[FOM] "Hidden" contradictions

Rob Arthan rda at lemma-one.com
Mon Aug 19 17:53:03 EDT 2013

On 13 Aug 2013, at 19:18, Timothy Y. Chow <tchow at alum.mit.edu> wrote:

> Mark Steiner wrote:
>> Are there any historical examples in which inconsistent systems actually yielded false theorems that could have made "bridges fall down" without anybody noticing the inconsistency?

> ...
> More to the point, if your response is that you're restricting your attention to explicitly articulated formal systems that have been widely adopted for use in science and engineering, then the problem is that scientists and engineers never work explicitly in any formal system. 

That is not true. Many computer scientists and engineers work with formal machine-checked specifications and formal machine-checked proofs. Donald MacKenzie's book "Mechanizing Proof: Computing, Risk, and Trust" is an accessible reference with some interesting observations on this.



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