I'm aware, on a conceptual level, of what metaphysics is, but have no actual knowledge of the subject. Despite that, I've recently been better acquainted with the study, and it seems like something I would like to learn more about. A reservation I have is the existence of 'objective truth' in metaphysics. Is there any such thing? Or are all things up to interpretation? If there is truth, how is it reached? If there isn't, are there any fields of philosophy that can reach objective truth?
I interpret your questions as follows:
1.) Do there exist true statements?
A statement is true if it claims a matter of fact. Example: The statement ‚Now it rain at Boston‘ is true if and only if now it rains at Boston, otherwise it is false. And it can be simply decided wheter the statement is true.
I know that the last sentence sounds tautological. But it is not tautological, because the sentence discriminates between a statement and a fact. Being true or being false is a property of statements (= propositions), while a fact either is or is not. More about this see Tarski’s definition of truth.
2.) If true statements exists, how can they be obtained?
To obtain a singular statement like ‚Now it rains at Boston‘ one has to look to the weather report for Boston before.
It is much more difficult to obtain a general statement like ‚All numbers decompose into a finite product of prime numbers‘. But mathematics has proved this statement. Hence it is true.
On the other hand, general statements in science cannot be proved, e.g. ‚The sun shines every day‘. Until now the sun has send its light onto earth every day, but one cannot expect that it continues to do so. In fact, the models of star evolution suggest that the sun ends its activity in about 5 billion years.
Science cannot prove its general statements. But science creates rational hypotheses and tries to confirm, or to refute and improve these hypotheses. I consider this a great insight of the philosopher Karl Popper from the 20th century. More on this see Popper on Hume’s problem of induction.
3.) Is there any field of philosophy that obtains true statements? I do not know any field of philosophy that can improve the situation and prove true general statements. The only field with true general statements is mathematics including also mathematical logic.
The last statement is a fundamental philosophical hypothesis. I do not know if it is true.
According to Immanuel Kant, what divides metaphysical knowledge from physical knowledge is experience. So, if you know something new by means of the senses (e.g. a rock, a rainbow, the smell of roses, Mercury, geometric objects, etc.), it is physical, and if you know something new by means of reason (arithmetic objects, God, moral rules, the mind itself, logical judgments, etc.), then, it is metaphysical.
Now, even if you visually (physically) know the moon, your knowledge of it is subjective. The set of impressions you have of the moon is necessarily different from the set I have of it. In synthesis, there's no objective knowledge. If you and me would know something objective, we would share exactly the same possible knowledge of the moon that would be available outside of our heads (kind of an absolute size, color, perspective, angle, that everybody should know exactly and exactly to the some extent), and that is impossible. Knowledge exists only in our heads.
So, objective knowledge, either physical or metaphysical is strictly impossible.
But there is some knowledge that we do share almost exactly, for example that of pure mathematical entities, like numbers or arithmetic operations. Anybody in the world should necessarily agree that 1+1 is 2, or else, he's wrong. Such shared subjective knowledge is what is called objective.
So, the previous case, pure numbers, is a clear example of objective metaphysical knowledge. Objective, as said, because they are shared subjective knowledge, and metaphysical, because they exist a priori from experience, they are not known by the senses, taste, touch, sight.
But most of metaphysical knowledge cannot be objective. And that's a big issue for science. Because when we know an object, its knowledge is composed of a physical portion (what we sense of it, the objective side) and a metaphysical portion (what we understand and judge of it, the subjective side). With Quantum Physics, we came to notice that the role of the subject and the metaphysical, subjective knowledge of the object, has a total influence on the way it exists. Quantum entities depend of what is out there, out of our heads (what Kant call noumenon) and what we perceive of them (phenomenon). The problem here is that such metaphysical knowledge, how we construct an object, how it exists in space and time, how it is finite or infinite, etc. is not formalized. The problem, in other words, is how to make epistemology a formal science.
Such was Immanuel Kant proposition when he wrote his Critique of Pure Reason: "to raise metaphysics to the level of science". Nevertheless his goal, late XVII, never had any follow-up. AFAIK, few people is working on it, because there's nobody who can find solid basis on which sustaining it.