In the 20th century the understanding of noncategorical syllogisms was extended to encompass complex and compound propositions as well as the dilemma with its constructive and destructive moods.
Simple (atomic) propositions are denoted by letters, and compound (molecular) propositions are formed using the standard symbols: · for "and," ∨ for "or," ⊃ for "if... then," and ∼ for "not".
Propositional calculus, also called Sentential Calculus, in logic, symbolic system of treating compound and complex propositions and their logical relationships.
Now consider the same pattern of argument with "or" in a compounded sense: "every proposition or its contradictory is true".
From the semantic point of view, this means the collapsing of the fundamental distinction in the common Aristotelian theory of meaning, the one between simple signs (like nouns) and compound signs (like propositions).
Curry allows that one can form compounds from elementary propositions by means of the usual logical operators in order to express complex propositions in the language of proof theory (Chapter IX).
There are various mental processes (compounding ideas, forming propositions, reasoning syllogistically) that we can describe without knowing that reasoning is computation.
But the compound creates a complicated recycling proposition.
