[FOM] FOM currents

Dean Buckner Dean.Buckner at btopenworld.com
Thu Oct 9 16:41:17 EDT 2003

Harvey Friedman ("FOM currents" FOM 7 October 2003), objecting to postings
from "philosophers of language", makes a number of serious points.

In common with other mathematicians, Friedman has a number of fundamental
misconceptions about "philosophy of language".  Philosophy of language is
not really about language, it is about thought itself, about what we think,
and in particular, about what sorts of thought are TRUE, and WHY they are
true.  For example, the thought expressed by "there are exactly two things,
and there are more than 3 things" is not true.  Why is that?

Thought is connected with language because thoughts are what language
expresses.  What language expresses is something that can be grasped by any
competent user of the language, thus independent of particular ideas,
emotions, images &c in any individual mind.  So the study of thought is of
something objective, not to be confused with psychology, linguistics,
sociology or any sort of experimental science.  These are the insights we
owe to Frege, who is the father of both linguistic philosophy and the
foundations of mathematics (the whole idea of "foundations of mathematics"
comes from Frege of course).

Friedman says

1.  Such philosophers confuse issues in the philosophy of language with
issues in the foundations of mathematics.

The relevant issue in philosophy of language is what we are THINKING when we
have the thought expressed by the sentence "there are 3 things on the
table", how this is connected with the thought that there are only 2 things,
and so on. Philosophers of language are of course concerned with ordinary
language, but their primary concern is with what language expresses or

2.  "It would help the FOM list by thinkers starting with the nature and
structure of mathematical thought - taking into account important features
that are second nature to competent precollege students. This is much more
appropriate than starting with features of natural language, and forcing
them on mathematical thought."

I don't understand how observations about natural language can be "forced"
onto mathematical thought.  Observations about natural language are, as I
said, about the thoughts expressed by ANY statement put into ANY language
(formal, informal, colloquial &c) that has "mathematifcal content".

3. F.o.m. is such a subtlety [sic] difficult matter, that it only really
came into being in the late 1800's and early 1900's, despite an enormously
successful development of mathematics over thousands of years, and a
tremendous development from the time of the calculus onwards.

And why did it only come into being in the late 1800's?  Out of the idea
that the prevailing psychology of the day sought to explain our concept of
number in terms of sensations (Mill, Wundt), and out of the idea that
explanation of mathematical and logical thought lay in a third realm
different both from physical reality and from the world of the mind.

4.  Philosophy of language has no "track record", and no obvious prospects
to success.

None obvious to Friedman, as far as I can see!!!

5. "One must be aware of the minimal prospects for doing serious
foundational work concerning more specialized and focused matters, before
the proper groundwork is laid with matters of a more basic nature."

Philosophers of language would agree with this, being concerned with the
"basic nature" of thought itself.

6. "Consequently, armchair suggestions as to what f.o.m. should instead be
doing are unimpressive unless accompanied by some striking insights that
would indicate prospects for success - e.g., how generally to proceed."

Philosophers of language would agree with this.  One way of indicating
prospects for success are references to the literature, which show
painstaking academic research conducted out of armchairs, but more on this .

7.  "It does not count to merely give some reference to the literature of
such an insight. It should still be encapsulated in some effective way right
here on the FOM list, in order to save time and effort."

It's useful to refer to the literature (a) so that people can go for
themselves and read it (b) simply to indicate that there is serious research
being done in a certain area, and that what is being claimed on a internet
discussion group like FOM is not mere hot air or an opinion that occurred at
breakfast time, in an armchair (c) because a serios paper takes a lot of
time and effort, not possible in volatile environment of an internet
discussion group like FOM.

7. "I believe that it is highly unlikely that any given foundational issue
of general intellectual interest, concerning mathematical thought, can be
dealt with in a truly profound and effective way - meeting f.o.m.
standards!! - without substantial use of current f.o.m. perspectives,
developments, and methods. "

What is f.o.m.?  My understanding is that "the foundations of mathematics"
is a subject developed in the late 1800's, by philosophers of language, see

8.  "The FOM is a great resource that has not nearly reached its potential.
There are many students across the world who subscribe and/or read the FOM
Archies [sic].  Because of their lack of experience, students can not be
expected to be able to tell what is of value on the FOM."

Agree the FOM is a great resource, allowing those working in areas of
philosophy can have meaningful (& friendly and civilised!) discourse with
those working within mathematics.  But this sinister argument is often used
in totalitarian regimes as a justification for CENSORSHIP, on the grounds
that "ordinary people" can't be expected to make a reasonable judgment for
themselves, so must be PROTECTED by those older, wiser, more experienced &c.

9.  "The vicarious thrill that may be associated with making grand
declarations of a negative nature one is not prepared to defend, should be

There are two ways of making progress.  One is negative, by showing
carefully that the existing explanation (e.g. as given in literal, Biblical
account of creation) is seriously flawed.  The other is positive, by showing
 an alternative account that is coherent and unflawed.

Most progress occurs throught the negative route first.  For example, most
scientists now accept that the once orthodox (Biblical, literal ) account of
creation is flawed.  This is based on arguments about the age of the Earth.
We still have no positive account of the second sort, as far as I know.
(Similarly for the descent of man - we are not sure where mankind came from,
though we are pretty sure the (literal) account given in Genesis cannot be


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