
Re: [HM] Language of Discovery
Posted:
Feb 25, 2001 5:01 PM


In the "theory of inventions" (e.g., by Altshuller), they invent what didn't exists before, but they discover what was existing before, however what wasn't known. For example, in physics they invent new devices, but discover new elementary particles and new physical laws. In chemistry, when a chemist synthesized a new compound (e.g., a new medicine), they say that he discovered it, though he also invented the compound since it didn't exist in nature before. So, a chemist is simultaneously an inventor and discoverer. In mathematics, I think, we just invent new math objects, definitions, axioms, and ways of proofs (but the proofs themselves are formal deductions from given axioms, and the pure logical deduction, according to Poincare, is able to generate nothing new, i.e., neither inventions, nor discoveries). It can be explained by the fact that mathematics objects are abstract and can exist only in a humanbeing head (as you see, the written, printed, etc. form of these object doesn't concern their invention or discovery). Therefore if they so far are not known, then they are simply not existing and can't be discovered by definition. But if we trust in Plato and Kant as to that ideas exist "outside, before and independently from a humanbeing", then all mathematical achievements are certainly scientific discoveries : ) From this point of view, there is a quite interesting question: whether G.Cantor was an inventor or a discoverer of his famous diagonal argument and his minimal transfinite integer "OMEGA"? : )
Best thoughts and regards,
AZ

