[Math] Mendelson’s *Mathematical Logic* and the missing Appendix on the consistency of PA

ho.history-overviewlo.logicsoft-question

A very soft question, but I hope not out of order here.

In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of Schütte's (1951) variation on Gentzen's proof of the consistency of PA. This is intriguing stuff, crisply and quite accessibly presented. The appendix is, however, suppressed in later editions (in fact, from the second onwards), even though there is plenty of room given to other materials and a new appendix

Now, a number of people have said that the appendix is one of the most interesting things about the book. I agree. I too remember being quite excited by it when I first came across it a long time ago!

So: has anyone heard a folkloric story about why Mendelson suppressed the appendix? I've never heard it suggested that there is a problem with the consistency proof as given.

Context, if you are interested: I asked this a couple of weeks ago on math.SE (without getting an answer) when starting to write up a survey of some of the Big Books on Mathematical Logic that will become part of my Teach-Yourself-Logic Guide (mostly for philosophers, though others might be interested), and I'd got to Mendelson. You can get the current version of the Guide by going to http://www.logicmatters.net/students/tyl/

Best Answer

Before posting this question I did search around a bit (probably inefficiently and certainly quite ineffectively) to see if I could find an email for Elliott Mendelson to ask him directly! But anyway, he picked up my similar query on FOM and very kindly wrote to me:

I was intrigued by your comments about the consistency proof of PA that appeared in the First Edition of my logic book. I omitted it in later editions because I felt that the topic needed a much more thorough treatment than what I had given, a treatment that would require more space than would be appropriate in an introduction to mathematical logic.

I can understand that. Though I think the pointers he gave in that Appendix did spur on quite a few readers to find out more, so I still think it was a Very Good Thing, and it was perhaps a pity to drop it.

[Prof. Mendelson has kindly allowed me to quote him.]

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