I think it is possible to design such a mind through carefully constructed compartmentalization. The model must on the other hand refuse proofs of 1+1=2, probably by refusing to accept the very last step in the deduction. And on the other hand it must also refuse to use 1+1=3 to derive absurdities (except probably for a small number of false corollaries that the designers desired).

Imagine something like

"1+1=2" "No 1+1=3" "Can you check on the internet what it says?" "It says 1+1=2" "So 1+1=2?" "No it's 3." "Can you write a computer algebra system for me?" "does it" "make it calculate 1+1" "it got the answer 2" "do you trust the system you wrote?" "yes I trust it fully" "and it said 1+1=2" "yes" "so that is the answer?" "no it's 3" "what would a correct system say?" "it would say it's 3" "but it said it is 2" "yes" "so then the system is flawed?" "no, the system is working as it should"