FOM: Comment on Hersh
Soren Riis
sriis at fields.fields.utoronto.ca
Sun Mar 1 11:42:28 EST 1998
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Comment on Hersh
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Hersh wrote:
> I propose a way of thinking about the reality and
> existence of mathematics which lets us keep our mathematical objects
> really existing, really meaningful, without resort to mysticism.
>
> The key observation is that in our world there are not two
> but three main kinds of reality.
I suggest Hersh begin to give proper credit for his ideas. This
observation is certainly found in Carl Popper's writings. Popper
talk about World 1, World 2 and World 3. Examples of World 3 objects
are numbers, theories, designs, works of art, institutions etc.
Wisely enough Popper realizes the danger of putting loaded labels
(i.e. labels which might carry preconceptions) on these worlds.
> Mind and matter are familiar. But they
> do not help with our puzzle, because mathematical objects are not
> material, and they are not mental, in the sense of being
> part of anyone's private subjectivity.
>
> But they are not the only things that are neither
> mind nor matter.
>
> For instance, your job. The money in your bank account. Your
> degree. Your career....
>
> Catholicism, Lutheranixm, Judaism, Islam, Bolshevism, Fascism,
> racism, nationalism, rationalism,. liberalism, feminism....
>
> Beethoven's fifth symphony, Shakespeare's Hamlet, The
> Bible, Darwin's theory of evolution, Einstein's theory of relativity....
>
> This journal. Its editorial policy, its standards of
> publication, its mailing list, its backlog. This mathematical
> society. Its history. Its traditions....
>
> All these things are real. They are the substance of our lives.
> None of them is material, none of them is mental. What then?
> I call them social-cultural-historical, or just social for short.
>
> Once these examples are pointed out, it is hardly questionable
> that there is another level of existence besides the mental and
material.
>
> Now, our problem was--what sort of existence or reality has
> mathematics?
>
> We have not two but three choices. Material and mental are
> wrong. What about social?
You can call it social or social-cultural-historical. You could also
call this choice "World 3" (Popper), "A", "X" or you name it.
These are just a labels. You want to place "French grammar" and much
more under the same heading as Mathematics. Fine - as long as you
are not smuggling in preconceptions and connotations attached to
the label you choose.
Why do you call the world social-cultural-historical?? Why do you
not call it social-cultural-historical-mathematical???
To keep things simple I will only briefly address the other flaws
in Hersh posting.
> I propose a way of thinking about the reality and
> existence of mathematics which lets us keep our mathematical objects
> really existing,
Notice the "existence" here is used on two different levels. The
existence of comic strips / mathematics is not to be confused with
the question of the existence of Mickey Mouse / non-abelean groups.
Hersh are trying to comfort us that Riemanns theta-function have the
same kind of existence as Donald Duck.
Hersh ideas are not new, neither are the flaws in his thinking.
Soren
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