How did you answer the physicalism question? If you think any physical duplicate of our world must also be a mental duplicate then I think you're committed to the impossibility of zombies.
Think about it this way: Do you think there can be a world where the distribution of micro-physical properties is identical to ours but which does not have tables? Presumably no, because you believe that once microscopic properties are distributed a certain way in some location, you can't avoid having a table in that location. But you don't think the same is true of phenomenal experience if you believe zombies are possible. You think that there needs to be something more than just the right distribution of physical properties for consciousness to appear.
I suspect you're conflating epistemic and metaphysical possibility when you say causeless effects are vanishingly unlikely. Take the sentence "2 + 2 = 5". I think its metaphysically impossible for that to be true (assuming the meanings of the terms are kept constant) -- there is no possible world in which it is true -- but I don't assign it probability 0 because (as Eliezer has pointed out) I acknowledge that there is some possible sequence of experiences that might lead me to believe it (or increase my credence in it). Thinking something is impossible does not mean assigning it probability 0.
Dennett doesn't think we're all zombies, BTW. He's skeptical of qualia as a coherent concept, but he doesn't deny that we have phenomenal experience.
I don't believe mental events have nonphysical causes, which is precisely why I consider zombies to entail causeless effects.
And yeah, perhaps I'm just reading too much into "metaphysically impossible" as distinct from "impossible"; the truth is I really don't know how to think cogently about what would be impossible if the laws of nature were different.
The "we're all zombies" bit was intended with tongue in cheek; it's actually a direct quote of his from some book or another -- Consciousness Explained, probably -- that I re...
Despite being (IMO) a philosophy blog, many Less Wrongers tend to disparage mainstream philosophy and emphasize the divergence between our beliefs and theirs. But, how different are we really? My intention with this post is to quantify this difference.
The questions I will post as comments to this article are from the 2009 PhilPapers Survey. If you answer "other" on any of the questions, then please reply to that comment in order to elaborate your answer. Later, I'll post another article comparing the answers I obtain from Less Wrongers with those given by the professional philosophers. This should give us some indication about the differences in belief between Less Wrong and mainstream philosophy.
Glossary
analytic-synthetic distinction, A-theory and B-theory, atheism, compatibilism, consequentialism, contextualism, correspondence theory of truth, deontology, egalitarianism, empiricism, Humeanism, libertarianism, mental content externalism, moral realism, moral motivation internalism and externalism, naturalism, nominalism, Newcomb's problem, physicalism, Platonism, rationalism, relativism, scientific realism, trolley problem, theism, virtue ethics
Note
Thanks pragmatist, for attaching short (mostly accurate) descriptions of the philosophical positions under the poll comments.
Post Script
The polls stopped rendering correctly after the migration to LW 2.0, but the raw data can be found in this repo.