Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man.
He did say “all exact science”, a phrasing I think he probably chose carefully, so I’d charitably interpret the remark as being about people uttering purported scientific truths.
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.
Bertrand Russell
Or a mathematician.
He did say “all exact science”, a phrasing I think he probably chose carefully, so I’d charitably interpret the remark as being about people uttering purported scientific truths.
http://xkcd.com/263/
I hope no-one takes the title-text of that as a challenge.
I actually did when I read it. If I ever get into an argument about the merits of racial segregation my speech is now prepared!
I think it’s safe to say that Bertrand Russell knew about mathematicians, as he was one himself. :-)
Hydrogen atoms have exactly one proton.
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.