My definition of "objectivity" is "the approach towards a philosophical matter that seeks to minimise the role of the subject in said matter".
For example:
If I say "two plus two equals four", I'm being objective. My statement should be true regardless of who is saying it, who's doing the maths, etc.
If I say "In my opinion, green apples are great", I'm not being objective. I'm being subjective: I'm acknowledging that the statement "green apples are great" is accurate for one subject (me), but it might not be accurate for other subjects (perhaps you don't like green apples).
what do you think of it?
Truth is objective and should be handled objectively. Gravity doesn't stop working because you're in a bad mood; 2+2 doesn't fluctuate between 3 and 5 depending on the observer; either a past event happened, or it didn't.
Other philosophical matters are better handled subjectively. For example, morality; something can be good or bad depending on the subject, and there's no way to handle this objectively.
If I say "two plus two equals four", I'm being objective. My statement should be true regardless of who is saying it, who's doing the maths, etc.
Even this is quite subjective, as it builds on the (subjective) acceptance of axioms. To most reading this, they would've been educated using the 8 Zermelo-Fraenkel (ZF) axioms, with the controversial 9th axiom of choice.
I disagree that this is subjective. Even if someone hypothetically doesn't accept the ZF[C], the statement still accurately describes reality, in a way that doesn't depend on the subject. For example, you can't start with two apples and two oranges and have five or tree fruits.
The volume of a mixture cannot be described by a simple sum of the volume of its components. As such, this does not make the statement "1+1=2" false in this situation; it's still true but irrelevant, there's no "+" here on first place.
Additionally, let us suppose for a moment that the reasoning above is invalid. Even then, it's still an objective matter - because then the truth value of "1+1=2" would vary depending on the object (are we dealing with apples, or liquid mixtures?), not on the subject (who's mixing the liquids - you or me?).
It's subjective as in: imagine a different society/species constructing a sense of reality and computation, based on liquid mixtures. Their basis of computation, their axiom is 1l of alcohol + 1l of water = 2l of mixture.
They meet us, and we exchange ideas.
They go: of course 1 + 1 = 2, look at our mixture. For fruits, apples and pears? That's outside of normal arithmetics, it's an exception. There's no + there, as you're not mixing. You have to correct for the non mixture nature, the answer will be larger than 2.