Bayesian Approach to the Philosophy of Science
Bayes’s Theorem: P(h/e) = P(h) · P(e/h)
P(e)
 P(h/e): the (posterior) probability of hypothesis h in light of
the evidence e
 P(h): the (prior) probability of h in the absence of the
evidence e
 P(e/h): the probability of the evidence e assuming that h is
correct
 P(e): the probability of e in the absence of any assumption
regarding the truth of h
Features of Bayes’s Theorem
1. is a mathematical theorem provable from the basic laws of
probability
2. enables us to assign non-zero probabilities to well-confirmed
theories
3. enables us to update probabilities of hypotheses in light of
new evidence
Objective vs. Subjective Bayesianism
 Objective Bayesianism: The probabilities are the
probabilities that rational individuals ought to assign in light
of the objective facts.
o problem—Where does the initial prior probability P(h)
come from?
 Subjective Bayesianism: The probabilities represent
subjective degrees of belief.
o Even if the initial prior probabilities P(h) are different
for different individuals, the posterior probabilities
P(h/e) will tend to converge. (pp. 180-181)
Implications of Subjective Bayesianism:
1. Repeating an experiment under the same circumstances does
not confirm a theory to as high a degree as the original
experiment did.
2. Experimental confirmations of a research program (Lakatos)
are more important than apparent falsifications of the
program.
3. The Duhem-Quine problem is solved by feeding in the
appropriate prior probabilities, calculating the posterior
probabilities, and dropping assumptions when their
probabilities become too low.
4. A theory is better confirmed by various kinds of evidence
than by evidence of a particular kind.
5. Evidence that is used to construct a theory can sometimes
legitimately be used as evidence supporting that theory.
6. The main reason that ad hoc hypotheses should be rejected is
that Bayesian posterior probability calculations show that
they are implausible—even when they are independently
testable.
Objections to Subjective Bayesianism:
1. Since there is no appeal beyond one’s initial (subjective)
prior probabilities, some scientific disputes may not be
rationally resolvable. (p. 188)
2. Since there is no appeal beyond one’s initial (subjective)
prior probabilities, it is possible for a scientist to believe a
theory so strongly that no evidence could ever force him/her
to abandon the theory. (pp. 189-190)
3. The idea that whether a particular scientific theory represents
“progress” in science depends on our access to private
degrees of belief is “implausible.” (p. 189)
4. Since much scientific research is collaborative, it is unclear
whose private degrees of belief are relevant in determining
how “progressive” the research is. (p. 189)
5. When the evidence predates the theory, it may be necessary
to assign counterfactual degrees of belief in order to measure
the prior probabilities and calculate the posterior
probabilities. (pp. 190-191)
6. Subjective Bayesianism makes no provision for evaluating
evidence, experimental technique, and other nuts-and-bolts
considerations.