Such [a semantic] approach to logic and its applications is not an arid academic exercise. Our pre-theoretical intuitions can often be ill-formed and misleading. The enterprise of providing a formal semantic definition often strengthens our grasp of the underlying intuitions by providing a precise formulation. Of course, it may turn out that our first attempts at formalisation do not quite capture our underlying intuitions. But it is precisely here that the power of formal semantics is most readily seen. Once we have a precise semantic theory we can measure it against our intuitions and if need be modify it if found inadequate. Moreover, such a formal theory provides a background and yardstick for axiomatisation. We require an axiomatisation which is both sound and complete, and such notions have no precise sense outside of a fully developed semantic theory.
Raymond Turner, Logics for Artificial Intelligence (Ellis Horwood, 1984), §8.2, p. 118.
See also Sven Ove Hansson’s article on formalization in philosophy, Wakker’s distinction of paramorphic and homomorphic models in Prospect Theory, and Hansson’s Beyond Language: Using Logic to Introduce New Philosophical Distinctions. He writes:
[O]nce a distinction or a concept has been developed in formal language it can often also be expressed in non-formal language. Another way to express this is that logic is often indispensable in the contexts of discovery and justification, but dispensable in the contexts of further elaboration and dissemination.