Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.
Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.
Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
- 526 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
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Information
Publisher
Princeton University PressYear
2008Print ISBN
9780691242040
9780691136103
eBook ISBN
9781400829040
saw
his
mission
to
propel
it
finally
on
the
path
of
science.
Since
each
of
the
two
previous
breakthroughs
had
been
the
revolutionary
achievement
of
one,
or
at
most
a
few
great
thinkers,
Kant
was
making
no
modest
claim
here.
His
idea—and
he
compared
himself
to
Copernicus—was
to
make
the
objects
of
metaphysical
knowl-
edge
conform
to
our
intuition.
Metaphysics
reformulated
in
this
way,
said
Kant,
would
necessarily
be
unable
to
make
known
the
thing
in
itself,
because
that
would
go
beyond
the
limits
of
experience,
but
within
those
limits
it
could
acquire
exhaustive
knowledge
of
its
entire
field.
Kant
offered
a
compromise:
all
we
can
know
is
ap-
pearances,
but
about
appearances
we
can
know
everything,
including
an
under-
standing
of
how
knowledge
is
possible
at
all.
Let
us
unpack
this
a
little
further.
A
particular
challenge
for
Kant
was
to
explain
how
increase
in
knowledge
is
possible.
Logical
reasoning
is
trustworthy,
but
if
all
completely
reliable
truths
are
analytic,
or
true
in
virtue
of
their
form,
as
the
term
is
sometimes
glossed,
then
any
deduction
from
a
reliable
truth
merely
brings
out
what
FIGURE
2.6.
Immanuel
Kant.
BEFORE
MODERNISM
79
Table of contents
- Contents
- Introduction
- 1 Modernism and Mathematics
- 2 Before Modernism
- 3 Mathematical Modernism Arrives
- 4 Modernism Avowed
- 5 Faces of Mathematics
- 6 Mathematics, Language, and Psychology
- 7 After the War
- Appendix: Four Theorems in Projective Geometry
- Glossary
- Bibliography
- Index
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Yes, you can access Plato's Ghost by Jeremy Gray in PDF and/or ePUB format, as well as other popular books in Mathematics & 19th Century History. We have over 1.5 million books available in our catalogue for you to explore.