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The most prominent critic of the distinction is Quine. You can read about the reasons for his opposition here. A quote:
Quine... offers a diagnosis of the persistence of the concept of analyticity. Philosophers find the idea plausible because they tend to assume, sometimes unwittingly, that there is a clear notion of cognitive meaning which relates each sentence to the experiences which count for it or against it and which can be applied to sentences taken one-by-one. Given that sort of notion of meaning, we could say: the synthetic sentences are precisely those to whose truth or falsehood experience is relevant; the analytic ones are those whose truth or falsehood is wholly independent of experience (and which can therefore be known a priori).
Quine criticizes this idea of atomistic (sentence-by-sentence) cognitive meaning.... Quine invokes holism, the idea that most of our sentences do not have implications for experience when they are taken one-by-one, each in isolation from the others. What has experiential implication is, in most cases, not an individual sentence but larger chunks of theory. Holism, Quine claims, undermines the atomism of atomistic cognitive meaning.
There is also Chalmers 2009 I guess paper about this, which breifly reviews the history of what happened after Quine polarized the topic.
Revisability and Conceptual Change.
Chalmers attemps (in my view succesfully) to rescue 80% of what matters in the distinction, avoiding Quinean and post Quinean traps.
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.