“Should the philosophy
of mathematics be precise? ...Mathematics is precise; philosophy
cannot be. Expecting philosophy of mathematics to be a branch of mathematics,
with definitions and proofs, is like thinking philosophy of art can be a branch
of art, with landscapes and still lives.... It happens that the creators of
foundationist philosophy of mathematics were mathematicians (Hilbert, Brouwer)
or mathematically trained (Husserl, Frege, Russell). This training may explain
their bias. They sought to turn philosophical problems into mathematical
problems, to make them precise. This bias was fruitful mathematically.
Some of today’s mathematical logic descended from the search for mathematical
solutions to philosophical problems. But, even though mathematically fruitful,
it was philosophically misguided.”
For many
years, the mathematicians, scientists and philosophers, had
tackled this issue and which are still being
asked today. The main purpose of the book is to confront philosophical
problems: In what sense do mathematical objects exist? How can we have
knowledge of them? Why do mathematicians think mathematical entities exist forever,
independent of human action and knowledge? The book proposes an unconventional
answer: mathematics has existence or reality only as part of human culture.
Despite its seeming timelessness, it is a social, cultural, historic
phenomenon.
What Is Mathematics, Really? opens
with an astonishing dialog between Hersh and a 12-year old girl about the kinds
of questions that can begin to help us understand what the philosophy of mathematics
is all about, and what is at stake in the process.
This
is a well written, well argued and fascinating book. It contains important
arguments that push back the boundaries of debates in the philosophy of Mathematics.
It proposes an important new position in the philosophy of Mathematics: Hersh's
humanism. It serves both a challenge to philosophers of Mathematics and even
normal citizens. It deserves to beread by all interested in mathematics and its
philosophy, from philosophers and mathematicians to students and interested
members of the public.
"Mathematics is precise; philosophy cannot be." Yes, indeed.
ReplyDeleteYou say that the book "deserves to be read by all interested in mathematics and its philosophy", but how about those that have no interest at all?
ReplyDeleteThe conversation with Laura did help a bit in understanding about the philosophy of math. i like how passionate Hersh was in writing the book.. you can really see how he loves math. Indeed, the book should be read by those who are interested in math and its philosophy.. but i think those who have no interest will think otherwise XD
ReplyDeletethumbs up for you reading and understanding the looong conversation of the author and laura. Amazing review.
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