The definitions you provide are traditionally associated with the analytic/synthetic distinction, not the a priori/a posteriori distinction. While many philosophers have held that all and only analytic propositions are true a priori, other philosophers have disagreed. Kant, for instance, regarded the truths of arithmetic and geometry as a priori true but not analytic, i.e. not true in virtue of the meanings of the terms involved. He thought our knowledge of these truths was based on the forms of our spatial and temporal intuition.
There are also those who argue that certain moral truths are justified a priori (Kant was one of them). Again, I doubt that they would say that this is because their truth follows from the meanings of the terms involved.
It's true that "sensory experience" is ambiguous, but that ambiguity has been at the heart of philosophical discussion about the a priori, so I think my definitions do capture the standard usage. I'd also note that "meaning" is similarly ambiguous.
I think both of our definitions are reasonably common, and that both are also somewhat misleading. I recommended mine partly because I've seen it from a lot of sources, e.g.:
Penguin Dictionary of Philosophy, entry on a priori: "'It can be known a priori that p, if anyone whose experience is enough for him to know what "p" means, requires no further experience in order to know that p.'"
Allen Wood, leading Kant scholar: "A proposition is known a priori when knowledge of it does not depend in any way on the specific contents of experi...
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.