I am in a political science class (international relations) and there is a lot of emphasis/criticism on methodological design. They all harp on a "logic" or a theory's "explanatory power." Granted, history and political science are different disciplines, but I was wondering the importance of explanatory power or logic in a historian's theory/methodology. I am not sure if this question is clear enough, what I am getting at is what role does logic have in history? Can inductive reasoning be used, can we create a system with rules and order? Is empiricism self-selected?
Not really. History is descriptive, not prescriptive, so we have no need or desire to create a system with rules and order. We describe what exists, and try to avoid any greater assumptions.
Logical thought is, of course, important to argumentation, to make sure you points are sound. There's a great work on this: Historians' Fallacies, by David H. Fischer.
IR Student here
I am assuming that you are writing from the US, but much of what you have just said is exactly the issues which the Less 'Scientific' Approaches which are more common in the EU and the UK are critical of.
When they talk about logic, the issue which is often raised is the problem of logical positivism and the associated causal logic of history which is associated with it which becomes highly deterministic in its outcome. I would assume that you will have encountered the main theory discussed in the US , Realism and its contemporary formations of Neo-Realism in its . This is a good example of the logical fallacies which many of these theories assume as in order to work, realism effectively reconstructs history to suit its own understanding of the international.
Paul Schroeder is one of the better examples of a critique of these kinds of issues. Worth reading if you can access it is Elmans & Elmans critique of his articles and his subsequent reply.
http://www.ort.edu.uy/facs/boletininternacionales/contenidos/55/schroeder55.pdf