Does Imagination Play a Role in Philosophy? I think imagination absolutely has a an indispensable role in philosophy, and not just speaking historically or solely about Continental as opposed to Analytic. It's difficult for me to conceive of how any kind of problem solving would NOT rely to some extent on imagination.
Once you get outside a very strict realm- say the realm of simple mathematics- logic doesn't immediately supply or infer an answer...I would say it plays 'gatekeeper' for possible answers. Take as an example the kind of modal realism subscribed to by Lewis. In formulating this theory of modality, philosophers started with the problem of what modal terms REFER to, which I think is a much more complicated answer than what "red", for example, refers to. They had to come up with a picture of existence that answers their problem and is also logically consistent with other premises or methodological approaches (such as Occam's theorem). The result- that all possible worlds are equally 'real', that the world we are in is not the only 'actual' one (though it might be from our point of view), etc. was a result of imagination constrained by reason.
Logic, inference, consistency, etc. act as bounds of imagination in cases such as this but don't supply 'answers'. It can, put very simply, tell us what is wrong but cannot tell us what is right. In a sense, consistency is imagination's editor but doesn't really have any output in the realm of metaphysics especially.