The Beginning ...

 I
magine that absolutely everything is removed from existence.
What is left which cannot be removed?

Nothing
and
the fact that there must be only One of them.

That is,
one 'state of nothing'. And this is precisely
two concepts: 1) nothing 2) one. But this makes
three concepts present in a state of nothing, i.e. 1) nothing, 2) one, 3) two.
And the presence of three things makes
four, i.e. 1) nothing, 2) one, 3) two, 4) three.
. . . and so on to infinity.

An infinite number of concepts are therefore forced out of nothing.

This introduces a principle of "Difference Congruency" (meaning: two concepts which cannot be separated by any logical mechanism whatsoever but which are nevertheless different -----like the front and back of a door). See Logic #3

 I dislike making up "new terms" which tend to confuse a subject. However, the above term and a few others are unavoidable.
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Zero ... (nothing, a quality)
cannot be divorced from
One ... (something, a quantity).
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'One' does not presuppose 'zero' or vice versa. They are discernibly different (there are two concepts) but they are also congruent, (neither is logically anterior or posterior to the other).

Thus, the bare concepts of quantity and quality cannot be removed from existence by any logical mechanism (without replacing them with more parts of which any hypothetical logical mechanism might be composed), i.e. the most basic division of existence is non-removable and constitutes it's "minimal set". The name of the set is "concept" and it contains two members (quantity, quality). Or ... the minimal folder is "concept" and it contains two files.

Then three,
Concept = [ quality, quantity, two ]
Then four,
Concept = [ quality, quantity, two, three ]
Then five,
Concept = [ quality, quantity, two, three, four ]
And so on,
Concept = [ quality, quantity, two, three, four, ... ]

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"For the generation of all things, one principle is sufficient" - Leibniz
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