Requiring an articulated proof structure imposes a post-hoc rationalization constraint that would have blocked historically fruitful analogical discoveries before their formalizations existed.

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Formalization(describing what Frege did with existence): The process of taking an idea and expressing it precisely using logical symbols and strict rules, like translating messy everyday language into mathematical logic.
Post-hoc rationalization(as used in epistemology and psychology): When you come up with a logical explanation for something *after* it already happened, rather than that logic being the real reason it happened in the first place.
analogical discoveries(as used in philosophy of science and epistemology): Finding new knowledge or insights by noticing similarities between two different things and reasoning from one to the other.
articulated proof structure(as used in logic and epistemology): A formal, step-by-step logical argument that explicitly lays out all the reasoning from start to finish, like showing your work in math.

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