[tsotha]

>...but himself falsely asserts that "The use of the phrase 'even number, or the number zero' implies that zero is not even", which is not true in the usual first order logic.

But in English it really does imply zero is not even. As a percentage of the population, just how many mathematicians do you think there are?

[anonymouz]

Without further clarifications it is at best ambiguous in English: Sometimes the "or" is meant to allow both options, sometimes not.

When mathematicians talk in English they usually (by convention) mean the "or" of first order logic (i.e., inclusive or). Since they happen to be the ones talking about even/odd numbers and they are a group of people that do require a language specific enough to have to specify whether the "or" is inclusive or exclusive, it seems like a good idea that such a statement should be taken in this framework.