(1) The propositional function
of the brain is naturally "conceptual," whereas the appositional is "perceptual." The "conceptual" relates to the world of connected, or visual space, and the appositional relates to the juxtaposed and discontinuous space which is resonant, acoustic, and total.
Since this is the only attributive strategy available in Krongo, we can say that the propositional function
of modification is expressed by relative clauses in this language, not by lexical modifiers.
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.g., Frege 1952, p.
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.
According to Russell, it expresses a "propositional function
," which is simply an "expression containing an undetermined constituent [i.e., a variable], or several undetermined constituents, and becoming a proposition as soon as the undetermined constituents are determined."(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.
In Science and Sanity, Korzybski says this of Aristotle's understanding of language, In the A-system the 'universal' proposition (which is usually a propositional function
) always implies existence.
(Tr is a propositional function
that takes an entity and returns the proposition with respect to it that it is true.
Moreover, when one says, "Some tame tigers growl," this asserts that the propositional function
x is a tame tiger and growls has a value which is a true proposition.