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, Chineses, Egypcians,Muslims developed further this idea. I'm trying to see if there was anything essential ( inductive/deductive logic, Wittgenstein's language-games on collection of objects ? ) that lead to the idea of numbers and spectially that latter 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 ?
Highly appreciate all kind of answers !
Maybe this question is more philosophy than mathematics, but possibly mathematicians can contribute some relevant things that philosophers cannot.
It is mentioned that physics, biology, and chemistry rely on inductive reasoning.
I would hold that mathematics does as well.
In empirical sciences, inductive reasoning on which the science rests is from observations to general propositions. (E.g.: the buoyancy equals the weight of the displaced fluid.)
In mathematics, inductive reasoning on which the discipline rests is from examples to general concepts. (E.g.: One observes groups of motions in geometry and groups of permutations of roots of algebraic equations, and then forms the algebraic concept of a group.)
One of these goes from empirical observations to general propositions. The other goes from examples to general concepts.