Russell's ramified type theory demands that propositional functions and their values occupy distinct ontological levels, prohibiting sentences from serving dual roles as both values and substituends.
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(as the outputs that must be distinct from propositional functions themselves)
The results or outputs you get from a propositional function—if a propositional function is a template, its values are the specific true-or-false statements you get by filling it in.
propositional functions(PM's logical system)
A foundational element of the logic of Principia Mathematica (PM), distinct from Frege's use of concepts (functions from objects to truth values)
ramified type theory
A theory that introduces a hierarchy of propositions and propositional functions by assigning them orders, where every function must have a higher order than its arguments