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This restriction makes it impossible to form a proposition of the form P(P): the type of P should be of the form (A), and P can only be applied to arguments of type A, and thus cannot be applied to itself since A is not the same as (A).
Note that Frege distinguishes between an n-place function f as an unsaturated entity that can be completed by and applied to arguments a1,…, an and its course of values, which can be seen as the set-theoretic representation of this function: the set {⟨a1,…, an, a⟩ | a = f a1,…, an)}.
Applied to arguments or sources of evidence, this could explain why desired conclusions are more likely to be believed true.
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Thus, 'φ(a)' will be used to indicate any sentence (simple or complex) in which the name 'a' appears; 'φ(a)' is not to be understood as Frege-notation for a function φ applied to argument a.
The same empirical objection applies to arguments that blame low interest rates on the increasing concentration of income and wealth.
This property can be generalized to apply to arguments with conditionals.
In Frege we have a fairly general interpretation of sentences as expressing functions applying to arguments.
Although this criticism is directed against a cosmological argument, similar to that of Samuel Clarke in his first Boyle Lecture, it has been applied to ontological arguments as well.
But it could as well have applied to his arguments for allowing parents to choose their children's schools, condemning abortions, weakening teacher tenure laws or cutting taxes.
Thirdly, an ethical analysis was applied to the arguments identified from the literature.
Perhaps, the simplest combinator is the identity combinator I, that applied to an argument x returns the same x.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com