Obligations and Duties
We wish to characterize obligations and duties (taken as essentially synonymous) in a more definite way than is typically used, specifically, as pertains to morality, as typically conceived. Many uses of the term have no relation to morality whatsoever. For instance, a legal obligation is merely something demanded of someone by the governing laws which, should he fail to fulfill it, would result in some sort of penalty. If the penalty were absent, the so-called obligation would be rendered irrelevant, as it would be merely up to the disposition of the one obligated whether to fulfill it or not, and no enforcement could be possible. Thus, legal obligations are no more than demands with enforced consequences: it is demanded of the person to do something, and, failing to do so, punishment will result. Another sort is a social or societal obligation. In this case, there is a certain expectation to behave in a certain way, and failing to behave results in some loss of social esteem, stigmatization, shunning, demotion, reduced access to social assets (like favors or company), etc.
However, clearly moral obligations are not of either of these sorts: with a moral obligation, even if no punishment or repercussion would be visited from without, there would still be the internal drive to act. Moreover, even if it were demanded of us by law to act immorally, or our society expected us to do so, that would have no moral bearing on whether we should so act. The missing ingredient, then, if an obligation or duty is to be different from a mere demand or expectation, with or without penalties for transgression, is the drive from within: there is no duty without a sense of dutifulness. If one feels no obligation to do a thing, then one simply has no such obligation.
"[D]uty has no hold on [a man] unless he desires to be dutiful."
Truth and Objectivity
The simplest way to analyze objective truth is to begin by looking at statements already agreed to be objectively true: (A) "If X is a triangle, X has three sides", (B) "Horses exist". How is it that these statements are objectively true? Surely it is that, when we interpret them correctly, we get a claim about the world that accurately describes it. The truth value of the propositions will depend on how we interpret the terms. For instance, if we interpret the term "triangle" (merely a word: a set of symbols) to mean what we normally mean by the word "square", then (A) would be false. It is only when the semantic content of the terms is specified (as well as the way in which the content of the sentence is to be educed from the terms, e.g. grammar) that the sentence or proposition can have an objective truth value. When the terms are left unspecified, or determined on a subject by subject basis, then the proposition is subjective. Thus, all that is needed to make a system as objective as, say, geometry, is to have the terms well-defined, be it a moral system or any other.
We will define a voluntary action as one a person does as a result of a choice they make. Involuntary actions are basically irrelevant to considerations, in any practical sense, except insofar as they can be changed via voluntary actions. It is then also clear that voluntary actions are the only ones that can be considered in any plausible morality: someone is not moral or immoral based on actions they can't control. This is often summarized in the dictum "ought implies can": regardless of what, exactly, "ought" is taken to mean in the end, it must imply that the thing one ought to do is one that one can do (though "can" might itself need some further analysis). Furthermore, "ought" seems to imply also "can not", as in "can do otherwise". If one can't help but do something, it cannot be meaningfully said that she ought to do it. Thus, oughts imply a choice, where the alternatives can each be acted on
In any choice between alternatives, choosing one must mean that one wanted that option, for if one wanted a different option, she would have chosen it. "Want" here is to be taken in a more general sense than it may often be. You may want to go with your friends to the movies, but do homework instead, and why? Because though you may prefer movies to homework in general, you prefer doing well in a class at the expense of spending less time with your friends to spending more time with your friends and doing worse in the class. In the greater context, you prefer doing homework to going to the movies in this case, as opposed to generally preferring movies to homework with no context. Thus, all voluntary choices are the result of the person doing what she wants: everyone always does what they want most, as far as they can. A clear corollary of this is that to change voluntary behavior, one must appeal to what the person in question wants or cares about. This is abundantly clear in experience as well. Moreover, the converse is also manifestly true: if something affected someone's voluntary behavior, it must have appealed to what she wanted or cared about. For, as everyone does what they want most, as far as they can, what affects their voluntary actions must have appealed to what they want or cared about.
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