If Mr. Black and Mr. White both individually believe they are right, which one is right

Mr. Black believes "X" to be true
Mr. White believe "Y" to be true
They cannot both be true

Can we philosophically come to a decision? Please give your arguments as to how you decide.

Thank you for your time and have a great evening

The key to this comes from the phrase "they cannot both be true".

Because you have said that one is definitely right then this means that
a) X is true implies Y is not true and
b) Y is true implies X is not true

This means that the statements X and Y are "mutually exclusive". x implies "not y" and vice versa.

However, and this is the important bit, what the individuals "believe" is irrelevant in terms of whether X or Y is true as a statement. For example, I might believe that all dogs have 5 paws. The statement "all dogs have five paws" is false, but I still might believe it. Opinion is not fact.

You might wonder what te point of this is, but what is useful is that because you know that x and y are mutually exclusive you can prove X right by proving Y wrong or vice versa.

Hope that is helpful

Best wishes Chris

They may both be wrong, but without further context, we can't determine who is in fact right. Just because one believes that he/she is right doesn't make it so.

Hmm, if they are both incorrect, maybe "Z" is true?

But does Mr. Orange need to come along to make that statement?

Why can't they both be true? Perhaps with a careful definition of terms, we call all agree.