>As an example, Arthur Eddington describes quantum uncertainty as a consequence of the fact that the language of physics switched from referring directly to phy

>As an example, Arthur Eddington describes quantum uncertainty as a consequence of the fact that the language of physics switched from referring directly to physical phenomena, to describing our knowledge of these things; so when we only have partial knowledge, we frame our descriptions in terms of probabilities. I have never heard this before, but it is _exactly_ what I have said about the subject. This usually causes me to have to explain how I'm not saying we _could_ know that stuff: the information may not even exist. But we can't even say whether or not that is true. >There's this question in philosophy of mathematics, whether math is discovery or invention. I have also had many discussions about this. A lot of it stems from the fact that mathematicians tend to say "we are free to choose our axioms," when all my experiences say otherwise. We cannot choose contradictory axioms because useless math isn't math. (I.e., there is more to good math than truth: it must have possible utility.) And furthermore, if I were to drop two pennies on the table and consistently get you to agree there are three cents there, then you would be damned sure some mathematician would want to have a model for what is going on! So mathematics is fundamentally tied to observation. That's why they spent so much effort trying to define things like 'continuity' and 'smooth curve': we need a model for reality, not just for our 'freely chosen' axioms. So mathematics is discovery in the sense that we must observe its correctness, but invention in the sense that we must invent its usefulness. In the end, all of our efforts are about developing language that allows us to describe our reality in a reliable and teachable manner -- Physicists and mathematicians are primarily trying to develop better language.