Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

126 MATHEMATICAL PHILOSOPHY
"On a Set of Postulates Which Suffice to Define a
Number-Plane," by R. L. Moore, Trans. Amer. Math.
Soc., Vol. XVI, I915.
"A Set of Postulates for Real Algebra, Comprising
Postulates for a One-Dimensional Continuum and for
the Theory of Groups," by E. V. Huntington, Trans.
Amer. Math. Soc., Vol. VI, I905.
"Set of Independent Postulates for Betweenness,"
by E. V. Huntington and J. R. Kline, Trans. Amer.
Math. Soc., Vol. XVIII, I917.
"Complete Existental Theory of the Postulates for
Serial Order," by E. V. Huntington, Bull. Amer. Math
Soc., Vol. XXIII, 1917.
"Sui principi fondamentali della Geometria della
Retta," by G. Vailati, Revista di Matematica, Vol. II, 1892.
"A Set of Five Independent Postulates for Boolean
Algebras, with Application to Logical Constants," by
H. M. Sheffer, Trans. Amer. Math. Soc., Vol. XIV, I9I3.
"Sulle ipotesi che permettono l'introduzione delle coordinati in una varietà a piri dimensioni," by F. Enriques,
Rendiconti del Circolo matematico di Palermo, Vol. XII,
I898.
Finally, I will add to the foregoing short list a reference to the famous postulate system by which G. Peanofounder and leader of the important Italian school of
workers in the foundations of mathematics, owning such
names as Pieri, Padoa, Vailati and others,-sought to
characterize the class of finite integers. It is found in
various editions of the Formulaire de Mathématiques (as
I899, I9oI) and has been often quoted and critically discussed-especially by Bertrand Russell in his Principles of
Mathematics, by Couturat in his Les Principes des
Mathématiques, already cited, and again, very recently and