[FOM] [Fwd: Re: Fictionalism About Mathematics]
Director CPFS
director at cpfs.res.in
Mon Mar 12 08:20:38 EDT 2012
At the
risk of missing the boat yet again, may I make two brief
observations:
1) I have not seen any mention or discussion of the Imre Lakatos
dissertation which was published as ‘Proofs and Refutations’,
which offers a constructivist view of mathematical objects in which new
objects are introduced by enlarging the axioms (e.g. dropping the parallel
postulate allows non-Euclidean geometries to be constructed and
generalizing operations such as arithmetical operations from natural
numbers to real numbers, complex numbers and transfinite
numbers.
2) As for quantum theory, Niels Bohr often compared the development
of physical concepts to the process of generalization that resulted, for
instance, in complex numbers. The introduction of non-Euclidean geometries
was another pointer in the same direction. The idea is that while the new
concept may be alien to our experience, it is related to yet different
from concepts that are well understood. Hence the counter-intuitive
‘ontology’ of quantum theory is attributed to the fact that
quantum systems are not experienced by us in the everyday world
3) The alternative to Platonism is not just fictionalism; it could
be structuralism. Mathematics can be viewed as an idealized science of
structure and measure which arose from everyday concerns in the physical
world to encompass wider domains.
_
Ranjit Nair
____________________________________
Professor Ranjit Nair
Director
Centre for Philosophy &
Foundations of Science
Darshan Sadan
E-36 Panchshila Park
New Delhi 110017
India
Tel. +91 11 65951738 / 46170795
/ 26490667
Fax +91 11 26495181
Cell 9810332846 (Delhi)
e-mail:
director at cpfs.res.in
director at cpfs.in
director.cpfs at gmail.com
URL
http://www.cpfs.res.in/
http://goidirectory.nic.in/ministries_categories.php?ct=39#groupE060
---------------------------- Original Message
----------------------------
Subject: Re: [FOM] Fictionalism About
Mathematics
From: T.Forster at dpmms.cam.ac.uk
Date: Sun, March
11, 2012 12:51 pm
To: "Foundations of Mathematics"
<fom at cs.nyu.edu>
--------------------------------------------------------------------------
It is true that there are people in Philosophy departments who
espouse
fictionalism, but i have yet to meet a working mathematician
who does. The
problem i have with this kind of talk is this:
ficticious objects have real
counterparts. People in novels, plays
etc, are fictions. We (sort-of) know
how to deal with this beco's
there are *real* people as well. But if
mathematical entities are to
be fictions, what real things are they
fictions of? And if they
aren't, why call them fictions?
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