[FOM] FOM currents
Harvey Friedman
friedman at math.ohio-state.edu
Thu Oct 9 22:47:16 EDT 2003
Reply to Buckner.
On 10/9/03 4:41 PM, "Dean Buckner" <Dean.Buckner at btopenworld.com> wrote:
> Harvey Friedman ("FOM currents" FOM 7 October 2003), objecting to postings
> from "philosophers of language", makes a number of serious points.
I hope against hope that you are taking my "serious" points seriously.
>
> In common with other mathematicians, Friedman has a number of fundamental
> misconceptions about "philosophy of language".
Perhaps you need to also include various philosophers who have written
professional articles in Journals concerning philosophy of language in your
"list" of people you claim have "misconceptions".
Is there any possibility that you have such misconceptions? Philosophers of
language and philosophers who write about philosophy of language have not
been telling me how relevant that subject is for the foundations of
mathematics. All of these people are fully familiar with the basics of
f.o.m. - certainly completely knowledgeable about the f.o.m. that you
mention in your postings. Do you have any special insight that these
professionals do not have?
> Philosophy of language is
> not really about language,
Have you thought about campaigning for a change of name?
>it is about thought itself, about what we think,
> and in particular, about what sorts of thought are TRUE, and WHY they are
> true.
Now I finally see why you want to force everybody to think about philosophy
of language when they think about f.o.m.!! (smile, grin). Does philosophy of
language have a monopoly on this? Does this mean that we can't build
bridges, can't visit the moon, can't splice genes, can't develop medicines,
can't build buildings, without working in the philosophy of language?
(smile, grin).
Which of the following hold?
"philosophy is about thought itself, about what we think,
and in particular, about what sorts of thought are TRUE, and WHY they are
true"
"logic is about thought itself, about what we think, and in particular,
about what sorts of thought are TRUE, and WHY they are true"
"science is about thought itself, about what we think,
and in particular, about what sorts of thought are TRUE, and WHY they are
true"
"psychology is about thought itself, about what we think,
and in particular, about what sorts of thought are TRUE, and WHY they are
true"
"story telling is about thought itself, about what we think,
and in particular, about what sorts of thought are TRUE, and WHY they are
true"
"probability/staistics is about thought itself, about what we think,
and in particular, about what sorts of thought are TRUE, and WHY they are
true"
Fields differ in what aspects of the world of ideas they are concerned with.
Contemporary philosophy of language is concerned with matters that don't
have apparent overlap with contemporary foundations of mathematics.
Your postings don't have any relevance to the foundations of mathematics -
because there is prima facie none, and no case is made for any such
connection.
Your postings are not contributions to the philosophy of language, nor to
the foundations of mathematics, nor do they clarify any issues in the
philosophy of language or the foundations of mathematics, nor do they
clarify the relationship between the two areas.
That doesn't mean that nobody could make postings of that kind - even great
postings of that kind.
> Friedman says
>
> 1. Such philosophers confuse issues in the philosophy of language with
> issues in the foundations of mathematics.
You continue to do this, and that is the main problem with your postings.
>
> 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
> states.
You have not said anything (new) about what people are thinking when they
say this. Furthermore, what the ordinary language user may think when they
say this does not prima facie bear on any issue in f.o.m. I grant that one
can try to make some case that it does bear on f.o.m., but the burden of
proof is on you, and you have failed to meet that burden for at least one or
two years of postings in this connection - starting with endless complaints
about the standard and elementary Cantor theorem - say in the form that in
every sequence of sets of integers, some set of integers is missing.
One could attempt a novel analysis of what ordinary people in ordinary
capacities mean by your sentence "there are 3 things on the table", but even
that would still be very very very far from saying anything interesting or
relevant for f.o.m.
Mathematicians have learned from antiquity that if they are going to do any
serious mathematics or its own sake, or for applications - even at any even
slightly competent level - they better not be bogged down by the obvious
limitations of ordinary language. The same is true of scientists and
engineers. This is also true of musicians.
These subjects - mathematics, science, engineering - are not even remotely
representable or appropriately representable in terms of natural language.
That's why the education required in these areas is substantial, intense,
and takes so long. Furthermore, for the overwhelming majority of people, the
thought processes in these subjects are not natural. Generally, one can only
gain professional level competence in such areas with some special affinity
for thinking that the overwhelming majority of people simply do not have.
The overwhelming majority of people obviously have affinity for natural
language. But that is well known not to carry them any significant distance
along the path of competence in mathematics, science, or engineering.
I am sure that you see this through your own education and contacts with
people who actually do mathematics, science, or engineering.
>
> 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.
You try to force them in virtually every posting you make to the FOM. I
admit the possibility that something could be learned from doing this. In
fact, recall the "counting arithmetic" formalization of arithmetic that I
set up some time ago.
For example, a completely standard piece of mathematics that you forced
ordinary language considerations on, is that
in any sequence of sets of integers, some set of integers is missing.
I repeat - what you should do is start with the nature and structure of
actual mathematical thought. Then go from there. Not the other way around.
This might have an effect on the number of postings that you make (smile).
Are you willing to think about the nature and structure of actual
mathematical thought at the level of competent precollege students?
>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".
No. Observations about natural language are simply observations about
natural language. On the fact of it, they are NOT observations about
mathematics or mathematical thought, and certainly not observations about
formal languages of the kind set up in f.o.m.
Mathematical thought isn't conducted within natural language. I don't
believe that it could even be conducted within natural language, without at
least causing a total breakdown in communication and productivity, and
effectiveness for applications.
Again, I admit the possibility of some interesting new connection. But there
is nothing in your postings that suggest any interesting new connection, or
for that matter, any significant connection whatsoever. Attempting to force
some prima facie irrelevant criteria on mathematical thought, over and over
and over and over again, posting after posting after posting, is not helpful
to the FOM list.
> 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.
The above paragraph of yours is not even remotely any kind of explanation of
anything.
>
> 4. Philosophy of language has no "track record", and no obvious prospects
> to success.
>
> None obvious to Friedman, as far as I can see!!!
I notice that you did not put quote signs around item 4. I have no idea what
the context is.
Oh! I can think of one context this applies to, that is relevant here.
Modern [hilosophy of language has no track record in modern developments in
the foundations of mathematics. I will not try to speak for the philosophy
of mathematics.
Of course there is the theoretical possibility that f.o.m. may have
something to gain by considering philosophy of language, but that case has
to be made - and you haven't even begun to make any such case.
>
> 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
> above.
Part of the problem is that your postings suggest a profound unfamiliarity
with the foundations of mathematics. Feeling that you are at least familiar
with the philosophy of language, you try to force relationships that are
unnatural and unproductive and utterly irrelevant.
If this list was called POL, philosophy of language, then your postings
could (not necessarily would) be read in a different light.
>
> 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.
Many people are naturally constrained by the fact that the FOM has a huge
audience of subscribers and readers (FOM archives). They are concerned that
their postings may create a bad impression and perhaps even clog up the
list. This is a natural constraint on irrelevant and misguided postings, but
this natural constraint does not always work.
The internet does have a very useful and relatively new feature. That is the
delete button, and indexing.
When FOM mail comes in under certain authors' names, one has the option of
not opening that mail, and instead deleting that mail. Also, one can go into
the FOM Archives and just open what one wants, or have the postings listed
by authors or threads, and not have to be bothered by irrelevant postings.
Don't you agree that this is a very useful feature of the FOM?
>
> 9. "The vicarious thrill that may be associated with making grand
> declarations of a negative nature one is not prepared to defend, should be
> avoided"
>
> 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
> correct).
>
The vicarious thrill I referred to is also connected with the fact that FOM
serves, for some people, as an outlet for either outright nonsense or
seriously flawed ideas or unconventional "crusades" that cannot be
disseminated through more standard means. As I said above, the standards are
very minimal for an FOM posting. Also, a merely blanket sending out of email
out of context generally is regarded as spam.
I am of course very glad that you have not resorted to spam in order to get
your "message" out.
So under current FOM policy, you are welcome to continue to work within the
minimal FOM rules in order to get your "message" out, and try to get your
"campaign" or "crusade" going.
Harvey Friedman
More information about the FOM
mailing list