If you’re curious to learn more about what Catarina Dutilh Novaes called conjunctive pluralism (as opposed to disjunctive pluralism), take a look at some of her blog posts from NewAPPS:
Methodological Pluralism in Philosophy
Intuition-based Philosophical Methodology and Belief
Empirically-informed Philosophy of Logic
Feynman on Precise Definitions and Philosophical Methodology
On the Origins of Analytic Philosophy
Instrumentalist and Intrinsic Value Defenses of History of Philosophy
History of Philosophy as Antidote to Philosophical Intuitions
In addition, keep your eyes out for her forthcoming book, in which she applies a combination of the methods we talked about to investigate the status of formal languages as a part of the philosopher’s toolkit:
Catarina Dutilh Novaes, Formal Languages in Logic (2012)
Philosophers want to answer big, sexy questions like how one should live or what knowledge is. How should one go about answering questions like that? Random guessing is definitely out. That’s because philosophical insight is supposed to be the result of some kind of rigorous investigation. But what is that kind of investigation supposed to look like? This is a question about philosophical methodology, and an extremely important one. After all, if we don’t know what methods we can use to gain philosophical insight, it’s hard to know whether we’re on the right track when we try to answer those big, sexy questions.
As it happens, nearly everything we say is imprecise. For example, when I indicate where I want you to stand while posing for a photo, I don’t give exact coordinates; I just point with my finger. When I tell you my friend Janine is really tall, I don’t specify her height right down to the last millimeter. Would six feet count as tall? Probably. How about 5’11″? Or 5’10″? 5’9″? The closer we get to the middle of the boundary between people who are tall and people who aren’t, the more of a challenge it is to say, because the boundary is blurry. And when I tell you that my sixth grade music teacher was bald, it isn’t clear exactly how much hair I’m saying he had. Maybe he had absolutely no hair, or maybe he had a little bit. In any event, he didn’t have much. But how much does it take to be ‘much’? What are we to make of the fact that we can’t give an exact answer to that question?
This month, we speak with Martha Nussbaum, Ernst Freund Distinguished Service Professor of Law and Ethics at the University of Chicago. You can listen to our conversation 
Disagreement in ethical matters is a common enough phenomenon. Yet, what exactly is the appropriate way to respond when one is confronted with it in one’s own life? Sometimes such disputes can be resolved easily enough—perhaps there is a piece of missing information or an error in reasoning that can simply be pointed out by one interlocutor to the other.