It depends – a phrase that I do not normally like to start an answer with, but here I do - so, it depends on what 2+2=4 means to me, what does it stand for. If the 2+2=4 means a mathematical expression, an arithmetical equation, then this is obvious that my mind is operative precisely within that context. Then I will see no good reason to know more, to listen to some weird but wonderful option, and thereupon change my mind on what is so obviously right, i.e. listen to someone, then ether mathematics is wrong of I am unreasonable - no need of a philosopher or a wizard in logic to come up to me to try to convince me otherwise.
In the human mind, and as it is in the human world, each thing is only relatively known, relatively a certain context, nothing is absolutely known, as nothing can be so defined. A tree is commonly known as an organically alive standing in the forest, and this is precisely what a tree means to all people; this is how it was observed and defined. Now if someone tells me about some tree on the seabed or deep in space, then that someone obviously is not talking about a conventional tree, but about something else, something like, for instance, a treelike structure of calcite or limestone or a cluster of satellites organised in a tree-like formation.
It is possible that someone is talking in signs and symbol borrowed from a wide range of context just to make very good sense of what someone is saying. The use of the mathematical expressions in common language is quite popular, like ‘a prime location’, ‘against all odds’, or ‘division of labour’ etc. The 2+2=4 could be just a symbol to mean 100% accuracy of something or to stand for something else, at a place where there is a gap and such a symbol needs to be inserted.
It is commonly quoted, ‘the whole is greater than the sum of its parts’, i.e. 2+2=5. Then if my mind is open to possibilities, and I have no particular need to remain within the precisely and unmistakably defined context of mathematics, then listing to opinions, apparently erroneously but true in a certain way, would, in fact, enable me to know better.
Our language, as well as the structures of normal thinking, are rich in meaningfulness as they are loaded with ideas, facts, observations, and concepts, purposefully and quite aptly transferred from one original context to be used within another. I do not know proper terms or phrase for this, but this is the fact. The fact is, we would not be able to think meaningfully or make ourselves understand easily if it were not for the reason that we are able to see through the fact, beyond into the abstract, extended, and transferable meaningfulness of things.
We commonly understand that ‘infinity’ is a mathematical concept represented by a specific symbol. But the fact is ‘infinity’ is not part of any mathematical calculation. The concept is philosophical, it is a philosophical question. Mathematicians or physicists use the infinity sign when and where they run out of ink, paper, or ability to go any further or deeper in thought.