Empirical Meaningfulness and Intuitionistic Logic

Abstract

CONSIDER A NON EMPTY BUT OTHERWISE ARBITRARY SET OFPROPERTIES CALLED OBSERVATION-PROPERTIES (O-PROPERTIES).CALL A PROPERTY P A MEANINGFUL PROPERTY (M-PROPERTY) IF ITIS EQUIVALENT TO A (FINITE OR INFINITE) DISJUNCTION OFO-PROPERTIES--I.E., A NECESSARY AND SUFFICIENT CONDITIONFOR P IS THAT AT LEAST ONE OBSERVATION-PROPERTY IN ACERTAIN SET O(P) BE TRUE. OBVIOUSLY THE CONJUNCTION ANDDISJUNCTION OF TWO M-PROPERTIES IS AN M-PROPERTY; INGENERAL THE NEGATION OF AN M-PROPERTY IS NOT AN M-PROPERTY.HOWEVER WE CAN DEFINE THE PSEUDO NEGATION OF AN M-PROPERTYP AS THE POSSESSION OF SOME O-PROPERTY INCOMPATIBLE WITH P.THE ALGEBRA OF DISJUNCTION, CONJUNCTION AND PSEUDO NEGATIONOF M-PROPERTIES TURNS OUT TO START IN THE SAME RELATION TOBOOLEAN ALGEBRA AS INTUITIONISTIC LOGIC (NOT 3-VALUEDLOGIC) DOES TO CLASSICAL LOGIC, AND SUGGESTS THEREFORE THATINTUITIONISTIC RATHER THAN 3-VALUED LOGIC IS THEAPPROPRIATE FORMALISM TO DEAL WITH THE PARADOXES OF THEBALD MAN, THE HEAP, ETC.