I do not agree with this part of the proposal:
I further propose to remove all references to indefinite-integrals in the definition of integration. In my perfect world, unless the fundamental theorem of calculus is being used, pure antiderivative calculations should not be using the integration tag.
My main objections are:
- I consider current system fine. The questions about calculation of integrals are differentiated by definite-integrals and indefinite-integrals, which I consider subtags of main tag integral.1
- I expect this change to cause confusion for new users. From the past experience it seems that new users typically apply integral tag to the questions of this kind.2
- Perhaps the proposal could work for computation question. But do not forget that there are also theoretical questions in the tag integration. 3
- This would require great amount of work going in individual evaluation and manual retagging of many questions.4
1Certainly, not all questions asking about calculation of definite or indefinite integral are currently tagged as such. But I think that there are many users who make effort to help with correct tagging of questions. I would certainly prefer the workload be directed towards improving tagging of incorrectly tagged questions rather than to retags connected to substantial changes of the tagging systems.
2In fact, this would also probably cause some confusion also among experienced users, which are used to the current system. If the consensus to change the current usage is reached, it would take some time until the users who do not visit meta too often learn about this. Definitely, if we go through with this, it would be good idea to create a comment template for this issue.
3This is probably the main objection against merging integration and definite-integrals. But I suppose that the proposal does not actually suggests that these two tags should be merged or synonymized. The comment about merging added in the edit of the original posts - "this may mean the merging of the integration and definite-integral tags" - should probably be interpreted as saying that these two tags might have big overlap.
In the past there was some discussion that we should try to keep computational and theoretical questions separate. There was a proposal to change the names of the tags in such way, that some of them would clearly indicate that they are for questions about computation/evaluation of integrals rather than about properties of integrals and results about them. However, this suggestion was later abandoned and the tags integration and integral were synonymized.
4A very conservative estimate is about 1k questions, since probably large part of the questions tagged integration+indefinite-integrals would have to be retagged. But seeing that the tag integration has 24k questions and calculation of indefinite integrals is quite frequent category, I think that there might be even more. (However, if we keep the current system, questions in integration of this type should also have indefinite-integrals. So they are incorrectly tagged both under the current scheme and under the proposed new scheme, so they do not really count.)
Of course, this would need a lot of effort and time, since we cannot retag too many questions at once.
If we compare this with the removal of (algebra) tag, which is probably the largest retagging effort on this site so far, it took quite concentrated effort of several users to get from 700 questions in October 2011 to 0 in February 2012. And the effort to remove this started probably earlier. This was discussed already in June 2011, when there was about 600 questions in that tag.
The removal of (algebra) is also cautionary tale from another viewpoint. We still have now and then some comments on main and meta (and occasionally even posts on meta) objecting to removal of this tag and replacing it with abstract-algebra and algebra-precalculus. So we should perhaps not be too hasty about drastic changes in tagging system - it is good to leave some time for people who disagree with the proposed changes to put forward their arguments.