erikp writes:
bluegenes writes:
I don't find Gdel's language weird at all. He knows the difference between "incomplete" and "false".
According to the definitions of "true" and "false", incomplete theories are indeed false.
As soon as water has been observed to boil at any other temperature than 100 C, the theory that says "Water boils at 100 C", has been proven to false. It cannot be rescued just by saying that it is "incomplete". The definition simply says that it is false.
Here's where I quibbled with your chosen phrase before. Had you chosen "Water
only boils at 100C", the statement would have been falsified, and is clearly false. As water frequently does boil at 100C, the statement isn't false, merely of little or no use to us in explaining anything about water. Here's an example of incompleteness:
"Biological evolution proceeds by variation combined with natural selection."
That's observably true. However, it also proceeds by other means, like genetic drift (neutral evolution), so:
"Biological evolution proceeds by variation combined with natural selection and by variation alone" is an improvement."
Neither statement is a comprehensive theory of all biology, but both are definitely true. Scientific procedure presumes the incompleteness of theories. They play a different role from the theorems of maths.
erikp writes:
So, the mathematical method of rigorously and systematically rejecting unreduced theories, is more of an ideal to strive to -- unfortunately unattainable -- for the other scientific disciplines.
In the rest of your post, you did bring in observations, correctly, and that's what I was looking for. It is observation and experimentation in the physical world that makes science radically different from maths, you'll agree, and that's perhaps why the effect of Godel's theorems will be different (but not non-existent).
You've got far too much to deal with from others, so I won't pile on!
Good luck!