This is all just a poetic way of saying that Mathematics does not suffer from the measurement problem, because mathematics is not part of the universe. Poor Max Tegmark could not be more wrong - the universe is not made of maths. Maths is what we make to cope with the fact that we cannot cope with the universe .
The idea of “a truth” is a statement that can be evaluated as true or false and is found to be true. According to Logic, if you have a two statements that contradict each other and are both true, then you can prove anything (using a tautology), so anything and everything can be proven to be true in this case. Generally, scholars, philosophers and mathematicians do not find such a system of ideas very interesting or helpful. To summarize, it is possible to have a system where multiple truths contradict each other, but then logically in this system every statement is true.
Neither logic nor science deal with truth, at least not with the truth of “what is ultimately real”. Let’s say they deal with different truths.
There are no exceptions. It is a rule. It’s a rule of logic. Even in the most radical forms of logic, such as multi-valued logic, where there are more than two truth values, the law of non-contra diction has no exceptions.
No way. An infinite number of things are completely true and completely false and this is obvious.
No. There cannot be multiple contradicting truths.
He is traveling west and he is traveling east cannot at the same time both be true. One or neither can be true, but not both (he could be traveling north, in which case both are false).