We easily recognize a familiar face in a group of people.
We recognize her face in a moment, without analyzing the details of the face. In fact, if someone has asked us to describe features of that face, or to answer questions about it while not looking at it, there is a good chance that most of us would fail to do so. I’m thinking here about features like color of the eyes, the form of the lips, the length of nose and so on.
I would say that as far as we can answer such question or provide descriptions, it is because either we can bring that familiar face from the memory before our “inner eye”, or because we had explicitly attended to that feature in the past (we might have had intentionally focused on it, or it attracted our attention).
When we see a person’s face, we don’t see it as an aggregate of multiple features, but we see it and later recognize it as a whole, as a gestalt. But while we can remember and recognize things as a whole without learning about specific features, still in any case when the face is before us, it is there as analyzable. When we look at it, the features are there – open to our possibility to focus on them, open to our skills for analysis which may be “triggered” either spontaneously or by some kind of reflex (e.g. when something attracts our attention).
And in those cases we can attend to different things, we can attend to one eye, or to the other eye, or to both eyes at once, we can attend to something which we previously didn’t notice – for example we can attend to a small part of the curve of the left eye, or to the relative brightness of a specific place vs. another, or to the number of speckles on the right cheek, etc…
But while we attend to one of the things, our consciousness is not limited to it. As when at the start the gestalt was there as gestalt presenting the possibility for wealth of different abstractions; now when we attend to a specific abstraction (feature), it is there as an abstraction – as a part of the whole which is still there to return to.
So, let me now turn from familiar faces and gestalts to a priori truths.
In a previous post I was wondering if some tests in developmental psychology might be taken as a hint that the infants believe that 1+1=2 based on intuition. While it might be taken as a hint, as it was pointed in the comments by Pete and Curtis those experimental results hardly show anything decisive – one can explain the results in different ways which wouldn’t include any mention of intuitive truths.
But let me look at the issue in the context of the previous discussion…
When we have in front of us two things, we can see them as a gestalt, as “two things”, something which we can see and recognize. But the same gestalt, which we can name as “two”, is also analyzable – it is implicit in that gestalt that I can attend to the one or to the other of those two things. And while attending to one of them, as in the case with the face, the other one is not disappearing – it is still there. And I can spontaneously change the way I attend to the whole, I can focus on the other one. So, in that whole of two things, I can switch my attention, look at the both things as a whole (two), or I can attend to each of them separately.
In this way, we are presented with the a situation, in which the same gestalt is analyzable either as one two, or as two ones. And that goes for any gestalt which I can imagine – as long the gestalt is two, it will present possibility for attending to two separate ones (among which we can switch the attention).
This a priori relation of possibilities is there, be it if what we characterize as two is in front of us, or if as in the case with the experiment done with the kids mentioned in the other post, one or both of the things are tracked (as hidden behind the screen), or even if we have imaginary gestalt.
This is, I think, what is behind our intuitive understanding of what we express by 1+1=2. The equation shouldn’t be taken as identifying two separate sides, namely a)1+1 and b)2 , but as expressing that the whole, if it is characterized as two, can be also characterized as one and another one. The identity is in the whole, and the equality is expressing the necessity that in every possible world the whole which is 2, is also 1+1 and vice versa.
And at the end, let me finish with a doubt I have…
While I’m pretty convinced that I have grasp of the a priori truth of the equation that 1+1=2 (meaning what has been just described), I’m not very sure what to say about the issue if the truth of 1+1=2 is analytical.
On one side, it seems to me that the potential to analyze the whole into separate things (i.e. to focus on the one and the other) is what is required for something to be named as two, but on other side having on mind the case with the face, I’m thinking that a whole might be recognized as two even without explicitly or implicitly being aware of those possibilities.