Most animals are capable of thinking about things only in terms of their properties. For example, a dog can interact with the family members only 1 to 1; it is incapable of understanding the relations between the family members. It is amazing how much one can do with only such a limited cognitive capacity. Think for example of the organization of a pack of wolves. Each of the wolves only relates directly to the other members of the pack - it cannot understand that some other wolf A stands in a certain way relative to some other wolf B. The organization of the pack is strictly hierarchical, without a complex social structure, without the web of relations we can see in a society of monkeys for example.
Suppose you are a wolf and you are seeing a she-wolf with cubs. A human would understand her behavior because the human can understand the relation between the mother and her cubs. If you are a wolf, however, that isn't available to you. You would understand that she has certain properties - when she is pregnant she would behave in a certain way, when she just had the cubs she would behave differently (and the fact that she just had cubs can be perceived). So, you could relate to her even if you are incapable of understanding the concept of relation. You wouldn't be capable of understanding why she behaves like that, but you could figure out certain correlations between her properties and her behavior. For a wolf that is sufficient.
The monkeys are capable of understanding relations. For example one can observe that monkey A has a conflict with monkey B and that at a later time monkey A attacks monkey C. This happens because B and C are friends or are related to each other. A wolf or a dog or virtually any other animal would never do such a thing. They simply couldn't even conceive the logic of such action. The ability of understanding relations has very important social consequences, and the monkey societies are not just hierarchical. A monkey can understand not only the power relations between itself and other individuals, but also between other two individuals.
However, what's interesting is that monkeys are incapable of understanding that other monkeys - or other animals as well - have goals. Any dog or monkey or even an amoeba has goals. But it's quite a different thing from having goals and being capable of understanding what a goal is.
A goal involves a relation between three things. The animal A, uses thing B for achieving the goal C. Except two apes, the chimpanzee and the human, no animal is known to be capable of understanding such relations. For example it has been discovered that the ability of cracking nuts is part of chimpanzee's culture - some populations of chimpanzees have it, some don't. The know-how of nut cracking has been discovered by some chimp populations and it was transmitted from generation to generation.
How does this transmission process look like? The chimp mothers don't really teach their kids how to crack nuts. The kids pick up that knowledge from seeing others doing it. But they can learn this only because their brains can comprehend the idea of goal. The young chimp sees chimp A using a rock B to crack the nut C. A macaque monkey is incapable of learning this.
This ability of understanding others as goal-driven individuals, instead of just individuals that have certain properties or individuals bound by certain relations, has important social consequences and it is the ingredient that makes cumulative culture possible. We're not just learning stuff from others, but we are part of a giant cultural snowball that grows bigger and bigger. (Read article.)
Dealing with information
Another way of describing this transition from the cognitive abilities of animals like dogs to those like the ones we have is to say that most animals understand the world just in a causal manner, while we also comprehend the informational connections between things. Moreover, we are capable of creating information connections between things.
You can do a simple experiment with a dog: try to point to something in order to tell him to go there. The dog will just look at your finger. If you move your finger it will follow its motion. It is just incapable of understanding the idea that you're pointing at something. If you pretend to throw something to a certain location the dog might go looking for what it thinks you have thrown, but it will not understand you when you're just throwing information.
We find the idea of pointing at something so natural that it is difficult to understand how complex this process really is. In fact in the wild not even chimpanzees use pointing - although when you point to things they can do better than just to look at your finger. Chimpanzees use pointing in the wild when they want to indicate to some other chimp that they wish to be scratched in some hard to reach point, but they don't point to other objects or animals.
The ability of understanding informational relations depends on the ability of attributing goals to others because any information serves a certain purpose. If it wouldn't it wouldn't be information but just a causal relation. However, informational relations exist independent of whether there exists somebody capable of understanding informational relations. All the processes that make life possible are informational - the DNA stores certain information about how the life form must look like and behave, and this information is decoded by the chemical processes in the cell. Moreover, the blood carries not only the nutrients or the hemoglobin with oxygen, but also information in the form of hormones. And then of course there is the more modern informational highway - the nervous system. (Read more on information.)
What I want to point out is that there are animals that have goals, but that are incapable of attributing goals either to others or to themselves. A bird for instance has a set of quite complex goals: it gathers leaves and sprigs for the purpose of building a nest, and it builds a nest for the purpose of keeping its chicks safe. But it isn't capable of understanding goals. It understands a predator for instance because the predator has certain properties and the bird reacts in such and such a way to a thing that has those "predator" properties. A dog can have the purpose of finding you when you're playing hide-and-seek, but, amazingly, it cannot understand that you have the goal of hiding from it (see article).
So, one could only wonder: if a bird has goals but it isn't aware of than, what features do we have and we aren't aware that we have them? Is it really plausible that we are aware of all of our features?
What are limits good for?
We reach our cognitive limits about here: We can be aware that somebody A is working together with B using some tool C for achieving the common goal D. This relation between four items is called "shared intentionality" by Michael Tomasello. As you can notice, we don't even have a word in usual language for this type of relation. Nonetheless, it is quite important and it has plenty of consequences. (Tomasello and his colleagues describe some of them in this paper.)
This type of behavior can be observed even among monkeys. For example I have seen a particularly spectacular clip with a bunch of baboons throwing stones at a lion and driving it away. But a baboon cannot even understand the concept of goal, even less that of shared intentionality. Nonetheless, sometimes they are doing it.
When things get more complicated and we need to follow many items at once we are grouping them together based on some of their properties. For example, it would be literally impossible for the human brain to follow a football match if the teams wouldn't wear uniforms - thus making it easier for us to think the whole situation as "team A against team B". Researchers have discovered that we have serious difficulties in dealing with more than three groups of objects at once. (Read article.)
When we try to pin point these extra features of human behavior that we don't have the capacity to understand, we find ourselves in quite an obvious paradox. It's tempting to say it's just impossible and dismiss the entire question. By "understanding" it is meant the ability to answer the "why?" question. The bird for instance might be able to deal with its predators but it cannot really understand why a predator acts like it does. The bird can just use certain correlations between the predator's properties and its actions, but to answer the "why?" question it would have to understand that the predator has certain goals. And the bird is just incapable of doing that.
Similarly, we might be able to describe the correlation between people's goals and their actions and yet still not fully understand why they act the way they do. It's pretty plausible that there might be something additional beyond this three-fold relation between individual, goal and means.
The reason why this is indeed plausible is that human cognition, like animal cognition in general, has been devised by natural selection and natural selection doesn't waste resources. It gives something to an animal only if that something is really necessary for its ability to act. Otherwise it is a waste of energy and a wasteful animal cannot win the competition against an efficient one. In other words, natural selection doesn't care whether or not we understand the world or ourselves; it just cares whether or not we can cope with the world efficiently. The ability to understand is often useful but not always. This is why from the natural selection perspective only the knowledge of correlations has to be implemented, not the ability to answer the "why?" questions. (However, the world we live in today is pretty different from the one natural selection has designed us for.)
The evolving cognition
But of course, although the knowledge of mere correlations might be good enough for natural selection it isn't really good enough for us and our curiosity. So, how could one go beyond the natural abilities? How can we evolve our psychology more?
There are two issues here: 1) What are the behavioral features that we have but we don't realize we have? 2) What are the mental features that we think we have but we don't actually have?
To give you an example from the second category: We all think that we are conscious and we feel that, unless we are asleep (or under the influence of various drugs), this consciousness is continuous. We also have the impression that there is a certain well defined "subject" that is experiencing all the stuff that happens - this is that famous unity of consciousness. However, if you take a watch and try to actually be aware of yourself, e.g. of your body or of your name or whatever, for as long as you can, you will find that after around two minutes at best you will lose it. That is about the length of your continuous consciousness, the duration of your unity of consciousness - when you strive for it. This is a quantitative description for about how much consciousness we have.
The reason why we have the illusion of a continuous consciousness is that we simply don't remember the unconscious moments. This is a major difficulty in studying consciousness - one has to determine how much of what we think is there really is there. Sometimes people desire explanations for various things that aren't really there, such as the unity of consciousness, and because, of course, the explanations cannot be found they start speaking about the "deep mystery" of consciousness. So, the issue sometimes is not that of explaining certain features that our minds have, but of actually acquiring those features (because we don't have them).
The first question concerns a largely uncharted territory. But we can obtain some clues. We can observe how animals go from understanding causality to understanding coincidence to understanding intentions and then try to extrapolate the process further.
The classic view on the difference between coincidence and causality comes from David Hume. He thought that coincidence is more fundamental than causality and wondered about the extra ingredient one needs to add to a correlation between two events so that the correlation wouldn't be just a mere coincidence but a causal relation. His view however was deeply flawed. In fact, we understand coincidence as a failure of causality and not causality as coincidence plus some extra ingredient. Hume though that we understand causality because we see the same chain of events happening again and again, and then we infer they always happen that way (i.e. we come up with the idea of causality). In fact however the ability to understand causality is innate and doesn't involve repetition. It is this way not only in humans but also in monkeys and even rats.
For example, babies 27 weeks old understand the causal relation that exists between a block that hits another block, although they haven't ever seen such an event before.
Marc Hauser and Bailey Spaulding from Harvard tested rhesus monkeys ability to understand causality by showing them successive images of absurd and plausible scenarios. For example they showed to a monkey an apple, a knife and then the apple in two pieces. Or an apple, a glass of water, and then the apple in two pieces. The monkeys were clearly baffled by a scenario of the second type. This meant that they understand causality instinctively, because rhesus monkeys have no knowledge of tools and haven't seen such scenarios repeated over and over again. (Read more about this experiment.)
One of the most interesting experiments concerning causality and coincidence was conducted by Anthony Dickinson from Cambridge. He experimented with rats. The rats had to find food each time they heard a sound (like the dogs in Pavlov's experiments). But then a change was introduced: sometimes the sound was produced by the rats themselves pushing a button. Would they still go searching for food? They didn't. (Read more abut this experiment.)
Dickinson interprets his experiment in Hume's key and he thinks that the amazing thing is that rats understand causality. I think that what's amazing is that the rats understand coincidence.
But unlike animals like rats we go beyond the distinction between causality and coincidence. We also have intentionality. The purposeful behavior is neither causal nor coincidental - one follows a certain goal as a choice, which is neither determined nor random. We infer the presence of intentionality when, first, cannot figure out a causal chain of events but also, second, cannot believe this is just a coincidence. When these two things happen we decide there must be some purpose involved.
Of course, sometimes we are just wrong and people have a long history of attributing intentionality to causal chains of events they couldn't understand. To a large extent the development of science involved cleaning out nature of wrongfully assumed purposes - thunder became a causal phenomenon and not the wrath of gods and so on. Some thought that we will eventually find out that no coincidence and purpose really exist. Fortunately, this was just an exaggeration and a mistaken extrapolation - real coincidences (events that happen without a cause) as well as intentions (goal-driven behaviors) do exist.
What I wonder is whether we cannot go even further and find some behaviors that are clearly not the result of a chain of causes, however they are not mere coincidences, but which still are not goal-driven either. I believe such still "higher" kinds of behaviors do exist. Not everything people do is to be pushed around by stimuli, roll dices and follow goals. There is more.
The most obvious candidate for such a behavior is art. It is neither causal (except for realism - "we have to depict how society..."), nor accidental (except for dada - "take a newspaper article, a scissor..."), nor intentional (except for propaganda or for profit-seeking art). It seems to me there is something in artistic behavior that cannot be accounted for by using any of the current models of human cognition. In the same time it seems to me that we don't really know how to use art so we could get its full potential.
The paradox of art
I obviously have no definite answer to any of these issues but I want to point out a nice paradox that offers a good suggestion to what art is (or could be if done properly). Suppose you want to describe yourself in a way others can understand. But there's a paradox: you are what makes you different, what makes you unique, but on the other hand communication is based on what we share. So how could you use what we have in common to express what makes you unique?
As far as I can tell, art is the solution to this paradox. It's obvious that you cannot express what makes you unique via what we have in common, so don't even try. How about a deliberate lie? How about a lie that we all know it's a lie, that isn't designed to mislead but to reveal? Maybe even to reveal something about you, something you couldn't express in any other way.
The point is this: When you tell the truth you have only (approximately) one option. But when you lie you have innumerate possible avenues at your disposal. So, when I see that somebody has told a particular lie, I ask myself why is it that he or she has chosen just that lie? Why not something else? Such an inquiry is based on what I call the "authenticity of lying". If one knows you have lied, one can use this knowledge to find out something about you. And one can try to use this indirect path for revealing something about oneself, something that cannot be revealed in any other way due to the paradox I have just mentioned.
Sometimes we lie because we want to achieve something. If we are caught our more or less secret aims are revealed. But that's the trivial case. The interesting case is when we lie just for the sake of it, without any profit. And, according to research, we're doing it all the time. I think that we're lying in such cases and so often precisely because, unconsciously, we want to offer others the possibility to peak into our "true souls" - and this is the only way this is possible. Moreover, I think that art is the institution of such authentic lies, it is an endeavor that takes this path in a more conscious way.