Christianity starts with sin
Which is essentially an ethical matter, I guess. Sin is a
violation, it's doing something
bad. In ancient Hebrew mythology, it's about disobeying a superior (in the Garden of Eden, original sin).
the commission of which banishes man from his paradisical state.
According to the myth the first humans were thrown out. It was the intentional act of the superior, imagined according to the absolute-monarch model of their ancient kings.
Buddhism starts with suffering
So does the Judeo-Christian tradition implicitly. Otherwise, why would it
matter to us whether we are living in Eden or not?
and the observation that all of us suffer. Christianity's answer to the question of suffering is free will, although it's not an answer that really solves the problem. What is Buddhism's answer to the problem of suffering?
Its
explanation is that suffering is a mental state, something that we do to ourselves. It's a mental state that arises due to causal (karmic) conditions, as the result of what the modern West would call a psychological process.
The
answer to the problem of suffering is to gain control of that process. Or perhaps more accurately, since in Buddhism "we"
are the process (which makes Buddhism very congruent with modern neurophysiological understandings of the mind) it's for the process to evolve in such a way that suffering no longer arises in it.
Is suffering even solvable, or is it something we just need to accept in our lives?
Suffering comes as the result of our own gross and subtle behavior.
Addressing the former, Buddhism places great emphasis on ethics so as to reduce that kind of suffering. (Notice that the point of ethics in Buddhism isn't to please a superior being, a cosmic judge. It's to produce less suffering in ourselves and others.) And note as well that the point of behaving ethically isn't because doing so is
good. (Buddhism doesn't really have the concepts of 'good' and 'evil'.)
Buddhism is entirely consequentialist, it's about the consequences of what we do, both externally and internally. The latter is very important in Buddhism and Buddhist ethics are typically conceived in the form of precepts which one adopts in living one's life, which in turn are conceptualized as
rules of training. So a big part of the goal of being ethical is the changes in one's own psychology (and the psychology of others too) that behaving in such a way brings about.
(The 'no-self' doctrine kind of reduces the distinction between 'me' and 'you'. We are all just different interacting strands in the universal flow of causality. And ultimately, that's what each of us are individually too. That realization is part of what motivated the growth of Mahayana's Boddhisattva ideal.)
And there are things like physical pain which will always be there, so long as we are human. It's hard-wired in to our physiology, into the process. But the Buddhists say that we are the ones who turn physical pain into suffering. Their goal there is to sever that connection, to just observe pain's presence with equinamity, yes my shoulder hurts, it's sending those signals to my brain, so what?