A Quote by David Berlinski on axiom, scheme, and formula
The same procedure may be used in the predicate calculus, but it is complicated, tedious, and ugly. It is for this reason--plain laziness, too--that the logiciain repairs to axiom schemata instead of axioms when formalizing the predicate calculus. Axiom schemata do not themselves appear in the formal system. They are part of the logician's own vernacular, expressed in the same language that he or she employs to talk about formulas and predicate symbols. Each axiom schemata specifies the form of a formula, and each axiom of the system itself is obtained from the form as an instance.
Source: The Advent of the Algorithm: The 300-Year Journey from an Idea to the Computer, Pages: 73
Contributed by: Chris