What points should I consider when applying for/accepting a position at another department? I specialize in Computability Theory which is part of Mathematical Logic at the intersection of Theoretical Computer Science and Mathematics. Therefore I could potentially apply for jobs (e.g. a lecturer) to philosophy (because of logic and foundations of mathematics), computer science and mathematics departments.

However, my research is of very mathematical nature. Hence, if I am going to collaborate with some other researchers, they are almost certainly going to be mathematicians. If I am going to have a PhD student, I would prefer if he/she took mathematical graduate courses since these are going to be more related to my research and the research I can supervise. Similarly, I would prefer to supervise the final year students writing their thesis more related to my research.

I am afraid this may pose a conflict, if I for example am not interested in the research of my employing department and do not collaborate with the colleagues there or do not attend their seminars. On the other hand I can imagine that the interdisciplinary collaboration with colleagues from other departments may be welcomed.

The reason why I ask this is because getting a job in academia is competetive and one cannot always get the preferred position. Therefore: what points should I consider when applying for/accepting a position at another department outside my nominal specialization?
You already have two questions there:


What should you consider when applying for a position at a different department?
What should you consider when accepting a position at a different department?


I'll concentrate on the first question here, and maybe you want to repost your second question separately, because it really deserves separate treatment.



You already hit the nail on the head in your question. The hiring department will wonder just why you apply there from a different specialization, and what you would bring to the table here. (And if they google your name, find this post and read something about "not attending their seminars", this might influence them further...) Being desperate for a job and having done something vaguely related will not be sufficient.

Therefore you need to convince the department you are hiring that you are a good answer to their needs.

Multi- or interdisciplinarity is good these days - but it's better to be interdisciplinary "looking out" from a department than "looking in". So:


In your cover letter, emphasize any work you have been doing that fits into the target department.
Get recommendations from the discipline of your target department, not your original one.
For these two points to work, you will need to actually immerse yourself in the target discipline and its culture. It's fine to come to philosophy from a mathematical point of origin, but be sure to have publications in journals of mathematical philosophy, not only in mathematical journals with a philosophical bent.
You will likely be required to teach introductory courses in your target department. Make sure the hiring committee can infer from your application that you can and will do so. It would be good if you could point to experience having done just that. Perhaps you could try teaching such a course before starting your applications?
Familiarize yourself with the research being done at your target department, and explain how you could collaborate with your departmental colleagues in your research plan. (You should be doing this regardless of what department you apply to, it's just even more important in your case.) 


And don't write anything about "not being interested in your colleagues' research" in an openly accessible forum under your real name, even if your question at this point is purely hypothetical.



When accepting a position in a different discipline, things like different conventions in negotiations may come to mind, but as I wrote above, I'd say this is really a better topic for a separate question.