Please see “Strongly-normalising agents” for a follow-up.
Throughout much of MIRI research work, there is an underlying assumption that a consistent system cannot prove its own consistency.
While it is usually acknowledged that the above assumption applies only to systems as strong as Peano Arithmetic (PA), it is done only in passing, with little consideration for the possibility of using other systems. Girard’s system F appears merely as a footnote, while Willard’s self-verifying systems merit just a brief mention. (YH2013, pp.6,9,18; F2013a, p.1; F2013b, p.1; FS2014, pp.3; FS2015, p.4b)