1) I worry when something is axiomatic. Things that are claimed to be axiomatic tend to be assumed without inquiry or justification. The fact that my perspective on responsibility is different violates the first definition of axiomatic (Self-evident or unquestionable) and the fact that I disagree with the vague premises you have offered shows that the axioms are not shared nor accepted (A statement or proposition that is regarded as being established, accepted, or self-evidently ). Now I understand if you have not taken the time to investigate your beliefs about Responsibility but the are not axiomatic as it pertains to this discussion.
(I am not trying to persuade you when I refer to free will existing. Rather I am describing my position so you can present your argument better.)
There exist people that don't believe in free will and still assign responsibility to others. This indicates that some people will assign responsibility even if they do not believe in free will. However being blamed is not the same as deserving blame. Nor is disbelieving in free will the same as not having free will. This statement does not seem to relate to either the existence/nonexistence of free will nor the existence/nonexistence of responsibility.
"It works because it's a commonly shared understanding, like language." There are other commonly shared understandings that are about as widespread. Popularity of an idea does not make it right.
Tiger analogy:
Why would pets and children not be responsible for their actions? If free will does not exist then they are not lacking any decision making ability because decisions are not made but rather are predetermined.
Parole board: Under your view of responsibility the actor (convict) is responsible (unless they are non sapient, children or mentally incompetent).
It seems like your exception for the mentally incompetent or immature is a sign that the ability to decide/choose is crucial to having responsibility. However you do not believe humans choose so adult humans are equally handicapped as the others in that regard.
2) Agreed. But if free will existed it would be an uncaused cause. I agree that there is no evidence that humans have free will other than the potential illusion of free will.
4) We are using the same string of characters for different concepts. Using the concept I was referring to (objective morality) it does not need beliefs about morality to exist. Metaethical positions that claim that beliefs about morality predate Morality are the Ethical subjectivism and Non-cognitivist theories[1 (http://en.wikipedia.org/wiki/Meta-ethics)].
1) Do you worry about axioms in math, too? I find these rules of responsibility no more troubling than the definition of a line segment. And as far as I know, you haven't disagreed with anything axiomatic that I've said. To repeat, my claim about responsibility existing independently from free will is not something I'm claiming to be axiomatically true. Have you actually disagreed with any of the rules of responsibility I've mentioned so far? I haven't seen an example of such disagreement. I've been fairly cautious with axiomatic statements to restrict them to things commonly agreed upon -- basic societal values that I believe are universal. They are deliberately vague so as to be more obviously true.
A basic disagreement we seem to have is that you think that morality could somehow exist independently from people (or other intelligent beings). I agree that popular agreement doesn't make a moral rule, but in many ways this is our best way of approximating one. There are limits to how well we can perceive a person's true instincts apart from what they say. If many people across many different cultures agree on a moral rule, it can be said to be universal fairly reliably.
Pets and children are not capable of higher forms of thinking that adult humans can do. They are more apt at making decisions, so they have greater responsibility (it is irrelevant that these decisions are predetermined -- they still come to conclusions based on reasoning that was always inevitable. My argument doesn't imply, as you suggest, that there is no thinking). Also, if an adult is caring for a child or an animal, this means that the adult has control over what they do and is thus responsible for it.
parole board: I do believe that humans (and even animals) choose -- but their choices are inevitable. So it's not "free will" in the sense that they could've made a different choice, but they are still "free" to choose what they prefer (which is definite/predetermined). Humans are more responsible for their choices because they are capable of more advanced thinking.
2) You can't fault me for claiming the rules of responsibility are axiomatic, then, since your argument relies on unsupported assumptions.
4) What does objective morality even mean? How could morality exist without people to perceive it? It seems to me to be very much like color in that regard. I can envision "universal morality," and I guess I thought that was what you meant by objective morality. I guess that's what I've been talking about, then. Why do you believe in objective morality? Is that another "preferred" idea like free will? After reading the article, I can conclude that I subscribe to the ideal observer theory, where the ideal observer makes decisions purely motivated by moral instincts. Which instincts are moral is certainly debatable, though I have my own ideas about them.