Since we do not know if morality has an independent existence, are we morally obligated to know if it exists?
The more general idea behind this question is: if I am unsure about proposition X, am I obligated to find whether X is true or false? The particular sort of obligation you have in mind is 'moral obligation'.
Obligation is defined by oxford as:
i. the condition of being morally or legally bound to do something. ii. a debt of gratitude for a service or favour.
In this context, (i) seems to be the definition to consider, and disregarding the legal aspects of obligation, the idea of obligation is essentially moral. One could also conceive of epistemic obligation, which is arguably an essential characteristic of a rational agent.
When is a rational agent obligated to know a proposition X? I can think of the following scenarios:
i. The agent asserts or denies X. ii. The agent cites X in the justification of some other proposition Y, where X >..>..> Y i.e. X is in the 'justificatory chain' supporting Y. iii. The agent's intention is grounded in a belief that X, and the agent acts in accordance with this intention.
i., ii. are mostly concerned with the epistemic obligation of a rational agent (that he or she possess some sort of justification for their beliefs.) iii. is the sort of moral obligation a moral agent will cite when he/she performs an action.
i. Epistemic obligation entails moral obligation i.e. all rational agents are moral agents (though some moral agents may not be rational) ii. Moral obligation entails epistemic obligation i.e. all moral agents are rational agents (though some rational agents may not be moral) iii. Moral obligation does not bear any relation to epistemic obligation and needs to be independently formulated.
If you are a rational agent, then you are at least epistemically obligated to take a position with respect to i, ii, iii when you assert/deny knowledge that is grounded in some implicitly assumed truth value of these propositions, or act in a way such that your actions are grounded in some implicitly assumed truth value of these propositions.
Furthermore, the question:
Is a rational agent obligated to articulate a justification for his or her assertions/denials/actions?
The answer to this question is much more difficult: depending on what idea of "knowledge" you subscribe to, the answer to this question will vary. A K-reliabilist, for example, might be sympathetic to a rational agent who acts within an implicit moral framework but is not aware of it. On the other hand, someone who subscribes to JTB, will probably demand justification, citing that an "adult, reasonable, rational" individual ought to be able to articulate the reasons behind his or her actions.
If moral obligation is real, then you are morally obligated to act in certain ways, and you cannot do this without first finding out what actions are obligatory and what actions are not.
Therefore, you are morally obligated to find out the rules of morality, if moral obligation is a thing that is real. If moral obligation is not real, then you are not morally obligated to do anything.
So, you may or may not be obligated to find out the rules of morality; you don't quite know.
Obligation may exist independent of the so called "reality" of ethics. You are misusing terms.
Of course, if moral scepticism is correct, then you are not "obliged" to do anything. Perhaps the appearance of "obligation" is a confusion of language.
Any which way, very few moral septics would say that all discourse is in error, or the equivalent. So you may still be rationally compelled to various conclusions, including - but not limited to - ones about the reality, facticity, etc., of ethics.
In the same way that you may be under no "obligation" to answer in a maths quiz, but some answers are nevertheless wrong.
From ethics perspective, there's a modern school of thought called "non-cognitivism" which believes that ethical sentences do not express propositions and thus cannot be true or false. Under this view and further via correspondence of truth, it implies that moral knowledge is not mandatory or even possible, and ethical sentences are primarily emotional expressions of one's own attitudes and are intended to influence the actions of the listener.
Having said that, there's still some subtle difference between morality and ethics, namely a moral precept is an idea or opinion that’s driven by a desire to be good, while ethics is a set of rules that defines allowable actions or correct behavior. For me, philosophy is essentially a moral study to help you find your own desire to be good facing a sea of different metaphysical or phenomenological views to choose from, thus you're still morally obligated to find an answer for your own problem, otherwise what good you're learning it?
Morality is not an object that can have "an independent existence" (a thing-in-itself, see Kant). Morality is a regulation system, that is, it is just a set of rules that regulate our behavior, like religion, formal law and justice, or gang rules.
Without some regulation system, I would be free to offend your child, and he would not be able to react because I can defend myself. But why does society (including you) react? Why do would they normally condemn my actions, and progressively isolate me? Because people follow rules in order to survive. Guess which regulation system are they following when they do so: morality.
Since we do not know if morality has an independent existence [...]
Morality does not exist except in people's heads, it is followed in order to increase the survival probabilities. Morality is relative to a human group. Groups with large probabilities of survival can be said to have the benefit of better regulation systems --which includes morals-- in comparison with other groups. Of course, survival does not depend only on morals. But morals are part of our instinct of survival. Moreover, you are forced to follow the moral rules of the group you live within, so you don't commit risky actions that could isolate you, like as in the example, offending a child.
Am I morally obligated to find out the answer?
No, if you want to be isolated, you can go living in a mountain where no moral rules will be imposed to you, if you take another person with you, you can offend him/her all the time, with consequences that are obvious for most people (you seem to doubt such consequences).
But if you want to have a good life, adopting the moral rules of a society you consider ideal would surely increase your probabilities of survival by increasing your well-being (the calculation of such probability has a huge difficulty).
One could also ask, "Am I permitted to learn what is permitted?" But it would be odd to say, "I am forbidden from knowing what is forbidden."
Now, let us suppose that we already know what is obligated, right, good, etc. so the issue is clarifying our knowledge to ourselves, of understanding what we know. One would not be obligated to do what was not something that is done. So we might thereby be obligated to understand what we know, instead.
But let us suppose we don't know the answers to various particular moral questions. If we knew a priori that we ought to act according to answers to those questions, then, "We only act on those answers if we know them," and there is a (however paradoxical) principle in standard deontic logic that would license us to infer, "We ought to know them," then.
If you are not sure about the existence of immorality, you are not sure about the existence of immorality also, right?
In this mundane world one can find morality and immorality. If you feel that you are obliged to find the answer to one question (about morality), you are equally obliged to find the existence of the other (about immorality).
It may be an obligation if you have to find the truth about the existence of something (including morality) as part of your job.
Because your purpose is to find the existence of morality for your own satisfaction, we can say that it is not morally obligatory.
Again,though you can't, suppose you were able to discover the existence of morality, it would not end there. Others would try to discover the existence of immortality also. Since there is a great possibility for this also, your effort would do no particular good to morality, or especially to society or the world. So you needn't worry about its moral obligation.