The

propositional function of the brain is naturally "conceptual," whereas the appositional is "perceptual.

Thus, in this example there is a one-to-one relation between

propositional function and lexeme class.

There are four favored ways of getting from linguistic meaning to proposition(s) expressed: i) by 'modulating' the meaning of overt constituents, ii) by 'saturating' overt constituents, such as indexicals, iii) by adding 'unarticulated' constituents by 'completing' a

propositional function or radical, or iv) by 'expanding' one proposition into a more appropriate one.

He argues that Wittgenstein solved Russell's paradox by preventing a

propositional function from being an argument of itself (2000: 439).

Certainly 'is a prime number' is then a function taking as values propositions which are true or false, but that means it is a

propositional function, not a truth-value function like those in Frege's "Function and Concept" (see, e.

The

propositional function corresponds to the content of the conversation, including meaningful speech as well as hand gestures (gestures that indicate size in the utterance "it was this big" or that represent fingers walking in the utterance "it took me 20 minutes to get here").

Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a

propositional function, the range of that variable includes absolutely every entity.

Similarly, it is reasonable to suppose that every

propositional function (or, in ordinary language, every term that one might use in a sentence, such as the word man) determines a class (in our example, all of the male members of the species homo sapiens).

32) According to Russell, the logical structure of this

propositional function is nothing more than, "There exists an x, such that x is a dependent being," which is either necessary (true for all values of x), possible (true for at least one value of x), or impossible (true for no values of x).

Otherwise put, in our terms, Aristotelian form is not--in particular, is not also--a

propositional function, but a function from matter to compound material substances.

However, if flexible classes are to be treated as multifunctional grams by virtue of their ability to occur in more than one

propositional function, they should be used in

propositional functions which are contiguous on the map.

Tr is a

propositional function that takes an entity and returns the proposition with respect to it that it is true.