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>
>According to Ivor G-G, the present book differs significantly from many
>others histories of mathematics in several respects. One of these is the
>following:
>
> "I take _the word 'history'_ to relate to the question
>
> 'What happened in the past?';
>
> by contrast, mathematicians (and scientists in general, and
> even a distressing number of historians) take history to mean
>
> 'How did we get here?'
>
> The difference between these two questions is worth pondering.
> Answers to the second one draw _only_ on those parts of the
> past that have led to our present situation; while a perfectly
> respectable form of research, they can give quite mistaken
> impressions about the aims and purposes of historical figures,
> and the priorities they saw in their own work."
>
>Now... the difference between the two questions mentioned above is worth
>pondering, but should these questions be placed in disjoint baskets? ...
>
>Greetings to all,
>Julio GC
>
>
This appears related to a topic which historians of sciences debated at
some length when I was (fairly) young. We used to use Herbert
Butterfield's characterization of the kind of history of science which
reads like a steady progress to some current mathematical orthodoxy as
"Whig history of science". I interpret the work of people like Imre Lakatos
some 40 years ago, and of people like Alexandre Koyre earlier, as attempts
to do a different kind of history of science, based to a greater extent on
what really happened. However, history "wie es eigentlich gewesen" ("as it
really happened"), in Leopold Ranke's often referred to phrase, is fraught
with difficulties.
There is a considerable contemporary literature by historians (not to
mention literary theorists and others) on the extent to which what really
happened can be recaptured, both for objective and subjective reasons. I
have about 30 or so of these on my shelves at the moment. To give some
idea of what they're about, here are the titles of a couple: *That Noble
Dream: The "Obectivity Question" and the American Historical Profession" by
Peter Novick (1988); *The Past is a Foreign Country* by David Lowenthal
(1985); *The Distorted Past: A Reinterpretation of Europe* by Josep
Fontana (1995)(this one challenges beliefs about the superiority of the
calssical Greeks).
So discussing this question would appear to open up some deep, or at least
widespread, historiographical concerns of the moment. To get to Julio's
specific question, though, it seems obvious that one can't separate "how we
got to where we are" from "what happened." The question is, how do we make
a selection from among what records we have of what happened? For example,
to what extent do we make a selection based on the present state of some
part of mathematical endeavor, as we as individuals see it, and to what
extent do we try to get into the minds of people of the past, and describe
the mathematical world and its transformations as *they* saw it?
I've not seen his recent book, but perhaps Grattan-Guinness had in mind
that historians of mathematics should describe paths which were once
crowded but seem to have led nowhere, or which have been abandoned for good
or bad or other reasons, and which were conditioned by factors (social,
cultural, political, etc.) outside of mathematics proper? (We used to
distinguish between "external" and "internal" history of science.) Or did
he mean we just stick to the records of an epoch when we are describing
mathematical work of that epoch, and not be guided by a current state of
mathematics, as we see it? If the latter, we are faced with vexing
historiographical questions about how we can sufficiently eliminate
relevant parts of ourselves and our cultures from our historical
interpretations, so as to give some decent approximation to or hints about,
say, the mathematical world and its surroundings the way Euclid or Newton
or Euler, or Gauss or Cantor or Hausdorff or von Neumann saw it, or as it
was seen by legions of mathematicians whose names historians of mathematics
customarily pay no attention to.
Gordon Fisher gfisher@shentel.net