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Inconsistency Robustness is performance of information systems withpervasively inconsistent information. Inconsistency Robustness of the communityof professional mathematicians is their performance repeatedly repairingcontradictions over the centuries. In the Inconsistency Robustness paradigm,deriving contradictions have been a progressive development and not "gamestoppers." Contradictions can be helpful instead of being something to be"swept under the rug" by denying their existence, which has been repeatedlyattempted by Establishment Philosophers (beginning with some Pythagoreans).Such denial has delayed mathematical development. This article reports howconsiderations of Inconsistency Robustness have recently influenced thefoundations of mathematics for Computer Science continuing a traditiondeveloping the sociological basis for foundations.  The current common understanding is that G\"odel proved "Mathematics cannotprove its own consistency, if it is consistent." However, the consistency ofmathematics is proved by a simple argument in this article. Consequently, thecurrent common understanding that G\"odel proved "Mathematics cannot prove itsown consistency, if it is consistent" is inaccurate.  Wittgenstein long ago showed that contradiction in mathematics results fromthe kind of "self-referential" sentence that G\"odel used in his argument thatmathematics cannot prove its own consistency. However, using a typed grammarfor mathematical sentences, it can be proved that the kind "self-referential"sentence that G\"odel used in his argument cannot be constructed becauserequired the fixed point that G\"odel used to the construct the"self-referential" sentence does not exist. In this way, consistency ofmathematics is preserved without giving up power.

Inconsistency Robustness in Foundations: Mathematics self proves its own Consistency and Other Matters