Carnap's later inductive logic explicitly showed that purely logical probability systems require a continuum of lambda values to handle negative analogy, which Keynes's single framework cannot accommodate.

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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.
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.
Keynes, John Maynard(a competing framework being contrasted with Carnap's): A famous 20th-century economist and philosopher who also developed his own system of logical probability and inductive reasoning before Carnap.
Lambda values(the variable elements that Carnap's system requires): Mathematical parameters (represented by the Greek letter λ) that adjust how strongly a system weighs new evidence when updating beliefs. Different lambda values represent different strengths of confirmation.

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