[FOM] Finitism and the Gold Standard
Helene.Boucher at wanadoo.fr
Tue Feb 21 15:41:42 EST 2006
Harvey Friedman wrote:
In fact, the same thing has been said by finitists:
2'. It doesn't make any difference anyways, since mathematicians do
infinitary arguments, or they do not use infinitary arguments for
"important" results by "important" people, or the infinite methods
"important" results are easily removed.
There are important counterexamples to ... 2'.
<end of quote>
I'm afraid I can't come to terms with this remark. In which sense of
"important" do finitists say this? I am certainly surprised by the
reference to "important" people.
Not that I am a finitist, but it would seem to me that finitists
would be on strongest ground if "important" were interpreted along
the lines of "important to science" or "scientifically
applicable". Are there any counterexamples if 2' is rewritten as:
2". Mathematicians do not use infinitary arguments, or they do not
use infinitary arguments for scientifically applicable results, or
the infinite methods for the scientifically applicable results can be
removed, or a result which needs infinite methods and which is
scientifically applicable can be reformulated to another result which
does not use infinite methods and which maintains the same level of
If there are any, what are these counterexamples?
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