The original question was:
Mathematicians sometimes say, “There exists a number such that . . .” Which provokes me to ask, Where does it exist? For how long has it existed? Did numbers exist before people did? Or did people somehow create (instead of discover) them?
In her “Incompleteness” quasi-biography of Godel (not a bad mathematician), Rebecca Goldstein emphasizes that he was a Platonist about math. What’s the current state of Platonism in math?
And such questions can be extended to the “laws” of physics: Do they exist? If so, where? And for how long? Are they discovered (implying prior existence) or invented/created by humans?
Some comments relating to such issues would be interesting!
Physicist: Discovered. Although most of the laws that can be re-arranged and expressed in different ways. For example you can express “conservation of total momentum” as “the velocity of the center of mass never changes”.
A good physicist (one who pick their words carefully) will avoid saying that one thing or another is “true”. Physics, and the laws we come up with, don’t exist “out there somewhere”. Boiled down to its most basic, what we study is “what has worked before, and still seems to work” as opposed to “what is true”.
For example: Einstein showed that Newtonian physics is wrong (so wrong), but it still “works”. If you learn Newton’s stuff you’ll notice that it’s fairly intuitive (compared to some other sciences at least), and seems to be true. It was taught as fact for over 200 years, but again: wrong. Taking this, and dozens of other similar stories as a warning, physicists try to talk only about what works and not what’s true.
That being said, some of the laws that have been found may actually be true, written into the nature of the universe. I’d like to say that we know at least a few of them for sure, and that if what we know is wrong then the universe is entirely fucked. However, that has been exactly the case before (I’m looking at you wave-particle duality), so who knows?
The laws we have could easily be special cases of the true laws (like Newtonian mechanics in relativistic mechanics), or could be merely the descriptions of the behavior created by those laws.
As far as the physical laws of the universe actually, physically existing in some form somewhere (this is the total extent of my understanding of Platonism): no, I don’t think there are very many scientists who think that.