Huber, Franz

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Reply to Crupi et.al.’s ‘Bayesian Confirmation by Uncertain Evidence’ ([2008]) 
Franz Huber 
Penultimate version: please cite the paper in the British Journal for the Philosophy 
of Science 
 
Crupi et al. ([2008]) propose a generalization of Bayesian confirmation theory 
that they claim to adequately deal with confirmation by uncertain evidence. Consider a 
series of points of time t0, …, ti, …, tn such that the agent’s subjective probability for an 
atomic proposition E changes from Pr0(E) at t0 to … to Pri(E) at ti to … to Prn(E) at tn. It 
is understood that the agent’s subjective probabilities change for E and no logically 
stronger proposition, and that the agent updates her subjective probabilities by Jeffrey 
conditionalization. For this specific scenario the authors propose to take the difference 
between Pr0(H) and Pri(H) as the degree to which E confirms H for the agent at time ti 
(relative to time t0), C0,i(H, E). This proposal is claimed to be adequate, because 
C0,i(H, E) < C0,n(H, E) if both Pr0(E) < Pri(E) < Prn(E) and Pr0(H) < Pr0(H|E). 
The authors show the last proposition to hold for all “Pr-incremental” measures of 
confirmation C0,i(H, E), that is, all functions that depend only on Pr0(H) and Pri(H) and 
that are increasing in Pri(H) and non-decreasing in Pr0(H). Examples include the distance 
measure, the ratio measure, the odds or log-likelihood ratio measure, and the normalized 
distance measure (Crupi et al. [2008], section 2). 
 
I agree that, from a Bayesian point of view, the authors’ proposal adequately deals 
with confirmation by uncertain evidence. In fact, for the specific scenario described 
above this is what I claim myself in section 11, pp. 111f, of Huber ([2005])1, even though 
I arrive at this conclusion in a somewhat different way. However, the account by Crupi et 
al. ([2008]) is more general than my stance on this specific situation. More importantly, 
the authors also distinguish between two crucially different readings of my claim (H) that 
‘[i]f some E speaks in favour of some H–say, because it is a logical consequence of the 
latter–then […] getting to know that E is probably true should provide confirmation for 
H–and the more probable it is that E is true, the more it should do so.’ (Huber [2005], p. 
105, italics added) Therefore their paper helps to clarify an ambiguity in mine, and it 
provides an important contribution to Bayesian confirmation theory. 
 
However, the target of my ([2005]) is not some specific issue–viz. confirmation 
by uncertain evidence–within Bayesian confirmation theory, but rather that theory itself. 
Crupi et al. ([2008]) reject–correctly, I think–one reading, called (H.2), of my claim (H). 
They develop a general Bayesian account of confirmation by uncertain evidence based on 
a second reading, called (H.1). I argue that Bayesian confirmation theory gets things 
wrong if it adopts the reading (H.2) rejected by the authors, and that it is subject to a 
triviality charge if it adopts the reading (H.1) accepted by the authors. 
 
More specifically, I use a feature of (H.1) to prove the following result: for any 
subjective probability measure Pri at time ti, for any hypothesis H, and any atomic 
evidence E that is relevant to H (in the sense of Pri), there are assignments of probabilities 
                                                 
1 There is an unfortunate typographical error at the bottom of p. 112, where the 
probability measure Pri should not be conditional on E. However, this is clear from what I 
say on the pages following that paragraph and does not seem to have misled the authors. 
Pr0, Pr0*, and Pr0** such that E confirms H at time ti (relative to time t0) if the agent starts 
with Pr0 as her first assignment, E disconfirms H at time ti (relative to time t0) if the agent 
starts with Pr0* as her first assignment, and E neither confirms nor disconfirms H at time 
ti (relative to time t0) if the agent starts with Pr0** as her first assignment. (This result 
holds for all Pr-incremental measures as well.) 
 
To illustrate, consider a community of scientists that has come to agree on the 
subjective probabilities to be assigned to the hypotheses of their interest. That is the 
situation of ‘objectivity as inter-subjective agreement for opinions that fall short of 
certainty’ (Earman [1992], p. 138). If these scientists also agree on the (cognitive) 
utilities they assign to these hypotheses and if the decision rule they use is determined by 
their probabilities and utilities (as is the case if they maximize expected utility), they 
accept, reject, and laugh at the very same hypotheses–even though they disagree as to 
whether the data that have driven their agreement is to be called ‘incrementally 
confirming’ or ‘incrementally disconfirming’ or neither (let alone to what degree). 
 
I am happy to concede that positive probabilistic relevance is the correct 
explication of the explicandum ‘confirmation’. If there were one and only one, I would 
even be happy to concede that the normalized distance measure (or, for that matter, the 
odds or log-likelihood ratio measure) is the correct explication of the explicandum 
‘degree of confirmation’. What I do not concede is that the very concept of (degree of) 
confirmation explicated in this–or, in case of degrees of incremental confirmation, any 
other–way is of any use. In fact, I claim the contrary, for this concept sees disagreement 
where there is nothing but agreement (with regard to all that matters). 
 
The history of confirmation theory is, to a large extent, a history of triviality 
results. Hempel ([1945]) shows confirmation to be trivial if it satisfies certain conditions 
of adequacy. Goodman ([2006/1954]) shows confirmation to be trivial if it is construed in 
purely syntactical terms. Bayesian confirmation theory escapes these triviality results 
since its notion of incremental confirmation violates Hempel’s conditions, and 
expressions that are syntactically alike need not be alike in their probabilities. 
 
In Huber ([2005]) I argue that Bayesian confirmation theory is nevertheless 
subject to a triviality charge: we can incrementally confirm everything by anything 
atomic and relevant as long as we choose an appropriate prior. That result depends on a 
particular treatment of uncertain evidence that I claim the Bayesian is forced to adopt if 
she wants to get things right. I take the fact that the authors’ general account of 
confirmation by uncertain evidence yields this treatment for the special scenario I focus 
on to show that my original triviality charge still holds. 
 
Acknowledgements 
 
I am grateful to Vincenzo Crupi, Roberto Festa, and Tommaso Mastropasqua as well as 
an anonymous referee for their comments and suggestions. My research was supported 
by the Ahmanson Foundation and the German Research Foundation through its Emmy 
Noether Program. 
 
 
Formal Epistemology Research Group 
Zukunftskolleg and Department of Philosophy 
University of Konstanz 
P. O. Box X 906 
78457 Konstanz 
Germany 
franz.huber@uni-konstanz.de 
 
References 
 
Crupi, V., Festa, R., Mastropasqua, T. [2008]: ‘Bayesian Confirmation by Uncertain 
Evidence: a Reply to Huber [2005]’, British Journal for the Philosophy of 
Science. 
Earman, J. [1992]: Bayes or Bust? A Critical Examination of Bayesian Confirmation 
Theory, Cambridge, MA: MIT Press. 
Goodman, N. [2006/1954]: Fact, Fiction, and Forecast, 4th ed., Cambridge, MA: 
Harvard University Press. 
Hempel, C. G. [1945]: ‘Studies in the Logic of Confirmation’, Mind, 54, pp. 1-26, pp. 97-
121. 
Huber, F. [2005]: ‘Subjective Probabilities as Basis for Scientific Reasoning?’, British 
Journal for the Philosophy of Science, 56, pp. 101-116. 


Reply to Crupi et al.’s ‘Confirmation by Uncertain Evidence’ ([2008])

http://philsci-archive.pitt.edu/10845/1/Reply_-_07072014.pdf

Reply to Crupi et al.’s ‘Confirmation by Uncertain Evidence’ ([2008])

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