On the definition of research I'm writing a proposal to acquire funding for a competition to be hosted at my university.  The competitors are restricted to graduate students who are engaged in research under the auspicies of a faculty advisor from my university.  In the process of making my proposal more clear and precise, I find myself struggling with the problem of defining what exactly is (and more importantly, what isn't) research.  

At first, I equated research with publishable in a peer reviewed journal, but I soon realized that the terms publishable and peer reviewed would have to be defined... And even if I do that, then I would have to define the words that I used to define those words, et cetera ad nauseam.

I want to approach it the same way I would approach mathematical set theory:  it's either research or it's not, and there should be no room for ambiguity.  But I suspect that any attempt to define research this way will certainly either circumscribe or inscribe the set of all things we call research. 

I don't think this is necessarily the best way to approach defining what is research, especially for my purposes.  Is there another way I can approach clarifying what constitutes research as opposed to other publishable works in the context of academia?
For purposes like this, I would define research as loosely, broadly, and generically as possible. If your definition is too strict, then you exclude valid efforts, and you will likely be bound by the language in your proposal. 

For example, if you define research to be "scientific investigation," then you exclude the humanities. If you define research as "investigative work leading to a peer-reviewed publication or conference presentation," then you may inadvertently exclude unpublishable and unpublished results. 

If the requirements of the agency do not specify the need for a definition of research, then do not supply one. If you are writing to an agency that regularly supports research proposals, then there is no need to define research - they know what it is. If you are writing to an atypical funding source, like a business, local government, or charity, then they would probably rather you be inclusive (and thus generic) unless you have specific instructions otherwise. Leave the job of deciding whether an entry is qualified research to the judges of the composition. 

If you feel that you absolutely need a definition, then "investigative work" is probably generic enough. Your institution's Office of the Provost may also have an "official" definition of research for your institution.