meaning - How does 'if not' mean 'perhaps even'?

I already understand, and so ask NOT about, the definition, but instead want to dig deeper:

if not = Perhaps even (used to introduce a more extreme term than one first mentioned)

How does (the juxtaposition of) if + not combine to mean the above,
which neither word alone means?

Answer

^†This is where logic or mathematics operates differently from human language (aka natural language). Strictly speaking and mathematically speaking,

1. "N is Y, if not Z" would be read as
2. "if N is not Z, then N is Y".

However, in many human languages, English included, saying 1 doesn't mean just 2. To understand this, we should think a little about the motive of a speaker who said 1.
Quite likely, the speaker's intention was

3. "If N is not so great as Z (or any quantity > Y), it is = Y"^‡.

But to say 3 exactly in those words would be clumsy,
and thus the speaker would naturally rephrase 3 as:

4. "N = Y if N ≠ Z",
or in plain English: 5. "N is Y, if not Z".

---

We can try another approach to show that if not can be used to mean perhaps even.

Let N is the number of people who has an attribute Q.
Consider these two following propositions:

(a) N is Y, if not Z.^†
(b) N is Y, perhaps even Z.

Let N_a is the set of all possible values of N for proposition (a).
It is easy to see that N_a = {Y, Y+1, Y+2, Y+3, ..., Z}.

Let N_b is the set of all possible values of N for proposition (b).
It is also easy to see that N_b = {Y, Y+1, Y+2, Y+3, ..., Z}.

Now, it is clear that N_a and N_b are equal. Hence, (a) and (b) are equivalent.
Thus, if not can be used to mean perhaps even.
Q.E.D.