**Is mathematics Invented or Discovered?**

**"Philosophy In The Flesh"**

**LAKOFF**:

When you start to study the brain and body scientifically, you inevitably wind up using metaphors. Metaphors for the mind, as you say, have evolved over time -- from machines to switchboards to computers. There's no avoiding metaphor in science. In our lab, we use the Neural Circuitry metaphor ubiquitous throughout neuroscience. If you're studying neural computation, that metaphor is necessary. In the day to day research on the details of neural computation, the biological brain moves into the background while the Neural Circuitry introduced by the metaphor is what one works with. But no matter how ubiquitous a metaphor may be, it is important to keep track of what it hides and what it introduces. If you don't, the body does disappear. We're careful about our metaphors, as most scientists should be..

So I asked myself a question.

What if the condensation of the human brain was the reverse, of Damasio's First Law. I mean we can train the neuron pathways to be reconstructed, by establishing the movements previously damaged by stroke. What is the evolution of the human brain, if "mind" is not leading its shape? A newly discovered ability called "Toposense," perhaps?

Okay now, what came first, "chicken" or "egg?"

If one had never read Kuhn, how would one know to respond in kind to the philosophical basis a David Corfield might in sharing perspective about abstractness in mathematical models?

The thesis of 'Proofs and Refutations' is that the development of mathematics does not consist (as conventional philosophy of mathematics tells us it does) in the steady accumulation of eternal truths. Mathematics develops, according to Lakatos, in a much more dramatic and exciting way - by a process of conjecture, followed by attempts to 'prove' the conjecture (i.e. to reduce it to other conjectures) followed by criticism via attempts to produce counter-examples both to the conjectured theorem and to the various steps in the proof.J Worrall and E G Zahar (eds.), I Lakatos : Proofs and Refutations : The Logic of Mathematical Discovery

Okay so you understand as a layman I like to see what is going on out there in the blogger world of mathematicians, I thought I would listen here, and do some research. I had to started out with the presumption that one may encounter and be moved from any positon.

I has to philosophical understand it first.

I have enjoyed both participating in a mathematical dialogue and, as a philosopher, thinking about what such participation has to do with a theory of enquiry. The obvious comparison for me is with the fictional dialogue Proofs and Refutations written by the philosopher Imre Lakatos in the early 1960s. The clearest difference between these two dialogues is that Lakatos takes the engine of conceptual development to be a process of

conjectured result (perhaps imprecisely worded) - proposed (sketched) proof - suggested counterexample - analysis of proof for hidden assumptions - revised definitions, conjecture, and improved proof,

whereas John, I and other contributors look largely to other considerations to get the concepts ‘right’. For instance, it is clear that one cannot get very far without a heavy dose of analogical reasoning, something Lakatos ought to have learned more about from Polya, both in person and through his books.

I was quick to point out what I say about "Observation pays off," and it quickly recieved the trash box. That's not dialogue. :)

Albrecht Dürer(self portrait at 28)

It's about paying carefull attention as to what is created for us in images and paintings. Noticing the "anomalistic behavior" that might be brought forth for our human consumption. It required a metamorphsis for change.

**Prof.dr R.H. Dijkgraaf**

In that case I pointed out the work of Melencolia II

[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf showing Albrect Durer's images repainted to suit his thesis? So I delved deeper into the image portrayed.

On the surface this information is about what we see, yet below it, it is about seeing in ways that we are not accustom. So, the journey here was to show the nuances that invade perception, and then show what leads further into the understanding of what happens out there in the physics world in regards to the summation of Prof.dr R.H. Dijkgraaf's picture of the original.

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