The faces were taken merely as an example in which we can focus on the “whole thing”, and then focus on some part of the face. I could’ve discussed a complicated texture and focusing attention on some part of the texture, seeing a piece of furniture and focusing attention on some specific thing about the furniture, or, which is closer to the case of math, seeing a bunch of ants and focusing attention on individual ant.

On the point that we have innate abilities, I fully agree. Abilities to focus on wholes or their parts, or focus attention to multitudes or to individuals which are part of those multitudes, to recognize different kinds of things (like faces), to recognize what other people look at, to track things which go behind other things, and so on…

Let me connect to what you say, and mention one issue I thought to also discuss in the post, but decided for the sake of shortness and clarity not to.
Namely, I mentioned that one can attend to the whole as a pair (and in that case we would have the right side of the 1+1=2 equation, i.e. ‘2′), but also that there are two separate ways to attend to the parts. One can attend to p, where p is “the one”, and q is “the other one”; and also one can attend to q, where q is “the one”, and p is “the other one”.
Now in concrete situation it is true that there is lot of determinations for p and q, e.g. p is to the left of q, q is to the left of p, p is bigger (e.g. apple), q is older (person), and so on.
However in the case of 1+1, we do abstract from this possibility for other determinations, and in such attending the two ones are not determined in any other way except by “being another to each-other”. In such abstract equality it is same for our spontaneous decision which we would take as “the one”, and which would be “the other”. So, abstracting from other determinations, there is a symmetry in which they are reduced to same abstractions from the pair.
While this might not very interesting in the case of 1+1, in the case of 2+1=3, there are few ways (3 to more exact) to attend to the whole, and which might be described by 2+1. However because of the abstract symmetry of the ones among each other, they are all covered by the formalism – 2+1.
One other thing to point to, is that when we attend to “the one” of the whole and thus abstract from “what is left (a pair)”, we can also attend to “the other (pair)” and abstract from “the one”. In that way we have symmetry 3=2+1=1+2.

This might be a bit off topic, but I’m fascinated by your comments on gestalt and its relation to the a priori. So, I hope these comments help and not hinder your thoughts on the matter.

I bet there is an alternative – one could read that word as ‘odd’ – a priori interpretation of the two objects. The alternative rendering could show that there are actually 4 (or possibly more) objects.

Let’s call one object p and the other object q. p is one object, and q is another object. Together, they are two objects.

But there is also a third object. That is, there is an object composed of p, q, and the two objects p and q.

Also, there might be a fourth object. Suppose that p is to the left of q. That means there is “p is to the left of q”, “q is to the right of p”, p, and q. Thus, there is a fourth object.

Based upon that there might be a fifth object. The fifth object is composed of “p is to the left of q”, “q is to the right of p”, p, q, and “p and q.” Thus, there is a fifth object.

You’re on to something here when you say that 1+1=2 is not analytic in the way we might say that “all bachelors are unmarried males” is analytic.

(I’m pretty sure that Hilary Putnam has an example like this in his work, but I can’t remember where it’s located. I remember it as him talking about 3 marbles in a bag and asking how many objects were in the bag. He suggested 7, which is based on a similar analysis as the one I offered above about p and q.)