When should you submit your papers to the arXiv? Before or after they are published in a journal? It turns out that this is a controversial question, with different right answers from different communities. Consider the following comment from a fascinating discussion on astrobetter.com:
...you want people to be using and thinking about the “final” version of the paper, not just something they found lying around on the internet. It would feel like cheating to me to post to astro-ph before having the paper formally accepted by the journal. I do pick out several people from the reference list whose work I cite...should they read it on astro-ph instead? I’d feel like a jerk...I will never referee a paper that has already been thrown up on astro-ph. If they have that little respect for the refereeing process, fine, let them “publish” on the web. But it doesn’t (and shouldn’t) count. IMNSHO.
(emphasis added)
Contrast this with the following question and answer on MathOverflow:
Q: How do people usually use arxiv to put their papers? At which stage does one usually put his/her paper/report there?
A:...it is standard to post on the arxiv as soon as one is ready to share one's work with colleagues...it is quite common to post on the arxiv at the same time as submitting, or not long prior to submitting. (But there is nothing wrong with posting on the arxiv and then spending some more time polishing your preprint before submitting it to a journal.)
There are many voices on both sides of the question in both of the discussions linked above. How can we have such different views of how to use the arXiv? People seem to have two very different concepts of what the arXiv is. The arXiv itself doesn't tell us what exactly it is meant to be*, so we're left to create a definition personally or as a community. The first attitude above seems to be based on the following definition:
A. The arXiv is an official outlet for papers whose quality and correctness has been certified already. Its purpose is to make those papers available without the need to pay a journal subscription fee.
The second opinion seems to be based on a quite different definition:
B. The arXiv is a one-stop outlet for the latest scientific research in my field. Its purpose is to disseminate new information as quickly and broadly as possible so that it can then be understood, evaluated, and added to.
Personally, I take viewpoint B, which I think is more common among mathematicians. What is the arXiv for you?
*: the most relevant statement from the arXiv primer is this:
arXiv supplements the traditional publication system by providing immediate dissemination and open access to scholarly articles (which often later appear in conventional journals). It is important to note, however, that arXiv is not a repository for otherwise unpublishable material, nor is it a refereed publication venue.