29BAYLE, PIERREGregory of Nyssa) who served as bishops
and wrote multiple works in the central
region of modern Turkey. Basil, the older
brother of Gregory of Nyssa, was raised
in a prominent Christian family and was
sent to Athens to be schooled in rhetoric
and the classical tradition. He later
devoted himself to Christianity becoming
a Christian ascetic, and he founded one of
the earliest monasteries. After becoming
bishop of Caesarea, Basil became a central
figure in combating Arianism and was
responsible for appointing anti-Arian
bishops including Gregory of Nazianzus
and Gregory of Nyssa. Basil’s works focus
primarily on defining and maintaining
orthodoxy as set forth at the Council of
Nicaea (325 C.E.) (e.g., On the Holy Spirit).
His writings on monastic life led to the
development of the “Rule of St. Basil,” which
came to define Eastern monasticism.
BAYES’ THEOREM. According to Bayes’
theorem,
Pr(h) x Pr(e/h)
If Pr(e) is not equal to zero, then Pr(h/e)
= ------------------.
Pr(e)In English, this says that if e is not cer-
tainly false, then the probability that h is
true given that e is true is equal to the
probability that h is true times the proba-
bility that e is true given that h is true
divided by the probability that e is true.
Bayes’ theorem is often used to assess
the effect of evidence on a hypothesis.
If h stands for some hypothesis and e
stands for a statement reporting a piece
of evidence, then Bayes’ theorem tells us
that the probability that the hypothesis h
is true given the evidence e [Pr(h/e)]
depends on three things. First, it depends
on how probable h is prior to discovering
the evidence: the higher Pr(h), the higher
Pr(h/e). Second, it depends on how well
h predicts (or “retrodicts”) e: the higher
Pr(e/h), the higher Pr(h/e). And third, it
depends on how surprising the evidence
is: the lower Pr(e), the higher Pr(h/e). In
short, hypotheses that are initially plausi-
ble and successfully yield data that would
otherwise not be expected are themselves
very probable given that data.
Some philosophers of religion believe
that Bayes’ theorem is the key to assessing
the epistemic status of the “hypothesis”
that God exists. Others think that it is
often misapplied to issues in philosophy
of religion and that it is popular because
of a sort of scientism that dominates ana-
lytic philosophy. Strangely, both of these
views are correct.BAYLE, PIERRE (1647–1706). Bayle
was a skeptic about rationalist philosophy
and theology. He defended the use of faith
in assenting to fundamental Christian
truths, but he was opposed to those who
taught that faith or reason could settle
disputes between Roman Catholics and
Protestants. He defended tolerance with
wit. He is the author of The Historical and
Critical Dictionary (1697, 1702), known