A support function can encode background regularities as framework principles without assigning them probability 1 relative to empirical evidence, as Carnap's lambda-continuum demonstrates.

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Carnap: Rudolf Carnap (1891-1970) was a highly influential German-American philosopher who believed that many traditional philosophical problems could be solved by carefully analyzing the language we use to talk about them. He pioneered the idea that philosophy should work closely with science and mathematics, using precise logical methods to clarify confused thinking. His work fundamentally changed how philosophers approach their discipline, making language analysis and logical rigor central to philosophical practice.
Empirical evidence(as a source of justification for knowledge): Information or proof based on real-world observation and experience, rather than just theory or reasoning alone.
Framework principles(as used in epistemology (theory of knowledge)): Basic foundational rules or assumptions that structure how we organize and understand a particular area of knowledge.
Lambda-continuum(as used in philosophy of science and inductive logic): A mathematical model Carnap created that shows different ways to measure how much evidence supports a belief—ranging from very restrictive to very flexible standards.

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