FOM: Unity or disunity of science, human knowledge?
rhersh at math.unm.edu
Mon Jan 19 14:11:03 EST 1998
You seem to agree that the "hard" sciences do rest on reproducibility
and the consensus based on reproducibility measurements and experiments.
On the other hand, this is not true of the behavioral, societal, and
What about mathematics?
Is mathematics like the soft sciences, in the persistence of unresolvable
controversies, in the dependence of scientific views on pre-existing
ideologies, and in general all the un-science-like features of economics,
No one would say so.
On the conrary, the glory and pride of mathematics is the "certainty,"
i.e., the near u;nanimity of its findings, based on an agreed on
(but informal) methodology.
I think most would agree that math is in some ways like physics but
I have claimed that the subjecyt matter, the content of math is
shared thoughts of mathematicians and other people.
Then it becomes incumbent on me to say how math is distinguished from
other disciplines that study the sharaed thoughts of human beings--for
example, history, literature, philosophy.
The obvious difference between math and allthse other subjects is its
high consensus--which is just another way of saying math problems
usually have defilnite answers which everyone who is interested accepts.
Is this reductionism? No. It would be reductionism to say, as some do,
that math is really just about physical reality, or physical possibility
(Putnam.) My characterikzation of math does not reduce it to anything else,
it singles it out in its uniquensss, as the one science that studies
human ideas and obtaines definite results, accepted by all.
I am just trying to explailn how math is real and meaningful without
calling in mysticism, or faith iln transcendental Over-Reality.
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