Since my contention going forward is that everything that can be considered Justified Trusted Knowledge is just Mathematics and Stories, I feel it is important to clarify what Mathematics is. So, let me bring back a man we have already met before - Professor George Lakoff, this time along with Professor Rafael E. Nunez. Where Mathematics Comes From.
In their book they describe a concept they call the Romance of Mathematics;
“In doing the research for this book, we have talked to a lot of mathematicians, mathematics students, and mathematics educators and analyzed a lot of books and articles. In the course of this research, we kept bumping up against a mythology — what we have called the Romance of Mathematics. As our research progressed, it became clear that our findings contradicted this mythology. This is not an unusual occurrence in cognitive science; it happens all the time when you study people’s unconscious conceptual systems and value systems. People’s conscious beliefs about time, causation, morality, and politics are typically inconsistent with their unconscious conceptual systems. It is also not unusual for people to get angry when told that their unconscious conceptual systems contradict their fondly held conscious beliefs, especially in sensitive areas like morality, religion, and politics. What we have found is that mathematics is one such sensitive area. Those who understand and use advanced mathematics tend to hold strong views about what mathematics is.
The discrepancies between the findings of cognitive science and the folk theories of the people whom cognitive scientists study is a particularly sensitive issue in the case of mathematics. The reason is that a great many of those who have a serious knowledge of mathematics not only tend to believe the mythology we call the Romance of Mathematics but tend to believe it fiercely. The Romance of Mathematics is part of their worldview, their very identity. Since our findings in general contradict the romance, we would not be surprised to find that this book infuriated such people.” (Page 339)
In the same way that George Lakoff and Mark Johnson tore down the pseudo-dichotomy between Cartesian Mind/Body duality, George Lakoff and Rafael Nunez perform the same maneuver in tearing down the Invented/Discovered duality in Mathematics. There is no, so called, Platonic Realm where Mathematical entities are lying in wait to be discovered.
Here they describe what the Romance of Mathematics is:
Mathematics is an objective feature of the universe; mathematical objects are real; mathematical truth is universal, absolute, and certain.
What human beings believe about mathematics therefore has no effect on what mathematics really is. Mathematics would be the same even if there were no human beings, or beings of any sort. Though mathematics is abstract and disembodied, it is real.
Mathematicians are the ultimate scientists, discovering absolute truths not just about this physical universe but about any possible universe.
Since logic itself can be formalized as mathematical logic, mathematics characterizes the very nature of rationality.
Since rationality defines what is uniquely human, and since mathematics is the highest form of rationality, mathematical ability is the apex of human intellectual capacities. Mathematicians are therefore the ultimate experts on the nature of rationality itself.
The mathematics of physics resides in physical phenomena themselves — there are ellipses in the elliptical orbits of the planets, fractals in the fractal shapes of leaves and branches, logarithms in the logarithmic spirals of snails. This means that “the book of nature is written in mathematics,” which implies that the language of mathematics is the language of nature and that only those who know mathematics can truly understand nature.
Mathematics is the queen of the sciences. It defines what precision is. The ability to make mathematical models and do mathematical calculations is what makes science what it is. As the highest science, mathematics applies to and takes precedence over all other sciences. Only mathematics itself can characterize the ultimate nature of mathematics.
None other than Galileo is quoted as having said, “The laws of nature are written by the hand of God in the language of Mathematics.” This quote is often used by Mathematicians as an appeal to authority on the subject. How could Plato and Galileo be wrong? If it’s all just Stories and Math, and we are eliminating Math, then doesn’t that just make everything a Story? The answer is Yes.
The Romance of Mathematics makes a wonderful story. It is the premise of most popular books on mathematics and many a science-fiction movie. It has attracted generations of young people to mathematics. It perpetuates the mystique of the Mathematician, with a capital “M,” as someone who is more than a mere mortal — more intelligent, more rational, more probing, deeper, visionary.
It is a story that many people want to be true. We want to know that amid the uncertainties and doubts of life, something is certain and absolutely true — that amid all the irrationalities around us, some people are supremely rational, some order is possible, and that at least in doing mathematics we can be rational, logical, and certain of our conclusions.
The Romance of Mathematics is sexy. Wouldn’t you want to be the mathematician in the romance, the hero of the story? And if you’re not the hero yourself, don’t you want such heroes to look up to? Don’t you want to live in a world where such heroes exist? It is a beautiful and inspiring story. We grew up with it, and it still reverberates within us. But sadly, for the most part, it is not a true story.” (Page 340-341)
In the end, Embodied Realism provides one more solution to many of the issues plaguing Philosophy. I hope to have highlighted a few of them up to now, and I hope to answer more in the coming posts. In the next post I will say a bit more about Mathematics before coming to another Summary post as I continue to fill out the Weltanschauung, or World View, that is the Philosophy of Evolution.
I come into this with an open mind, but I find several things here that leave me unpersuaded. First, there are some dubious assertions in the text above:
> "Mathematicians are the ultimate scientists, discovering absolute truths not just about this physical universe but about any possible universe."
I don't know anyone in the science community who would vouch for this. Math is a *tool* in science but not science itself. (If it were, then string theory would be the TOE and physics would be over.)
> "If it’s all just Stories and Math, and we are eliminating Math, then doesn’t that just make everything a Story? The answer is Yes."
Lakoff does not assert this in the video you linked. If that's *your* contention, you have a long way to go in grounding it. Lakoff starts off by stating that the dichotomy between invented or discovered math is false. He goes on to argue that patterns exist in nature (Nature's language?) and that we have emergent metaphors that align with those patterns. I'm not convinced, because in the video, at least, Lakoff implies, without evidence, that finding neural functions that are extendable into higher mathematics rules out the possibility that math exists independent of brains.
I have high regard for Lakoff and would not want to dismiss his case without reading his book, but on the face of it the argument seems trivial. Regardless of whether math is invented or discovered, human brains *must* have the capacity to model it, or we wouldn't be having a debate on its ontology.