The part of the sentence 'cannot be convinced that' is correct and usable in written English.
It expresses strong disbelief towards an idea or suggestion. For example, "I cannot be convinced that this plan is the best option for us."
In the case of Syria, Moscow cannot be convinced that U.S. motives are driven purely by the humanitarian calamity that Assad created.
Unless football gives that signal and does so quickly, we cannot be convinced that the game is finally ready to move into the 21st century.
Yet virtually all (93%) say they cannot be convinced that global warming is happening and attempting to change their minds through argument is likely to cause them to defend their views even more strongly.
He does not believe anything has any value other than its fiscal one, so he cannot be convinced that culture, documentaries, drama, comedy and music are of any worth in and of themselves.
Though there are a lot of people out there who are incredibly bullish on voice-first interfaces, I'm convinced there is a very real danger of them becoming a huge fad because people cannot be convinced that they are indispensable.
As a result of this false yet dominating image, many have not seen, "and therefore cannot be convinced that there exists a quiet, self-respecting, dignified class, …of cultivated tastes and habits…" among Negroes, (VAJC, 149).
[An editor] liked it and fixed up a piece and the fiction staff liked it and they held it about four months and I thought they were going with it and then I got a note that said, 'David cannot be convinced.' That was given me on Christmas Eve on a Muslim island off the coast of Kenya.
A mixed approach is not recommended but some enterprises may find it necessary because of different customers that cannot be convinced of the genius of a single method for an enterprise.
My Christmas present was that: 'David cannot be convinced.'.
He later concluded that those voters are virtually untouchable, in that they simply cannot be convinced to take "personal responsibility and care for their lives".
Still, if you cannot be convinced — if you are so narrow-minded that you can't accept me simply because I left the vast majority of you dead or crippled — then I suppose I will take my leave.
