FOM: Nonmonotonic Reasoning & Posting Surgery

John Pais paisj at
Tue Jun 8 15:28:33 EDT 1999

Reasoning in ordinary language is fraught with reasoner-dependent
nonmonotonic consequence relations.  Here is a fun example (anonymous

1. A man fell from a plane.

2. Fortunately, he was wearing a parachute.

3. Unfortunately, the parachute didn't open.

4. Fortunately, he fell from the plane at a low altitude over a large

5. Unfortunately, there was a pitchfork in the haystack.

6. Fortunately, he missed the pitchfork.

7. Unfortunately, he missed the haystack.

8. ...

As we consistently expand our background information starting with 1,
there is a tendency to jump back and forth between opposite conclusions
regarding the ultimate fate of this skydiver.

This example helps one to see that when responding to a posting it is
important to avoid *contractions* of a posting that may destroy what was
intended by the original author, however well it may help one jump to
one's own intended conclusions and/or extensions. Through membership in
various lists, I've notice that some contributors very skilled in
predicate calculus reasoning, behave as if radical posting surgery was
just as monotonic. Before responding to a posting, in which I quote the
original poster,
I try to ask the question:

Suppose someone came upon *only* my Re: ... of (or my response to)
someone else's ..., does my Re: ... (or my response) fairly preserve the
intent of the original author or does it significantly distort the
original author's intent (e.g. as a consequence does it attribute a
position to the original author which he or she did not intend or may
find odious)?

*** Example 1 ***

             FOM: surreal numbers
             Mon, 24 May 1999 20:39:04 -0400 (EDT)
             Stephen G Simpson <simpson at>
             Department of Mathematics, Pennsylvania State University
             fom at
             conway at

[Here below, Steve claims to be quoting me, but I didn't write these
three consecutive lines. The surgery on and Frankensteinian reassembly
of my original posting with the resulting nonmonotonic consequences,
quotes me as quoting Harry Gonshor as claiming to introduce the surreal
numbers as a new structure. Nothing could be further from the truth.
Gonshor's trying to provide motivation for writing and reading his book,
which can serve as a vehicle through which a general audience of
mathematicians can easily acquire knowledge of a new structure--to them.
Steve unfortunately produced a contraction of my original posting, which
fit nicely with the conclusion he wanted to jump to, spurious (and
odious) as it may be. My original posting:]

John Pais 24 May 1999 18:50:34

 > Harry Gonshor's book "Introduction to the Theory of Surreal
 > Numbers," CUP 1986, ... ``the enrichment of mathematics by the
 > inclusion of a new structure with interesting properties.''

But the surreal numbers were *not* a new structure.  They were (and
are) isomorphic to the saturated real closed ordered fields.  This is
easy to prove.  See my posting of 21 May 1999 19:59:44.  Correction to
that posting: I used Tychonoff's theorem, but it would have been more
appropriate to cite the Rado selection lemma.

So apparently even as late as 1986, the followers of Conway were not
aware of the relevant general model-theoretic results and
constructions, which were first published in the 1950's or early
1960's and expounded in model theory textbooks in 1972 (Sacks) and
1973 (Chang/Keisler).

Today, in 1999, are they by now aware of those old model-theoretic
results and constructions?

-- Steve

*** Example 2 ***

             FOM: formalization; Pais/Gonshor confusion
             Mon, 7 Jun 1999 14:45:01 -0400 (EDT)
             Stephen G Simpson <simpson at>
             Department of Mathematics, Pennsylvania State University
             fom at

[Here below Steve contracts my original posting in such a way as to
destroy the context and main import of my original question, and to
apparently answer one he liked better. My original posting:]

John Pais 06 Jun 1999 11:17:50

 > is the 'foundational' activity I describe above in 3 and 4 within
 > the scope of the FOM list?

The question of elucidating the precise relationships among (a)
informal non-rigorous mathematics, (b) informal rigorous mathematics,
(c) formalized mathematics, is certainly of interest with respect to
f.o.m. and therefore within the scope of the FOM list.  I would not
assume that this is an easy question.  If Pais and/or Tragesser have
anything coherent to say vis a vis this question, that would be most
welcome.  Have they done any research along these lines?


-- Steve


Steve--Please be more careful.
John Pais

P.S. When I ask a question it's ok for you to explicitly say 'no' ;-)

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