Plato - Descartes - Hume - Kant - Newton - Einstein - Quine
Plato, like Descartes, was something of a rationalist which in the philosophical sense means someone who believes new knowledge of the world out there could be acquired through thought or reason alone un-aided by the senses - such as by merely sitting in an armchair, eye's shut, and meditating or carrying out thought experiments.
Hume, in section 4 of his short book "Enquiry concerning Human Understanding" demonstrates how new knowledge of the world cannot possibly come from reason. He uses great examples like asking us to work out the reasoning one uses to determine that sticking one's hand in the flame a second time would not be a good idea. He says we cannot claim to have now forgotten the reasoning previously used because otherwise he will go and ask a rabbit or an infant child why they do not want to stick their paw/hand in a flame a second time since clearly they are at that very age where such reasoning is required. If we want to claim that infants and animals do not reason then we must accept that we all learn of the world like all other animals by pure experience and reflection upon that experience.
Kant wrote the very famous "Critique of Pure Reason" in response to Hume's attack on the rationalists - Hume was claiming that all knowledge of the world comes from Pure Experience free of all reason. But Kant admits in that book, and his follow-up summary of it (The Prolegomena), that the only way he sees that humans could possibly reason to new knowledge of the world is via Euclidean Geometry - Hume explicitly denied this in Section 4 of his "Enquiry".
Newton mapped the solar system's ways with Euclidean Geometry but he could not account for the open elliptical orbit taken by Mercury. Some Newtonian's tampered with the inverse square law to see if a solution could be found. They had no concept yet of a non Euclidean curved space-time.
It turned out that in order to map the solar system's behaviours precisely a Geometry different from Euclid's had to be used. During the 1800's a few mathematicians had decided to tamper with Euclid's 5th Postulate and so doing created a large number of different geometries all unlike Euclid's. One of them was a German by the name of Riemann. In Riemannian Geometry no two lines are parallel forever and triangles have internal angles adding up to greater than 180°. Riemannian Geometry was the Geometry Einstein found in a German University's archives in its basement when he visited a friend there and told that friend that his view of the universe cannot be mapped with Euclidean Geometry and a geometry that could map curved space-time was needed. His friend, a professor at the university, happened to have remembered Reimann's papers were gathering dust in the basement.
The American philosopher WVO Quine, fascinated by this story, concluded that if expectations borne out of our theories do not come to fruition then perhaps we should always consider questioning our very reasoning itself - we should question even the assumed eternal nature of the axioms from which any math system we use arises - he even thought that we should be willing to discard our current logic for a new logic since already a different logic is used for quantum theory. In later years, after arguments against him related to Godel's incompletedness theorum, he back tracked on the notion of alterable logic systems, however, today philosophers do accept that while we can map the universe with math we can only know which math system might best do so by first attaining experience of the universe. This is what makes David Hume the Philosopher of all time so far.
And so was cast aside forever the hope of those who thought that knowledge of the universe could come from anything but a shared public sense experience. This is why we humans have the need for the likes of CERN. If Quine was wrong then we would not need to build atom smashers - we would just sit in our arm chairs and work it all out.
The famous "Enquiry Concerning Human Understanding" which explained why reason could never give us new knowledge of the world. Section 4 is the relevant part - quite short but brutal. Section 4 starts on page 11.
Wittgenstein on the matter...
Newtonian mechanics, for example, brings the description of the universe to a unified form. Let us imagine a white surface with irregular black spots. We now say: Whatever kind of picture these make I can always get as near as I like to its description, if I cover the surface with a sufficiently fine square network and now say of every square that it is white or black. In this way I shall have brought the description of the surface to a unified form.
This form is arbitrary, because I could have applied with equal success a net with a triangular or hexagonal mesh. It can happen that the description would have been simpler with the aid of a triangular mesh; that is to say we might have described the surface more accurately with a triangular, and coarser, than with the finer square mesh, or vice versa, and so on. To the different networks correspond different systems of describing the world.
Mechanics determine a form of description by saying: All propositions in the description of the world must be obtained in a given way from a number of given propositions -- the mechanical axioms. It thus provides the bricks for building the edifice of science, and says: Whatever building thou wouldst erect, thou shalt construct it in some manner with these bricks and these alone.
(As with the system of numbers one must be able to write down any arbitrary number, so with the system of mechanics one must be able to write down any arbitrary physical proposition.)