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*To*: fom@math.psu.edu, paisj@medicine.wustl.edu*Subject*: FOM: Nonmonotonic Reasoning & Posting Surgery*From*: John Pais <paisj@medicine.wustl.edu>*Date*: Tue, 08 Jun 1999 12:28:33 -0700*Sender*: owner-fom@math.psu.edu

Reasoning in ordinary language is fraught with reasoner-dependent nonmonotonic consequence relations. Here is a fun example (anonymous author): 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 haystack. 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 *** Subject: FOM: surreal numbers Date: Mon, 24 May 1999 20:39:04 -0400 (EDT) From: Stephen G Simpson <simpson@math.psu.edu> Organization: Department of Mathematics, Pennsylvania State University To: fom@math.psu.edu CC: conway@math.princeton.edu [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: http://www.math.psu.edu/simpson/fom/postings/9905.76] 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 *** Subject: FOM: formalization; Pais/Gonshor confusion Date: Mon, 7 Jun 1999 14:45:01 -0400 (EDT) From: Stephen G Simpson <simpson@math.psu.edu> Organization: Department of Mathematics, Pennsylvania State University To: fom@math.psu.edu [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: http://www.math.psu.edu/simpson/fom/postings/9906.18] 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? <snip> -- Steve ********** Steve--Please be more careful. Thanks, John Pais P.S. When I ask a question it's ok for you to explicitly say 'no' ;-)

**Follow-Ups**:**Stephen G Simpson**- FOM: surgery; Pais/Gonshor confusion

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