in the world [somewhere], and none is destitute of [its own power of] expression and meaning. 11 But if I do not know the force and significance of the speech (language), I shall seem to be a foreigner to the one who speaks [to me], and the speaker who addresses [me] will seem a foreigner to me. [AMP]

Language is key to rational intelligence, and is a key sign of it. Which of course points to the significance of the DNA code.

No wonder, Crick observed in a letter to his son Michael on March 19th 1953 written to explain the discovery of the DNA double-helix:

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