Quality & Quantity 33: 353–360, 1999.
© 1999 Kluwer Academic Publishers. Printed in the Netherlands.
Swinburne’s Challenge: A Note on Probability
Estimates for Nontypical Potential
STEVEN I. MILLER
Department of Educational Leadership and Policy Studies, School of Education, Loyola University,
Abstract. General conﬁrmation theory, and especially its Bayesian variant, has never been able
to adequately address the issue of how to handle qualitative evidence instances. Such statements
encompass a wide class including historical claims, those of the human sciences not incorporating
quantitative models, legal statements and the like. The issue was recognized by the philosopher Swin-
burne (1973) who puzzled how such statements as, ‘Caesar crossed the Rubicon’, could be assigned a
meaningful probability estimate. The present paper suggests that such statements can be transformed
into, at least, plausible probability estimates. This requires a two step process: judgements made by
credible raters, and the transformation of judgements into one or more reliability co-efﬁcients. These
reliability estimates can then be utilized in the standard Bayesian model to yield plausible degrees of
belief between hypothesis and evidence.
Key words: Swinburne’s challenge, probability estimates, Bayesian model.
In Swinburne’s (1973) classic review of the ﬁeld of conﬁrmation theory, he makes
the off-handed remark in the opening pages that, although he would think it de-
sirable, he has no idea how to assign probability estimates to certain types of
statements. He uses the example of the alleged fact that Caesar crossed the Ru-
bicon. If the claim is treated as an hypothesis, how is it possible to ‘conﬁrm’ it?
Widening the issue a bit, the problem I wish to address here is what status can be
given to certain sentences (or classes of sentences) that are referred to as ‘evidence’
but which are problematic in terms of exactly knowing how they serve as possibly
potential and then actual evidence for an hypothesis.
I especially wish to view the issue within a general Bayesian framework, not
because it is without controversy but rather the intent of the framework captures
fairly well what it means (or would take) to quantitatively demonstrate support
for h (Howson & Urbach, 1990). Nevertheless, the issue I wish to address has a
broader signiﬁcance within the entire ﬁeld of conﬁrmation theory in that it repre-
sents a small, but signiﬁcant, anomaly for that ﬁeld and, if nothing else, should