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

306 MATHEMATICAL PHILOSOPHY
await the coming of modern science. I refer to such
scientific concepts and dogmas as: natural law-the atomic
constitution of matter-conservation of mass-conservation of energy-organic evolution-spontaneous or chance
origination and variation of organic life forms-struggle
for existence in partly friendly and partly hostile environment-survival of the fit (the well adapted) and destruction of the ill adapted-and sensation as the ultimate basis of knowledge and as the ultimate test of reality
-not to mention other equally brilliant anticipations of
"modern" scientific thought.
In extant appreciations of the work of Lucretius his
employment of the notion of infinity is indeed commonly
indicated but it is indicated only more or less incidentally,
without due signal of that notion's rôle in the poet's
thought. For example, in Masson's large and, in many
ways, excellent volume,-Lucretius, Epicurean and Poet,
-the term infinite has only a subordinate place in the
index of important terms; in the very extensive Notes to
Munro's famous translation the term receives but scant
attention; and it receives even less in the Notes found
in Cyril Bailey's recent and deservedly much praised
English translation of the poem. What is missed in
such appreciations and commentaries and what I wish
especially to signalize here is the fact that the concept of
infinity,-of infinite multitude and infinite magnitude,is not merely one among the many ideas employed by
Lucretius but is indeed the dominant idea in his system
of thought. A critical examination of the work as a scientific structure can hardly fail to discover that in the
author's judgment the concept of infinity was not only
the most powerful of his logical instruments but alsowhich is quite another matter-the one most obviously