[SystemSafety] Logical difficulties in mathematics

[Martyn Thomas]

In this context, may I recommend /Proofs and Refutations  /by Lakatos?

Martyn

On 15/02/2019 18:21, Peter Bernard Ladkin wrote:
>
> On 2019-02-15 15:07 , Derek M Jones wrote:
>> Perhaps somebody ought to tell mathematicians about formal methods.
>>
> Leslie Lamport has been on this thirty years ago. I was at a talk he gave in Berkeley in which he
> pointed out a mistake in the intro to John Kelley's book Topology, then a pervasive graduate
> textbook, which he claimed showed that mathematicians were a lot less careful about proofs than (he
> suggested) they ought to be. There ensued a riveting open discussion with VelVel Kahan.
>
> Those were the days! Dick Karp was the only Turing Laureate at the talk, but there were three more
> to come - Kahan, Manuel Blum and Leslie.
>
> The debate had the usual content. Let's see if I remember:
>
> LL: Here's the mistake
> WK: But it's not important. People who learn topology know how to fix it.
> LL: Kelley apparently didn't even know it was wrong; his book has been through a number of editions.
> What are we supposed to make of that in terms of rigor in math?
> WK: He didn't pay attention to it because his (correct) mathematical intuition told him the general
> theme he was addressing was being handled in the right way.
> LL: How are students, who don't necessarily have that intuition and are trying to find out if they
> do, supposed to handle it? Apparently they all suck it up/have all sucked it up for decades. Glossed
> over a mistake because "it's in Kelley". Is this how "rigor" is supposedly taught in mathematics?
> Something is missing. Computer scientists now know what rigor is, and much of mathematics does not
> have it.
> WK: There is nothing really wrong. The people who know the subject gloss over it because it is
> generally right and the individual details are a homework exercise, even if they are not correctly
> portrayed in the text.
>
> And so on. It is eerily parallel to discussions I have had more recently with engineers in standards
> committees: "it might be wrong, but the general idea is *practical*". "If you agree it is wrong,
> then why don't you fix it?"
>
> PBL
>
> Prof. Peter Bernard Ladkin, Bielefeld, Germany
> MoreInCommon
> Je suis Charlie
> Tel+msg +49 (0)521 880 7319  www.rvs-bi.de
>
>
>
>
>
>
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