I think the contemporary empiricist would say that all the information you have about the thousandth flip comes from your past sensory experience -- your experience of the previous 999 flips plus other relevant experience (such as, say, experiences that form the basis for your beliefs about the base rate of unfair coins). The extent to which your belief about the thousandth flip justifiably differs from maximum entropy (or zero information) is entirely attributable to your prior experiences.
OK, so an contemporary empiricist doesn't deny the possibility of inference. Good.
Does a contemporary empiricist deny the possibility of inference engines being constructed in ways that bias them towards certain conclusions? E.g., that two people might be born with their brains wired such that, given the same sensory experiences, one of them infers A and the other infers B? (In both cases, presumably, the information about A or B comes from past sensory experience, it's just that the process for getting one from the other differs.)
If not, then I no longer have a crisp sense of what contemporary empiricists and rationalists actually disagree on.
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.