On Diagonal Quantifiers; 3 of 9

3.    Constancy and Equality Compared

Compare and contrast:

(x = y)        =       For any property P,   P(x) iff P(y).

Con(P)       =       For any objects x and y,  P(x) iff P(y).

Equality and constancy are complementary. Both start from objects having a property equally; equality generalizes the property, constancy generalizes the objects. Equality defines entities; constancy defines laws.

          Their negations are also similar:

(x  y)       =       For some property P,   P(x) xor P(y).

Var(P)        =       For some objects x and y,  P(x) xor P(y).