Mathematics Essential

Question

I started reading History of Philosophy and readily noticed that the origins of our actual natural sciences were due to the proper use of inductive logic. Our Physics/Chemistry and Biology all are known to have started by the revolution of Thales and the Pre-Socratic Thinkers, conscious human-beings that decided to stop relying on mythical and supernatural explanations for all phenomena and started using inductive logic specially in cosmology.

I was trying to device the same understanding about Mathematics. I read in History of Mathematics that the first accounts of something similar to mathematics was the activity of our ancestors (in Pre-Historic period) in perceiving that different collection of objects did actually have the same property, they noticed they might had the same "number" of elements, as we now know. From there, the Babylonians, Indians, Chinese, Egyptians, and Muslims further developed this idea. I'm trying to see if there was anything essential (e.g., inductive/deductive logic, Wittgenstein's language-games on collection of objects) that lead to the idea of numbers and specially that later lead to the development, by those societies, of Arithmetic, Geometry and Algebra, some foundations of our modern Mathematics.

As inductive logic lead to the development of the natural sciences, is there anything essential in our human existence (brain, mind, etc.) that lead to the development of Mathematics?

Answer 1

It may not be an answer to your question, but to those things you wrote before asking your question.

It seems to me that your starting point, that the pre-socratics stopped relying on mythical and supernatural explanations, is utterly wrong.

Meet Parmenides, who wrote a poem:

The proem is a narrative sequence in which the narrator travels "beyond the beaten paths of mortal men" to receive a revelation from an unnamed goddess (generally thought to be Persephone or Dike) on the nature of reality.

--> mythical and supernatural

Also, Thales:

Accordingly, the sources say that Thales believed that "all things were full of gods."

And here is Pythagoras, who...

was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism.

Just to name a few. Also Plato relies upon supernatural and mythical explanations, just read his metaphor of the sun, or his platonic number, which is mythical indeed. I don't want to laugh about them, or make them any smaller than they are, but besides being awesome and working out the foundations on which we all stand, they were mythical, religious and believed in supernatural stuffs.