The enumeration of the special atoms true and false. All primitive interrogatives use classical (Boolean) bivalence and all stable primitive interrogatives obey the three classical (Aristotelian) laws of thought.
Bivalent logic assigns either true or false as the unique truth value of every proposition. A primitive interrogative, i.e. boolean-valued primitive, is stable iff it reliably answers either true or false for a given set of arguments.
The three classical laws of thought are:
- The law of identity: P → P. For every stable primitive interrogative
prim A, B, C = prim A, B, C.
- The law of noncontradiction: ¬(P ∧ ¬P). For every stable primitive interrogative
(prim A, B, C ∧ ¬prim A, B, C) = false.
- The law of excluded middle: P ∨ ¬P. For every primitive interrogative
((prim A, B, C = true) ∨ (prim A, B, C = false)) = true.
unknown. Implementation of this system would proceed directly from creation of an atom to represent
unknownand the formation of a new enumeration that contained the standard true and false atoms and also the
unknownatom. New logical operations could then be written in terms of this new enumeration.