I am not sure I agree with your second concern. Sometimes premature formalization can take us further off track than leaving things with intuitively accessible handles for thinking about them.
Formalizing things, at its best, helps reveal the hidden assumptions we didn’t know we were making, but at its worst, it hard-codes some simplifying assumptions into the way we start talking and thinking about the topic at hand. For instance, as soon as we start to formalize sentences of the form “If P, then Q” as material implication, we adopt an analysis of conditionals that straightjackets them into the role of an extensional (truth-functional) semantics. It is not uncommon for someone who just took introductory logic train themselves into forcing natural language into this mold, rather than evaluating the adequacy of the formalism for explaining natural language.
I am not sure I agree with your second concern. Sometimes premature formalization can take us further off track than leaving things with intuitively accessible handles for thinking about them.
Formalizing things, at its best, helps reveal the hidden assumptions we didn’t know we were making, but at its worst, it hard-codes some simplifying assumptions into the way we start talking and thinking about the topic at hand. For instance, as soon as we start to formalize sentences of the form “If P, then Q” as material implication, we adopt an analysis of conditionals that straightjackets them into the role of an extensional (truth-functional) semantics. It is not uncommon for someone who just took introductory logic train themselves into forcing natural language into this mold, rather than evaluating the adequacy of the formalism for explaining natural language.