This statement that you made, that "truth can never be objective," is this statement a subjective statement? Or is it always true? If it is subjective, then the opposite could be true, that "truth is always objective." On the other hand, if this statement is an objective truth, then objective truth is possible. Either way, the statement "truth can never be objective" is self-refuting, and shows that truth is always objective.
Again, I disagree. Truth is not objective, in and of itself, because when you logically introduce truth as objective it is limited by the fact it is seen subjectively as a hypothesis. It is indifferent to existence in the sense of actuality, (i.e., it logically cannot be objective, hence absolute, and hypothetical together).
Yes, you are correct, that it lacks flexibility. It is always true that 2+2=4, and this is an inflexible truth that does not account for various values and opinions...
Exactly, mathematics, in and of itself, is objective and absolute. 2+2 never equals 5. Truth, however, is speculative and abstract. Even when claiming truth is objective, we are, as previously mentioned, subjectively presupposing the objective and the hypothetical together.
This statement that you just made, is this statement to be applied to everyone, or just to you? If this statement is to be applied to everyone (as it presumes to be), then it is an objective truth that is true for everyone. But if it is only true for you, then it is OK for me to hold to objective truth. Either way, objective, absolute truth wins out.
See, what happens is that all this "true for you, but not for me" statements, and the "truth is relative" stuff sounds nice at first, but what is actually happening is that the people who say these things are standing on the pinnacle of their own truths, that they hold to be objective, and ask everyone else to believe. The person who says "truth is relative, not objective" is making a statement that is supposed to be true for everyone.
Again, I disagree. To be sure truth exists, but our perpetual striving to attain truth, cannot be understood metaphysically. Think of it this way. In the ethical sense, striving to attain something as abstract as truth is really the representation of the constant learning by existing individuals. What do we know? We know that truth exists, although it is abstract, and we will never really know all that it entails. We also know that we exist. We are "real" and truth is "real", but striving after truth is nothing more than realizing truth exists abstractly. Which again leads to the subjective conclusion that "what is true for me, may or may not, be true for you".