In the Feynman lectures, it is mentioned that [Vol 1; Gravitation]:
Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle of inertia—if something is moving, with nothing touching it and completely undisturbed, it will go on forever, coasting at a uniform speed in a straight line. (Why does it keep on coasting? We do not know, but that is the way it is.)
How Gallileo discovered the law of inertia ? In those time, there were probably no frictionless area so that he could test his hypothesis. And uncontrolled "thought experiment" can lead you astray like Aristotle (who belived that continuous force is required to get a particle moving all the time).
Here, I do find Feynman's quotation (of Tycho Brahe's "idea" ) relevant, but I can't make the connection:
This [debates about the nature of the motions of the planets would best be resolved if the actual positions of the planets in the sky were measured sufficiently accurately] was a tremendous idea—that to find something out, it is better to perform some careful experiments than to carry on deep philosophical arguments.
A quote by Paul Dirac is also relevant here (not directly, the bold words are only relevant):
". For example, rough experiments about the relation between the pressure and volume of a gas at a fixed temperature give results fitting in with a law of inverse proportionality, but it would be wrong to infer that more accurate experiments would confirm this law with greater accuracy, as one is here dealing with a phenomenon which is not connected in any very direct way with the fundamental laws of motion.",
How you can be sure that the less friction you use, the more accurate it becomes ?
Update: Since most of the person are focusing on galileo did that (my ill written title misled them), I actually wanted to know how scientists get rid of their Aristotlian intuition and developed the idea (notion) of inertia.