The claim conflates the difficulty of complete formalization with impossibility, committing a fallacy of inference that Carnap's program for inductive logic explicitly warned against when critics declared inductive formalization hopeless.

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Carnap's program(as used in history of philosophy and logic): Rudolf Carnap's ambitious project to create a complete mathematical system for inductive logic—a formal language that could express all scientific reasoning.
Carnap, Rudolf(philosopher who extended Frege's ideas): An Austrian-American philosopher (1891–1970) who built on Frege's ideas and developed new ways of thinking about meaning and logic in formal languages.
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.
Inductive logic(describes the type of logical system being discussed): A method of reasoning that starts with specific observations or evidence and uses them to draw general conclusions, rather than starting with general rules and deriving specifics from them.

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