[FOM] Re: FOM currents

Harvey Friedman friedman at math.ohio-state.edu
Wed Oct 15 11:09:51 EDT 2003

Reply to Buckner.

On 10/11/03 11:49 AM, "Dean Buckner" <Dean.Buckner at btopenworld.com> wrote:

> Reply to Friedman, Tait, Davis
> Friedman:
>> .. is the freedom to continue irresistable [sic]?
> Certainly not, given there's nothing in this latest tirade except, to
> consider working with Mayberry, the true subject matter of "logic", and an
> exhortation to read Godel, plus plenty of abuse.

I am gratified to hear that the freedom to continue is not irresistable.

However, I am less gratified that you didn't notice what I had written, in
addition to pointing out the very real issues that your postings raise
concerning the conduct of moderated email lists.

I dealt with your suggestion about natural language concerns of the founders
of set theory by displaying some of the contents of the Cantor biography by

You might not have realized Cantor's role in set theory, and that he
actually looked at some mathematics to do his work.

Perhaps you didn't relaize that It was not the result of pondering natural

As I quoted from Dauben:

"Chapter 1, Preludes in Analysis
Chapter 2, The Origins of Cantorian Set Theory: Trigonometric Series, Real
Numbers, and Derived Sets."

Perhaps you didn't notice this:

"Also I repeat that you have presented no evidence that contemporary
philosophy of language has bearing on contemporary foundations of

In addition, I suggested that you try to work with others to make postings
with some intellectual content, with the goal of making at least one with
some sort of relevance to the foundations of mathematics.

 > (i) On "working with Mayberry", I first met John Mayberry 30 years ago
> I was his student, and I learnt much from him over the next ten years.  You
> could say I grew up with the contents of the book he finally published in
> 2000, and to which I frequently refer.

So why don't you work with him now on making your first posting relevant to
the foundations of mathematics?

> As to a "campaign" to change the name back, well, in England we just call
> one tradition "philosophical logic" and the other "mathematical logic", so
> none is really needed, no one is confused.

That may solve an immediate problem of confusion in England at least, but
you still seem to want to campaign for relevance of what you call
"philosophical logic" to the foundations of mathematics.

For that, you are going to have to start by giving examples.

>It's worth adding that the older
> tradition dominates here in England, and we regard mathematical logic as
> particularly American.

This is an email list devoted to foundations of mathematics.

>Someone is bound to question this, so can I cite
> Jeff Pelletier's excellent "A Brief History of Natural Deduction".  He
> writes "British philosophy schools, and those heavily influenced by them,
> tended instead to study "philosophy of logic" [sic] as presented by Strawson
> (1952). ".
> The tradition is very much alive, so why does Tait write that it is dying?

If one were to judge this tradition by your postings, one would come to the
conclusion that it is dead.

However, it is grossly unfair of me to even consider judging this tradition
on the basis of your postings.

Without personally looking into this matter, I would naturally assume that
Bill Tait knows this tradition more than well enough to come to proper
definite conclusions as to its status and value.

Consider the following. Your continued failure to present any relevance of
this tradition to the foundations of mathematics on the major moderated list
devoted to the foundations of mathematics, after being asked to do so, may
well give a very bad impression to the outside community as to the status of
this tradition you call "philosophy of logic".

> *Individuals* by Strawson, is a key text of philosophical logic, OK it was
> written in 1952, but then we had Gareth Evans, whose work is internationally
> respected, and then there is the current generation.  Arthur Prior, from New
> Zealand, then lecturer at Oxford, is also a key figure in this tradition,
> also Peter Geach.

And what relevance does Strawson have to the foundations of mathematics?
This happens to be a book I looked at as a student.
> I believe Mayberry's book itself is influenced by the same tradition.  At
> least, he got plenty of exposure to the Prior/Geach stuff from CJF Williams
> being a regular attendee at Christopher's weekly seminars for many years,
> and there is much in his book to suggest that (I may be wrong).

Perhaps you should bounce your ideas off of Mayberry now, before posting?
> So what is presented here in FOM is very much a US-centric view of "logic".
> And of course Americans are famous for their detailed understanding &
> respect for other cultures & intellectual traditions.

We are better known for intellectual standards, and the rejection of the
importance of tradition for its own sake.

> (iii) On Godel.  As noted, Godel is a peripheral figure in the British
> tradition.  

In the British tradition of what? Chemistry? Music?

Sure this makes sense if one wants to continue a tradition of some sort of
logic that has nothing to do with mathematics, computer science, statistics,
science in general.

I am not adverse to seeing postings from another field - even if it doesn't
have any clear relevance to the foundations of mathematics - PROVIDED it has
sufficient interesting intellectual content. Of course there are limits - I
don't think that even very serious postings on mainstream Chemistry are
appropriate for this list.

>For example he gets 1 column in my (British) encyclopedia,
> whereas Strawson gets 2, Wittgenstein gets 7.  In CJF Williams' book "Being
> Identity and Truth", which as the name suggests covers the core concepts of
> philosophical logic, there are references that include the following
> logicians, in order of citations:
> Aristotle (10, passim), Russell (10, passim), Wittgenstein (8, passim),
> Geach (7), Prior (5, passim), Frege (5), Quine (5), Leibniz (3), Strawson
> (2), Lewis (2), Kneale (1), Ockham (1), Goedel (0)
> The reason for the omission is I suspect Godel's treatment of truth, which
> is alien to the British tradition.

No. The reason is that this tradition you speak of is not concerned with the
foundations of mathematics.

>Also I notice that Prior's history of
> Logic, which includes Strawson, Wittgenstein, Russell, Lukasiewicz, Frege,
> Mill, Aristotle, is remarkably silent about Godel.

Apparently Prior is not concerned there with the foundations of mathematics.
> Ditto for Fred Sommers' book, which is another classic in this tradition
> (Sommers *is* American, btw).   Admittedly it is called *The Logic of
> Natural Language*, but he still manages to reference Quine, Russell,
> Wittgenstein, Dummett, Kneale, Prior, Putnam, blah blah.  Even our own FOM
> "regular" Prof. Slater gets a mention.  But nothing on Godel, I see.

Apparently Sommer is not concerned there with the foundations of
> Only when I turn to Dummett's monumental work on Frege do I at last find a
> reference to "the greatest logician of the 20C".  He gets 4.  But then
> Wittgenstein gets about 100, Zermelo 8, Quine 150, Prior 4, Kripke 30, Geach
> 40 and so on.

Dummet is not (primarily) concerned there with the foundations of
> Note I AM NOT using this to suggest Godel is not actually the greatest
> logician, or that if we repeated this exercise 50 years later, there would
> not be a very different result, just as logic books of about 80 years or
> more ago would have been silent about Frege.  I'm just using these facts to
> question the view of Godel as the greatest *logician* of 20C as being
> "generally held".  It's not, at least not in England.

It is certainly also generally held in England, if you ask people who are
concerned with the foundations of mathematics. Ask, e.g., MacIntyre, Wilkie,
Zilber, who are at Oxford (two of them FRS). MacIntyre recently went to
Scotland. Ask them what they think of the relevance of philosophical logic
to foundations of mathematics (smile).

>I think it has more to do with an entire German
> tradition transplanted to the U.S. at a certain well-known period in
> history, whereas in England we have our own native tradition.

In England, you tend to value tradition for its own sake so that weak ideas
tend to go on for much longer than they would here.

> Tait writes
>> That [philosophy of language] school has very largely been one of
>> off-the-top-of->the-head theorizing, based on no expertise of any kind other
>> than a way with >words
> That is also true.  But are we going to say the same of Geach, Strawson,
> Sainsbury, Evans, to name a few?  The analytic (Oxford) tradition is still
> THE dominant school of philosophy in England, and it is a great school, with
> a proud history.

The only one of the main British figures that I KNOW was concerned with the
foundations of mathematics is Bertrand Russell. He is the greatest
philosopher of the 20th century, and he would obviously have thought of
Godel as the greatest logician of the 20th century. I read his remarkable
"Introduction to Mathematical Philosophy" in high school, where he gave a
very clear outline of basic foundations of mathematics, and raised the issue
of the logical status of the axiom of choice as a pretty definite problem of
great importance. Also Godel, in one of his very few philosophical papers,
titled it "Russell's Mathematical Logic".

I would surmise that Godel would have thought Russell to be the greatest
philosopher of the 20th century, although, that probably should not be
regarded as all that complimentary to Russell. I say this on the basis of my
recollection of a conversation I had with Godel in 1974(5?) when I visited
IAS briefly. Of course, judging from quotes presented to us by Urquhart, and
other sources, Godel regarded Wittgenstein as insipid (at least regarding
foundations of mathematics, possibly more broadly).

Harvey Friedman 

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