322 mind
refutation of a mathematical proof is a private, first-person event. The external
manifestation of a sophisticated mathematical proof is unintelligible to the
nonmathematician, so the evaluation of its validity is confined to professional
mathematicians. Who is in a position to judge whether a student of mathe-
matics has in fact understood a particular proof? This may not be done by a
fellow student, let along a layperson, who represents a third-person perspective,
nor can the student rely entirely on his or her own first-person judgment.
Rather, the level of the student’s understanding must be judged by a competent
mathematician, serving in the role of mentor. Only if this mentor has already
fathomed the proof in question can he or she authoritatively judge whether
the student has done so. In this regard, mathematical discoveries are compa-
rable to contemplative insights. According to many contemplative traditions,
the student enters into formal training and regularly reports his or her expe-
riential insights to a competent mentor, who then evaluates them and guides
the student to yet deeper insights. Advanced contemplatives, on the other hand,
may claim to have gained specific insights into certain facets of reality, and
their claims are then subjected to sophisticated peer review by other senior
contemplatives of their tradition.
Once a mathematical theorem has been logically proven to be internally
consistent, one may move on to empirical criteria for evaluating whether or
not it accurately describes or predicts certain phenomena in nature. There are
also pragmatic criteria for evaluating such a theorem, testing whether it is
useful for creating new technologies. Empirical and pragmatic criteria are also
used in evaluating contemplative theories and practices. Empirically, one ob-
serves whether or not they correspond to or predict the types of experiences
that emerge in the course of training. Pragmatically, one tests their usefulness
in terms of their practical benefits in the life of the contemplative and those
with whom he or she engages. The benefits are of course not technological in
nature. Rather, they have to do with the attenuation of vices, the growth of
virtues, and the enhancement of one’s own and others’ well-being, especially
of the kind early Christianity calledeudaimonia,or a “truth-given joy.”
Contemplative experience is, of course, only one facet of religious experi-
ence at large. For some religious traditions it is regarded as being of central
importance, while for others it is marginal or even absent altogether. How is
one more generally to evaluate the truth-claims made by scientists and religious
people? Such truth-claims may be based on one or more of three foundations.
First, some scientific and religious assertions are purely dogmatic in nature,
which is to say that they cannot be confirmed or refuted solely on the basis of
logic or experience. The metaphysical principles of scientific materialism and
religious claims based solely on divine authority fit into that category, and it is
primarily these claims that form the basis of heated debate between believers
of these different scientific and religious ideologies.^29 Second are truth-claims
that are based on logical reasoning, and these are subject to rational analysis.