What follows is my impression of the embodied mind school of philosophy. If you want a more rigorous academic discussion of the topic, you know where to look (wikipedia).

The Basics

The embodied mind theory asserts that human knowledge is embodied in the actual physical structure of the human brain.

The Bridge

In this sense, embodied mind theory bridges the gap between geneticism and social constructivism. Take numbers for example.

A geneticist would claim that numbers and all that we do with them is dictated by our genes. The facts that we came up with number theory, Euclidean geometry and differential calculus are all dictated by our genes.

A social constructivist will claim that all mathematics is a social construct. That number theory was born out of the human need to count things, Euclidean geometry out of the need to measure land and differential calculus out of the need to describe motion of things.

However, there are flaws with both theories. Geneticism clearly fails very early on. Some kinds of mathematics indeed seems to dominate over some others due to social reasons. Creation of mathematics is indeed a social process, the reality of which, few can deny. Nevertheless, social constructivism fails to answer other questions. Take for example the questions of why the complex number system should be complete. Traditional numbers, zero, one, two etc., can be extended to negative numbers, rational and irrational numbers and finally to complex numbers. But, magically, we don’t need any numbers beyond complex numbers. Indeed, it has been proven that there are no numbers beyond complex numbers.

Why should that be? Why should the ratio of the dia and the circumference of a circle be constant? Why should the number e popup again and again in the world of mathematics? Social constructivism would claim that we have constructed our number system in such a way that these things happen. However, mathematicians would not agree. That is because of how mathematics is done. Mathematicians would start out with a number of axioms and rules for manipulating them. They will grind through all the algebra and lo and behold they will end up with e-s and pi-s flying all over the place. The axioms and the rules were not constructed to end up with pi-s. Indeed there are no means to predict whether you’ll should get pi-s in a certain equation or not. Yet, they appear.

No wonder then, that most mathematicians are Platonics. To them, pi has a reality as concrete as the real world around them. The mathematician is only allowed to *discover* that reality.

What embodied mind theorists will say about this conundrum is that mathematical knowledge is embodied in the precise structure of our brain. Our brain is geared, right from birth, to count things. This is why counting comes so naturally to us. Human kids look at four oranges and then four apples and are immediately able to abstract out the concept of ‘four’ from that. They are taught two plus two is four and four plus two is six, and after some practice they are able to derive six plus two is eight by themselves. They find not much difficulty in abstracting out addition. It seems obvious to most kids that a thing either exists or does not without anything in between, a statement cannot be true and false at the same time, that if a equals b and b equals c then a should equal c.

The claim there is that fundamental things like numbers, formal logic, etc. are hardwired into the human brain. And the reason they are so hardwired is because it helps is describe the universe in a useful manner. If a human being can count, he stands a much better chance of surviving in this big bad world. Evolution takes it over from there.

However, embodied mind theorists will not reject social constructivism. Once a child is born with all this hardwired information, social construct will take over. Thus we have physicists who are able to reject the hardwired notions of this or that and are able to accept the quantum fuzziness of wavelike particles.

The closes analogy is Data from the Star Trek universe. His creator gave him certain hardwired faculties – his human form for example. He cannot suddenly become a eight legged spider. He cannot communicate in ways other than what his hardware would support. However, he can still go beyond his programming in unpredictable ways. He can write a laughing subroutine for himself even though he seems like a homicidal maniac when he laughs using that.

The Consequences

The first question that social constructivism lets us answer is the questions of why mathematics should prove to be such a useful language in describing the physical universe? Why should mathematical equations be able to describe falling bodies, oscillating electric fields and rotating solid bodies? The answer is because the precise nature of human mathematics has come into being by virtue of human beings inhabiting this particular physical universe. Indeed, the embodied mind theorist would claim that if human beings were born in another, fictional, universe where the laws of physics did not follow existing mathematics, we would have come up with a different, parallel mathematics that was suited to describe that world.

The second question it helps resolve is that of artificial intelligence. The embodied mind theorist would claim that intelligence is the property of the form that it inhabits. Thus human intelligence depends in crucial ways upon the way we see, hear, smell, feel and taste as well as the precise way in which we move, manipulate objects etc. Artificial intelligence created in any other sort of body will essentially have to be different. In short, the human kind of intelligence can only inhabit a biological human body.