[FOM] "Proof" of the consistency of PA published by Oxford UP

Charlie silver_1 at mindspring.com
Wed Mar 4 15:34:03 EST 2015

	Consider the axioms of Peano Arithmetic minus the induction schema, plus Robinson’s axiom, which says that if x differs from 0, then it’s a successor.  Every one of these axioms is “obviously true” for the natural numbers.   One might say — I’m *not* saying this —  that since every single axiom is obviously true of the natural numbers, plus since they do not *seem* to interfere with each other, the entire system (Q) *must be* consistent.   If we wished to dignify this reasoning by calling it a real proof, we could say it’s a proof of the consistency of Q “by intuitive inspection”.

> On Mar 2, 2015, at 6:51 PM, Timothy Y. Chow <tchow at alum.mit.edu> wrote:
> Gyorgy Sereny wrote:
>> I would like to inform you about a strange publication.
>> I have just come across a book newly published by
>> Oxford University Press:
>>   The Consistency of Arithmetic: And Other Essays Hardcover
>>   24 Jul 2014 by Storrs McCall (Author)
> I have to agree with Gyorgy Sereny that the first article in this book is strange.  Here I mainly want to point out that the full text of the article is linked from the author's website:
> http://www.mcgill.ca/philosophy/people/faculty/mccall
> Or you can go directly to the Word document:
> http://www.mcgill.ca/philosophy/files/philosophy/the_consistency_of_arithmetic_feb_10_2011.doc
> Skimming through the paper, I do not see any interesting mathematical insight.  I would characterize it as an argument for the consistency of PA based on physical intuition.  Perhaps there is an audience for this sort of thing, but I'm having trouble imagining one.
> Tim
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