What do you mean by “hydrogen atom” and “have” and “exactly” and “proton”. (“One” I can deal with for now, but quantum physics makes the rest of your sentence meaningless (i.e. it makes your sentence an inexact high level description.))
By “proton” I mean a thingy that creates a potential well where an electron bops around, and by “hydrogen atom” I mean a single of these with a single electron in it, and by “have” I mean that when the electron has high enough energy you don’t call it an hydrogen atom but “a proton here and an electron over there”. This is of course a tautology.
By “one” I mean S(0) (and by “0″ I mean the empty set), which is also a tautology. And if you don’t know what I mean by “exactly” then you don’t understand the parent quote anyway.
Admittedly a good counterexample would involve an exact truth that is not a tautology.
But you can construct rigid, exact definitions for all of those things.
Though I suppose those definitions would have to be approximations. So Mathematics gets to have exactness to it, but of course Mathematics is typically not considered a science.
What do you mean by “hydrogen atom” and “have” and “exactly” and “proton”. (“One” I can deal with for now, but quantum physics makes the rest of your sentence meaningless (i.e. it makes your sentence an inexact high level description.))
By “proton” I mean a thingy that creates a potential well where an electron bops around, and by “hydrogen atom” I mean a single of these with a single electron in it, and by “have” I mean that when the electron has high enough energy you don’t call it an hydrogen atom but “a proton here and an electron over there”. This is of course a tautology.
By “one” I mean S(0) (and by “0″ I mean the empty set), which is also a tautology. And if you don’t know what I mean by “exactly” then you don’t understand the parent quote anyway.
Admittedly a good counterexample would involve an exact truth that is not a tautology.
There are exactly zero unicorns.
But you can construct rigid, exact definitions for all of those things.
Though I suppose those definitions would have to be approximations. So Mathematics gets to have exactness to it, but of course Mathematics is typically not considered a science.