[FOM] "Hidden" contradictions

[Carl Hewitt]

Mark Steiner raised some interesting questions in his post about Wittgenstein versus Turing.

A very important point that Wittgenstein made on the subject was:  "...even at this stage, I predict a time when there will be mathematical investigations of calculi containing contradictions, and people will actually be proud of having emancipated themselves from consistency."

Today, we have such inconsistency robust (paraconsistent) calculi.  There are whole conferences devoted to the subject, e.g., Inconsistency Robustness 2011/2014 (see http://robust11.org and http://ir14.org) and there are even scientific societies (e.g. iRobust see http://irobust.org).  However, the subject is still in its infancy.

Inconsistencies are pervasive in large software systems.  Unfortunately, these inconsistencies cause "bridges to fall down" with alarming regularity.  In some cases, it has been impossible to trace back which inconsistencies caused a disaster.  See the ACM Risks Forum newsgroup moderated by Peter Neumann for an ongoing saga. Some contradictions have been discovered using subtle reasoning.

Initially attempts were made to deal with software inconsistencies in large software systems by "sweeping them under the rug" by denying that there are "real" inconsistencies.  Failing this, the following were attempted:
* developing a procedure to prevent the introduction of inconsistencies
* developing a procedure to systematically find and eradicate inconsistencies 

Neither of the above have been very successful in reducing the pervasiveness of inconsistencies.  Consequently, it is expected that inconsistencies will remain pervasive in large software systems.

Regards,
Carl Hewitt