Starting from the observation that the consequential relation does not happen when the antecedent is true and the consequent is false, and from the tendency to reduce the relations between sentences to truth functions, the consequential relation is represented through the truth function of material implication.
As a result, it cannot be represented through a truth function as it is the case of material implication.
Then the semantic value of A must be a function from pairs of truth values to truth values--that is, a truth function.
So, if this semantic value is a truth function, it must be the familiar truth function for disjunction; if it is a world-set function, it must be the function that maps any two sets of possible worlds onto their union.
The stereotypes, in cartoon form, are hard-nosed, rigidly rational analysis of truth function
in a rule-bound methodological context against playful, tricksy, overly intellectual, usually French textual charlatanism masquerading as metaphysics.
The goal is, in characterizing admissibility, to give some explanation of why an assignment which, for instance, assigns the classical truth function
for conjunction to the concept of alternation is not an admissible assignment.
Although they present the same truth function
, they present it in different ways; a proposition asserting the equivalence of a conjunction and its Sheffer stroke counterpart is potentially informative.
The semantic value for and might be that truth function
which makes the classical elimination and introduction rules for and truth-preserving for all assignments of conjuncts.
Boole (1815-1864) that define a new branch of mathematics based on a couple of truth functions
(future operators) defined on a set made by only two values: true and false (0 and 1).
If the first creator of such systems interprets the proposition on norms (id est, the propositions--and the truth functions
between propositions--on coercitiveness, permission, interdiction and the other deontic--derived --characters of acts (and performance functions between acts--von Wright 1967: 306) in the field of the achievement or performance values of the normed acts restricted to the bi-valent "fulfilled" or "unfulfilled" register, Kalinowski (1972: 115) ensures entries for the deontic matrices in the trivalent value space: intrinsically good (action), [1.
The author ends with a proposal as to how to understand Wittgenstein's claim that all propositions can be analyzed as truth functions
of elementary propositions.
In addition he reviews Wittgenstein's remarks about truth functions
, molecular propositions, generality, types, identity and other more specific topics.