[FOM] FOM currents
Harvey Friedman
friedman at math.ohio-state.edu
Fri Oct 10 21:37:35 EDT 2003
Can a series of postings that is
i) utterly devoid of any significant connection with the foundations of
mathematics;
ii) not bearing on the relationship between the philosophy of language and
the foundations of mathematics;
iii) generally having no identifiable intellectual content;
iv) using the rhetorical methods of quoting authorities and making stark
declarations without argument.
be exposed as such on the FOM email list, so clearly that the author of the
series of postings, perhaps with the benefit of feedback from many scholars,
at least implicitly acknowledges the actual state of affairs by putting an
end to the series of postings? Or is the freedom to continue irresistable?
More generally, can a series of postings that is
i) utterly devoid of any significant connection with the topic of a
moderated email list;
ii) not bearing on the relationship between any other significant subject
and the topic of the moderated email list;
iii) generally having no discernible intellectual content;
iv) using the rhetorical methods of quoting authorities and making stark
declarations without argument.
be exposed as such on the moderated email list, so clearly that the author
of the series of postings, perhaps with the benefit of feedback from many
scholars, at least implicitly acknowledges the actual state of affairs by
putting an end to the series of postings? Or is the freedom to continue
irresistable?
The answer to such questions may well have bearing on optimal ground rules
for moderated email lists which attempt to be open forums.
For example, experience may show that the standards for postings in
moderated email lists of a scholarly nature may have to be raised, or raised
considerably, in order to avoid getting clogged with unproductive material.
Such unproductive material may have negative effects. One is that it may
confuse students who are trying to learn about the subject, with a possible
view towards doing professional work in the subject.
I certainly am not deterred from making postings on the FOM, including most
of my latest research efforts in f.o.m., simply because of the presence of
contentless postings, even if the prospects for their ending appear dim.
However, that is me, and that is not necessarily true of other people. In
normal academic life, one simply is not exposed to such material in any
comparable sense. One is protected from it.
It is inevitable that truly important articles will appear in Journals which
publish unimportant articles in the very same Journal issue. But this isn't
a comparable situation. This is because of a generally high standard for
publication in Journals.
It would of course defeat most of the main purposes of the FOM to enact any
kind of standards even remotely comparable to that of Journal articles.
The way that this situation is clearly avoided in the vast preponderance of
Journals is that the referring process generally weeds out articles that
constitute *negative progress in the field*. At least if a Journal article
is uninteresting and/or uninspiring, it will be generally be regarded as at
worst harmless, in that it does not represent a step backwards. Its
publication does not harm the field. It, at worst, adds nothing to the
field.
If sometime in the future, this problem gets out of control, not only for
the FOM, but for moderated email lists generally, then a higher standard
which excludes postings representing *negative progress in the field*,
perhaps should be considered. Of course, one will need both theoretical and
practical criteria for making such an assessment.
On 10/10/03 1:50 PM, "Dean Buckner" <Dean.Buckner at btopenworld.com> wrote:
>... Set
> theory was thought, by its founders, to be a formalisation of how we
> ordinarily think about numbers.
A well regarded biography of Cantor - probably the leading biography - is
Dauben, Georg Cantor, his mathematics and philosophy of the infinite.
See Dauben, table of contents:
Chapter 1, Preludes in Analysis
Chapter 2, The Origins of Cantorian Set Theory: Trigonometric Series, Real
Numbers, and Derived Sets.
and ten more chapters.
According to this account, Cantor was not driven by any ordinary language
concept of number. Cantor was driven by the need for some extended concept
of number (among other things), going far beyond anything in ordinary
language. In particular, he was driven by the deep contemplation of some
highly nontrivial and involved actual mathematics of his time (infinite
trigonometric series).
Also, completed infinite sequences are all through even early Cantor, as
well as the vast preponderance of his contemporaries.
So, at least prima facie, even your very last posting would appear to
represent negative progress, just on the basis of these two relatively clear
"points" that you make. This doesn't include the seriously obscure "points"
that you make.
> As to what is expressed by elementary English versus mathematical language,
> are you saying "two things and two things are four things" is true, if it is
> true, for a different reason than "2+2=4" is true? Do they NOT express the
> same fact? So if mathematics really is talking about an entirely different
> fact, what is that? What is mathematics talking about?
I have not seen anything in your postings that shed light on these matters.
>Agreed, there might
> be very complex and subtle facts that only complex and subtle mathematics
> can express. I have conceded this point some time ago (in order to avoid
> dull polemics). At the elementary level, we seem to be talking about the
> same thing. And the "foundations of mathematics", for philosophers,
> involves the question: on what ultimate basis can such mathematical
> statements as these be called "true"? "Why and how are mathematical
> statements true?"
>
> On what f.o.m. actually is - there seems to be a fundamental disagreement.
> My understanding is that ...
If you have need to clarify your understanding of major work in f.o.m., I
suggest that you read the collected works of Kurt Godel, volumes 1-5. They
are heavily annotated by contemporary f.o.m. professionals.
This will give you a good idea of what f.o.m. looks like at the highest
professional level.
I see that you quote Mayberry:
> ". there is a surprisingly widespread misunderstanding among mathematicians
> concerning the underlying logic of the axiomatic method. The result is that
> many of them regard the foundations of mathematics as just a branch of
> mathematical logic, and this encourages them to believe that the foundations
> of their subject can be safely left in the hands of expert colleagues. But
> formal mathematical logic itself rests on the same assumptions as do the
> other branches of mathematics: it, too, stands in need of foundations .."
> (Mayberry)
Have you considered working with Mayberry to add content to your postings?
Merely taking a quote that like that out of context doesn't add content to
your posting.
>
>> In common with other mathematicians, Friedman has a number of fundamental
>> misconceptions about "philosophy of language".
>
> You asked for evidence of this.
I repeat that you have presented no evidence that contemporary philosophy of
language has bearing on contemporary foundations of mathematics. I am
waiting for this evidence, although I can still sleep without having it
(smile). Perhaps this is your evidence that "Friedman has a number of
fundamental misconceptions about philosophy of language"?
Do Urquhart and Tait and Heck have "fundamental misconceptions about
philosophy of language"?
Does Buckner have fundamental misconceptions about the foundations of
mathematics?
Does Buckner have fundamental misconceptions about the relationship between
foundations of mathematics and philosophy of language?
In fact, in all of your postings, you haven't even presented any findings of
any kind in foundations of mathematics, contemporary or otherwise.
Without a presentation of any findings in f.o.m., you can't begin to make a
case for the use of philosophy of language in f.o.m.
>Evidence for this comes from the silly
> things that mathematicians write, mostly in private mailings to me.
Perhaps the mathematicians that make private mailings to you are a skewed
sample of mathematicians. The Buckner-corresponding mathematicians form an
interesting subclass of mathematicians with perhaps rather unusual
properties (smile). E.g., is their cardinality even or odd or even prime?
(smile)
>... Also the hot air that
> rises in vast quantities whenever those who are patently not philosophers
> indulge in what they imagine is philosophical talk. These are hugely
> cringe-making but I've avoided embarrassing their authors out of politeness
> and sensitivity. Also they would hardly get the joke.
Might Buckner also say this?
"Also the hot air that rises in vast quantities whenever those who are
patently not mathematicians [including Buckner?] indulge in what they
imagine is mathematical talk. These are hugely cringe-making but I've
avoided embarrassing their authors out of politeness and sensitivity. Also
they would hardly get the joke."
>
> As a final piece of evidence I simply quote Mayberry again " . the
> complacency among mathematicians concerning the foundations of their subject
> has had a deleterious effect on philosophy. Deferring to their mathematical
> colleagues' technical competence, philosophers are sometimes not
> sufficiently critical of received opinions even when those opinions are
> patently absurd".
Have you considered working with Mayberry to add content to your postings?
Merely taking a quote that like that out of context doesn't add content to
your posting.
>> Have you thought about campaigning for a change of name [of "philosophy
>> of language"]?
>
> Yes, to the name "LOGIC". which before the 1930's was the universally
> accepted name for the branch of philosophy now called "philosophy of
> language". E.g. Mill did not call his book "A system of linguistic
> philosophy"). If I used it, however, it would nowadays be confused with
> something quite different.
And since every logician I know would cringe at putting what you call
philosophy of language into the category of logic, how do you intend to
fight your campaign?
Just what do you think Godel would have thought of your campaign to call
(what you call) philosophy of language logic? I am sure you don't need to be
reminded of the generally held opinion that Godel was the greatest logician
of the 20th century. The view that Godel was the greatest contributor to the
foundations of mathematics of the 20th century is virtually universally
held.
>> Contemporary philosophy of language is concerned with matters that don't
>> have apparent overlap with contemporary foundations of mathematics.
>
> I still need to understand what "contemporary foundations of mathematics"
> means.
As I said earlier, start with Godel, Collected Works, volumes 1 - 5.
>Why does Mayberry say that contemporary mathematicians are
> "complacent" about the foundations of their subject? Mayberry's book
> itself, the first two chapters of which are a profound analysis of ordinary
> mathematical language, is called "The Foundations of Mathematics in the
> Theory of Sets", and it was published in 2000, so I assume he is also
> concerned both with "contemporary foundations of mathematics" and
> "philosophy of language". And there's that title again, by the way!!
> Nothing about bees!!! Ray Monk, a respected philosopher of language, is
> also writing a book on foundations of mathematics. So all in all I see
> PLENTY of overlap.
Have you considered working with Mayberry to add content to your postings?
Merely taking a quote like that out of context doesn't add content to your
posting.
>> Mathematicians have learned from antiquity that if they are going to do any
>> serious mathematics for its own sake. they better not be bogged down by the
>> obvious limitations of ordinary language. . This is also true of
>> musicians.
>
> Musicians? WHAT are you talking about? We can embed ordinary FOL
> statements into a that clause such as
>
> John thinks that (E x, Ey) [ Fx & Fy & x <> y ]
Yes, and one can take Godel's literal unedited collected works, call it
alpha, and consider
Buckner thinks that alpha.
Is that an advance in the philosophy of language? (smile).
>> 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.
>
> I might say exactly the same, if by "foundations of mathematics" we
> understand that tradition which began with Frege, through Russell and
> Wittgenstein, which you don't, from many of your remarks, show a deal of
> knowledge.
I again refer you to Godel's collected works if you wish to gain some sort
of familiarity with f.o.m.
>I have a profound unfamiliarity with "reverse mathematics", I
> admit. I'm trying to learn more but the natives aren't that friendly and
> show a profound contempt for other tribes, or try to set upon them & seek to
> kill them.
Forget about reverse mathematics. You are not ready for that. Start with
Godel's collected works, volumes 1-5.
>
> Buckner
>> why did [f.o.m] 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.
>
> Friedman:
>> The above paragraph of yours is not even remotely any kind of explanation
> of
>> anything.
>
> I was alluding to a commonly held explanation of the origins of f.o.m, which
> I assumed would need no further comment. For more, search in Google using
> "Frege" plus any of the following key expressions - psychologism - "third
> realm" - compositionality - Wundt. For a VERY good background, which
> explicitly connects 19C work in language to Frege's foundational work in
> mathematics, try http://www.maths.qmw.ac.uk/~wilfrid/demorgan00.pdf by
> Wilfred Hodges.
Start with Godel's collected works, volumes 1-5.
>> . 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.
>
> It's not "mine", for the hundredth time. See again the list of references
> of published work, by respectable philosophers, in my previous posting. I'm
> just an underlabourer, reporting on the progress of others (some of whom are
> regular private correspondents).
Have you considered working with Mayberry to add content to your postings?
And/or the others whose progress you cite?
>> [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."
>
> This is a standard and elementary theorem of ordinary language, too! Why
> should I make complaints about it? My complaint is about the idea that any
> set of integers constitutes ALL integers.
The set of all integers has every integer in it (as an element). Yes, there
are some people who are uncomfortable with this idea. Not Cantor, and not
the overwhelming number of mathematicians. But certainly there are some.
E.g., Sazonov. But note that Sazonov's postings have some connection with
the foundations of mathematics, even though - in my opinion - he has not
convinced anyone to be any more skeptical about the set of all integers than
they were before they read his postings.
Have you considered working with Sazonov to add content to your postings?
Harvey Friedman
More information about the FOM
mailing list