Is it a bad idea to mention in a paper that I plan to address some of the questions it rises in a future paper?
Background: While discussing some results from a recent preprint with other people, we came to the conclusion that with similar methods we can prove a much more general statement. In fact, we are working on it now, and already have some preliminary results (not quite as general as we hope to get though). Now, while revising the original preprint, which I hope to send to a journal soon, I am faced with a dillema: Should I mention that we are currently working on the more general problem, and hope to publish its solution in an upcoming paper? It is a very natural generalisation, so I certainly should mention the problem itself as a possible future direction.
Positives: The positive aspects of mentioning the future project are, I think, quite self-evident. For us, it gives marginally more peace of mind (people are less likely to try and obtain our future result if they know we are working on it), and marginally more publicity (possibly someone will be interested in the problem after reading the first paper and will look up the upcoming one later). For the public, it gives a fair warning (so less chance someone will start working on this problem and be disappointed we did it first) and a reference for where future results might be found.
Negatives: There are also several reasons why mentioning the future project may be counterproductive, and/or/hence put us in bad light. I'm not sure how valid the following concerns are.
I'm claiming rights to something that's not mine. Until we have a proof of the new result, we have no special rights to it; while here I am, claiming the problem as ours. This may especially irritate people who would also like to work on the problem, but now feel compelled not to.
I'm obstructing future progress. Perhaps someone would have produced a better solution to our problem if we didn't deter them. This is especially important if at some point we discover that our project was overly optimistic and that we do not have a solution in the end.
I'm putting irrelevant things in the paper. Someone might argue that the purpose of a mathematics paper is to communicate mathematics. References to past papers serve to give credit where credit is due and to enable the reader to look them up. Conjectures and divagations about future directions are also fair game, as they are ultimately about mathematics. But writing about our future directions is about as relevant as saying that I'll be working on the problem while listening to classical music and doodling on a piece of white paper with a green pen.
(If relevant - my field is pure mathematics. Perspectives from other disciplines are very welcome.)
Edit to clarify: My impression is that for questions like that, there is a clear-cut (but often unwritten) set of rules which say what you can and cannot do in a paper. If this is a border-line case where the decision is genuinely opinion-based, then I would be very eager to learn this as well.