of the
imperfect reckoning of the length of the {624} year as exactly 365 1/4
days; thus every four centuries there would be three days too much. It
was proposed to remedy this for the present by leaving out ten days,
and for the future by omitting leap-year every century not divisible by
400. The bull of Gregory XIII, [Sidenote: February 24, 1582] who
resumed the duties of the ancient Pontifex Maximus in regulating time,
enjoined Catholic lands to rectify their calendar by allowing the
fifteenth of October, 1582, to follow immediately after the fourth.
This was done by most of Italy, by Spain, Portugal, Poland, most of
Germany, and the Netherlands. Other lands adopted the new calendar
later, England not until 1752 and Russia not until 1917.

[1] _I.e._ the principle thus formulated in the _Encyclopaedia
Britannica_, s.v. "Mathematics": "If s is any class and zero a member
of it, also if when x is a cardinal number and a member of s, also x +
1 is a member of s, then the whole class of cardinal numbers is
contained in s."

[2] Eratosthenes (276-196 B.C.) had correctly calculated the earth's
circumference at 25,000, which Poseidonius (c. 135-50 B.C.) reduced to
18,000, in which he was followed by Ptolemy (2d century A.D.).

SECTION 5. PHILOSOPHY

[Sidenote: Science, religion and philosophy]

The interrelations of science, religion, and philosophy, though complex
in their operation, are easily understood in their broad outlines.
Science is the examination of the data of experience and their
explanation in logical, physical, or mathematical terms. Religion, on
the other hand, is an attitude towards unseen powers, involving the
belief in the existence of spirits. Philosophy, or the search for the
ultimate reality, is necessarily an afterthought. It comes only after
man is sophisticated enough to see some difference between the
phenomenon and the idea. It draws its premises from both science and
religion: some systems, like that of Plato, being primarily religious
fancy, some, like that of Aristotle, scientific realism.

The philosophical position taken by the Catholic church was that of
Aquinas, Aristotelian realism. [Sidenote: The Reformers] The official
commentary on the _Summa_ was written at this time by Cardinal Cajetan.
Compared to the steady orientation of the Catholic, the Protestant
philosophers wavered, catching often at the latest style in thought, be
it monism or pragmatism. Luther was the