Bulletin of Death and Life Studies, Vol. 2

Philosophy of Uncertainty
and Medical Decisions

21st Century COE Program DALS•

Graduate School of
Humanities and Sociology
The University of Tokyo

Contents

This publication is a collection of the proceedings in the symposium held on 11-12

December 2004 hosted by the 21st Century COE Program "Construction of Deathand Life Studies (DALS)," one of the research institutes in the Graduate School of
Humanities and Sociology, the University of Tokyo. This institute is sponsored by
Japan Society for the Promotion of Science aSPS).

Cover design by NOBU. The text of this book is set in a computer version of Palatino
with a computer version of Optima for display.

9

lntroduction
Masaki Ichinose

PART ONETHE PHILOSOPHY OF F ACING UNCERTAINTY:EPISTEMIC LIMITS, PROBABIUTY, AND D ECISION

Bayesianism, Medical Decisions, and Responsibility
Masaki Ichinose
Is a Decision-Theorist a Friend or Foe of a Bayesian-Theorist?
Comments on Professor Ichinose's Paper
Daisuke Kachi

First edition, 2006
Published by the 21st Century COE Program DALS, Graduate School of Humanities and Sociology, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 1130033, Japan. Copyright © 2005 by the 21st Century COE Program DALS; all rights
reserved. Printed in Japan.

1543

Confirmation in Economics
Colin McKenzie

47

The Limits of Knowledge
Graham Priest

53

Comments on "The Limits of Knowledge"
Takashi lida

65

5

6

CONTENTSCONTENTS

The Logic of Probable Inference
Colin Howson

7

PART THREE

67

SYMPOSIUM ON CONSENT AND DECISIONCONCERNING LIFE AND DEATH

Comment: The Logic of Probable Inference
Kazuo Shigemasu
Subjective and Objective Probabilities in
Medical Decision Making
Donald Gillies

87

Some Questions for Professor Gillies
Nobuharu Tanji

101

Probability and the Notion of Luminosity
Timothy Williamson

103

PART Two
CHOICES ABOUT LIFE AND DEATH

Decision Making in Medicine
Isao Kamae

141

83

115

The Decision-Making Process in Medicine:
Treatment Choices That Affect Life and Death
Tetsuro Shimizu

119

The Choice between Life and Death:
Reports of Actual Medical Lawsuits
Toshihiro Suzuki

125

From the Health-Care Economics Point of View:
Information, Philosophy, and Decision-Making
Takashi Asao•

133

The Authors

151

DALS Organization

153

Bayesianism, Medical Decisions, and Responsibility

Masaki Ichinose

1. Probabi Iistic Strategy

We are always surrounded by uncertainty. It is true that we sometimes
say, 'It is certain that a typhoon is coming', but what is the source of thatclaim of certainty? Perhaps it is the information we have at the moment.
However, most of the information we get in our daily life is only secondhand, by means of those in authority or the mass media, hence in principle we should not give complete credence to it. Strictly speaking, evenprimary information that we experience directly or that originates withthe authorities or eyewitnesses themselves could be regarded as uncertain
because of our epistemic limits on such factors as perception, vague words
used to describe such information,! or memory. As is suggested by thetyphoon example, we often use information that we have already had topredict future events or to justify general scientific laws. This type of procedure is called induction. Yet, this whole procedure of induction must be
taken tQ be uncertain from a philosophical point of view, because that
information relied on is simply uncertain. Additionally, nobody can knowwhat will happen in the future. Undeniably there is an intrinsic asymmetry between the past and the future. In other words, if inductive procedure aims to justify general scientific laws in a perfectly rational way or to
predict the future with absolute certainty, that aim is completely hopelessfrom the outset. Someone might hesitate to accept such all-out uncertainty
about induction, thinking that we could reach certainty with regard not to•

1. There has been a massive accumulation of philosophical literature on the problem ofvagueness in connection with the sorites paradox. As to logical problems about vagueness,
Priest (2001) section 11 is very helpful for quickly understanding its Significance.

15

16

TilE I'III LOSO I'II Y OF " ACi N(, UN( I III",N

BAYESIANISM AND RESPO NSIBILITY

1\

information itsel f but to a logica l fo rm of Inh' I \"Ht' In d\",li ng with infor-

0'

mation. However, this is a problem of the v,l lldl ly ",kr,'nce mther thana problem of certainty. The validity of in fe rence gua rantees Ihc truth of aconclusion only if the premises are certainly truc. If Ihc premises are
lUlcertain, even a valid inference must involve uncerta inty.2
Here I will focus my attention on some aspects of the problem of induction mentioned above. Currently, no philosopher seeks to explain how tojustify general scientific laws in a perfectly rational way or how to makean absolutely certain prediction about the future when discussing the
problem of induction, because he or she fully recognizes that only clairvoyance could accomplish such tasks. So, instead of facing the problem
directly, he or she evades it by only elucidating the relation between evidence and hypothesis in terms of introducing the notion of confirmation.
In short, if evidence (e) positively supports a hypothesis (h), in other words,
e makes h more acceptable, then it can be said that e confirms h. On thecontrary, however, if e makes h less acceptable, we say that e disconfirms h.
Roughly speaking, two strategies have been dominant in philosophy as
theories of confirmation, that is, the deductive strategy and the probabilistic
one. According to the deductive strategy, evidence confirms a hypothesis
if the evidence can be deduced from the hypothesis, whereas the probabilistic strategy claims that there is a conditional probability for any
hypothesis given any statement of evidence, wherefore confirmation relations are analysed in terms of probability relations' However, it seems
that the deductive strategy cannot adequately reflect an actual circumstance of confirmation in scientific activities, where the confirmatory process is dynamically carried out by degrees as new evidence is obtained,even though no certainty is expected. In this sense, I think that the probabilistic strategy deserves the most careful consideration, which also actually fits well the observation about uncertainty that I have made.'
In the following, I examine first the most influential method in theprobabilistic strategy, namely, Bayesianism, conSidering the crucial objections to it. Then I will propose a different approach to correctly understand the problematic situation that those objections describe, that is tosay, an approach to face problems about confirmation by finding confir2. Problems concerning deductive inference where premises are uncertain, that is, thelogic of uncertainty, are now actively discussed in the context of examining a probabilistic
inte rpretation of conditionals since Ramsey and Adams. Edging ton (1995) is the basic literature.

3. Glymou< (1980), pp. 12- 13.
4. The fo llow ing argument, in particular the first half o f it, is partly based upon my previous paper, lchinose (2004).:,17

mation involved in some process of decision-making. I will suggest it byrefe rring to medical cases. Those arguments seem to show that Bayesianideas are unacceptable, but I finally try to indicate that Bayesian ideas canstill be highly significant, although in a restricted and different sense.
2. Bayesian Confirmation Theory
Well, exactly, what are Bayesian ideas about confirmation? Let us take asimple example for the sak~ of understanding the argument clearly.
Suppose that an oculist proposes this hypothesis:(h, ) consuming blueberries helps our eyes to function well,and that I have this evidence:(e,) I actually suffered from less eye fatigue in front of my computer

screen after consuming blueberries thiln when I didn' t have them.

Obviously e, gives some positive support to h" therefore we can safely
say that e, confirms hl' The main idea of the probabilistic strategy is tointerpret this confirmation relation as 'e, raises P(h ,) (i.e., the probabilityof the truth of h,Y. A relation for evidence to raise the probability of ahypothesis is regarded as crucial to confirmation. One of the most influential approaches following this idea is definitely Bayesianism, or exactly
Bayesian confirmation theory, in which changes of probability of a hypothesis are expressed by Bayesian Conditionalisation. According to that, we canformulate the principle of how to update the probability of a hypotheSiS(H) on the receipt of evidence (E) in terms of conditional probability andBayes's Theorem (that is why it is called Bayesianism) in this way.
P"",(H) = Ppri(H I E)
Ppri(H&E)
Pp,,(E)

Pp,,(E IH)P pn(H)Ppri(E)

Ppn(E I H)Ppn(H) + Ppri(E I-H)Ppri(-H)
This is the principle of Bayesian Conditionalisation (BCOND), in which
Ppri(X) stands for prior probability of X and P"",(X) posterior probability of
X. Here I take the bearer of probability (E or H in this case) to be sentences.

18

Ti lE PIII LOSOI' II Y O F FA ' IN\: UNU IU AlN"

Two basic cha rac te ristics o f Oaycsion onfl l'Jl).\tltll1 thl'u ry mus t be mentioned here. First, subjective probab ility thnt hns been tr"d it ionally definedas degrees of belief since Ramsey may be used, in pal'ti ulal' as prior probabilityS This is the most well-known characteris tic of l3ayesianism, which
also generates very broad applicability of the Bayesian approach 6 Second,
Bayesians stipulate that such degrees of belief should satisfy the basic
mathematical rules of probability, which is usually made through the socalled Dutch Book Argument (or sure-loss contract) . As this second characteristic suggests, Bayesians are supposed to offer their arguments asnonnative ones rather than descriptive ones, because we often unknowingly
violate the rules of probability as a matter of psychological fact. In any
case, apparently Bayesian confirmation theory skillfully evades the traditional insoluble problem of induction, because, as Hacking expresses well,in Bayesian arguments 'the question is not whether these opinions (i.e.,
hypotheses) are "rational"'. The question is whether we are reasonable inmodifying these opinions in the light of new experience, new evidence'.'
Bayesian confirmation theory is also undoubtedly a lucid and plain methodology for estimating degrees of confirmation. If Ppo>(H) > Pp'i(H), thenH is confirmed by E, and if P poJH) < Pp'i(H), then H is disconfirmed by E.
That is sinlple and seems to be intuitively reasonable enough to explain
our common-sense feeling about induction' Actually, Bayesian confirmation theory or Bayesian epistemology acquires strong applicability andpracticability in a current context by means of developing a graphicalmodel which is called Bayesian Networks (or Bayesian Nets) . Bayesian Nets
5. I won't put forward here an argument concerning how to interpret the concept of probability, which is a quite perplexing subject. As to interpretations of the probability concept
see Gillies (2000), which examines the propensity theory minutely as well as gives a subjective interpretation, so is highly useful as an overview of the controversies about this problem.
6. However, precisely because of allowing subjective probability, the Bayesian approach isoften avoided by some philosophers. Instead, likelihood (that corresponds to Ppn(E I H) in
the formulation on the previous page) is sometimes highlighted, since it can be evaluated ina relatively objective way, and since the likelihood ratio is a very easy and convenient toolfor comparing different hypotheses. Such a standpOint is occasionally called likelihoodism.
As to some problems concerning Bayesianism and likelihoodism, see Sober (2002), pp.
21-38. Howson also makes an interesting point about likelihoodism, namely that in order tomake likelihoodism meaningful, we eventually appeal to Bayesian theory. See Howson(2002), pp. 51-53.
7. Hacking (2001), p . 256.
8. Talbot (2001) compactly explains the main ideas and positive effects of Bayesian epistemology, as well as its potential problems. That is quite helpful. Bovens and Hartmann (2003)
is an eminent work about Bayesian epistemology in the present context, which considers
problems of coherence or reliability as well as confirmation.

•

BAYESIANISM AND RESPONSIBILITY

19

consist of two components: (1) a directed acyclic graph in which evidence
and hypotheses are taken to be variables and are connected by arrows,and (2) a probability distribution (or a probability specification) ' That is atool by which we can easily recognize dependency and independency
between variables.
However, as usual with regard to any philosophical theory, many criticisms have been levelled at those Bayesian ideas, whereby a lively controve rsy has been aroused until now. In the course of this, Bayesians haveactually refined their ideas to answer the criticisms and surely achieved
some improvement, but we have to say that fundamental difficulties still
remain as far as a simple application of Bayesian ideas or BCOND is concerned. Broadly speaking, it seems to me that there are two directions of
crucial difficulties, namely, (1) BCOND might include some cases irrele,vant to confirmation as examples of confirmation, and (2) BCOND could
no t explain some cases relevant to confirmation. To put this in a nutshell,
BCOND is sometinles too tolerant, and sometimes too intolerant.
3. Evidential RelevanceThe first difficulty is directly concerned with the essential question, thatis, why can we connect the issue about degrees of confirmation simply
with conditional probability? As Glymour straightforwardly pointed out,'the evidence confirms or disconfirms the hypothesis with respect to thetheory',1O so 'if a hypotheSiS is not tested by a piece of evidence with respect
to a theory, there is always some other theory with respect to which theev idence confirms or disconfirms the hypothesis' ll In other words, confirmation is established between evidence and hypothesis BY VIRTUE OF
background theory or background knowledge, hence the relevance of evidence to the background theory (and to the hypothesis through the theory)is intrinsically required. This is suggested by the previous blueberry case.
We believe that e, confirms h" which is supported by, at least, our back).;round knowledge about the influence that a computer screen has on oureyes. Were it not for such knowledge, we could not establish that confirmatory relation. Nevertheless, BCOND itself doesn't impose such a
9. See Pearl (1988), pp. 116-31, and Williamson (2005), esp. pp. 14-48. According to
Wil liamson, Bayesian Net does not necessarily imply that we use Bayesian subjective probahility, and the reason why this is called '8ayesian' is only that it appeals to Bayesian( ·und itionalisation. Williamson puts forward a view of Objective Bayesianism which is based
Ilpon p rior probabilities that are publicly acceptable.
10. Glymour (1980). p. 110.
11. Ibid .• p. 120 .

20

TilE PI II LOSOPII Y OF FACiNC UN 'H i I AIN

I'require ment for the ev idential rc lcvo n C 1.0 ~ II h bnl'k~r() und know ledgeor theory, because it simply regards Bayes's th 'o rc m, D mathematicalequation, as the expression of confirmation. This siluation of BCOND
might produce some cOWlterintuitive cases that are ta ken to be confirmation relations despite lacking such evidential relevance. In order to recognize this clearly, let us take two counterexamples to BCOND.
First, [want to give an example about a causal relation which is related
to the blueberry example again. Certainly, as [said, we can accept that my
reduced eye fatigue after consuming blueberries (e,) raises the probabilityof the hypothesis (h , ) that consuming blueberries causes our eyes to function well. But what about the next hypothesis? :(*h , ) having our teeth discoloured by blueberry juice causes our eyes tofunction well.
Perhaps whenever we consume blueberries we automatically discolour
our teeth with blueberry juice more or less. Then, according to our experience, it can be said that having our teeth discoloured by blueberry juice
has been regularly conjoined with the amelioration of our eye function.
Now, let us think of the next evidence:(*e , ) [ actually suffered from less eye fatigue in front of my computer
screen after discolouring my teeth with blueberry juice than when
[ didn't do that.

As far as conditional probability is concerned, we have to say that *e ,would also raise the probability of *h" i.e., *e, confirms *h,. However, thisconfirmatory relation is utterly unacceptable, because we don't think that
discolouring our teeth with blueberry juice causally affects our eye function. In reality, we firmly believe that, even if we discolour our teeth withartificial blueberry juice, the discolouration would have no effect on oureye function, because there is no causal relevance. This is nothing but the
problem of spurious cause in Suppes's terminology in the context of probabilistic causality 12 Of course, such a problem could be coped with byapplying the idea of 'screening off'. Suppose that we compare the case (1)of consuming blueberries while carefully trying not to discolour our teeth
with blueberry juice with the case (2) of consuming blueberries without
so trying, and the probability of the amelioration of our eye function
remains the same in either case. Let EA be 'my eye function is amelio12. Suppes (1970), pp. ~1-28.

BA YESIANISM AND RESPONSIBILITY

21

rated', CB '[ consume blueberries', and DTB '[ discolour my teeth withblueberry juice', and that the conditions can be expressed like this:
P(EA ICB & DTB) = P(EA ICB).
That is to say, CB screens off DTB from EA (or we can also state that CB
screens off EA from DTB), which means that DTB is just a spurious causeof EA. But this very situation seems to show that BCOND by itself is insufficient to treat that confirmatory process with causal relevance. Thus, w ehave to be careful of the conceptual difference between conditional probability and causal relation, both of which are intertwined but nonethelessrn ust be distinguished from each other. BCOND cannot correctly consider
Ihis delicate difference between probability and causality, as far as it.1 ppeals only to conditional probability.
However, the current notion of Bayesian Nets tries to refine Bayesianconfirmation theory by simply incorporating an operation of 'screening
off' into the Nets. When networks are constructed, causal relations among
variables are often used as a foundation of the Nets. Such a process of construction is supported by the next principle called Causal Marcov Condition:
Causal Marcov Condition
Each variable is probabilistically independent of its non-effects, conditioned on its direct causes.13
This Causal Marcov Condition is linked with 'Principles of the Common
Cause', which 'claims that if two variables are probabilistically dependent
then one is the cause of the other or they are effects of common causes andthose common causes screen off one variable from the other, i.e., render thetwo variables probabilistically independent'14 In this way the operationof 'screening off' is integrated into Bayesian Nets. However, even thoughsuch refinement is introduced, the Nets still could not perfectly distin~ uish a probabilistic relation from causation. For there can be a case ofprobabilistic dependence that could not be screened off although suchdependence is not causal at all. For instance, Williamson mentions thecase about 'having flu' and 'infection of Orthomyxoviridae (a generalclass of virus including flu as one subclassification),. They have related
meaning and are probabilistically dependent, so the one cannot screen off
Ihe other even if a common cause is supposed, but nevertheless there is nocausal relation between them. Yet, if we simply infer by using Bayesian
13. Williamson (2005), p. 50.
14. Ibid., p. 51 .

22

TilE 1'1 11 LOSO I' I IY OF FACiNC UN 'II<J A IN I \Nets, we will have to conclude that the re is a nUKoln.' lolion bdween thesetwo variables. " This is a serious defect in developi ng the theory of confirmation, since many hypotheses to be confirmed definitely involve causal
relations. 16
Second, I mention an example created in connection with logical relations. Let us appeal to the blueberry example again. As already recognized, e" evidence of my reduced eye fatigue after consuming blueberries,
confirms h" a hypothesis of a causal relation between consuming blueberries and amelioration of eye function. Then consider the next hypothesis:(h,) swallowing mercury causes our brain to work better.

Then think about this probability of the conjunction of h, and h, conditional on e, (ignoring temporal order, which causes no problem here):P(h, & h,l e,) =P(e, I h, & h,)P(h, & h,)P(e,)

According to the initial supposition, it seems that the likelihood, P(e, I h,),is very close to 1, hence, if we follow a logical characteristic of conjunction, the likelihood of P(e, I h, & h,), is also very close to 1. So, as far as theprior probability that P(e,) is clearly less than 1, it will come to P(h, & h, Ie,) > P(h, & h,), because P(h , & h, I e,) is mostly equivalent to what resultsfrom P(h , & h,) divided by a number less than 1. Thus, BCOND must
declare that e, confirms h, & h" but we would find it quite absurd to thinkthat my reduced eye fatigue after consuming blueberries gives evidential
support to the claim of blueberries' causal effect on the eyes and mercury's causal effect on the brain. Perhaps Bayesians react to this by asserting that an increase of P(h, & h,) given e, is less than an increase of P(h,)
given e, because the prior probability of h, & h, is less than that of h,.
15. Williamson (2005), p. 53.
16. Currently theories of probabilistic causality are developed by being sensitive to the
problem of causal relevance. For example, the notion of 'Contextual Unanimity' that Nancy
Cartwright introduced borrowing John Oupre's terminology reflects this trend, as this
implies that causes are context-independent, i.e., causes are causes no matter what relevanceis concerned. See Cartwright (1989), p. 143 et a1. This notion itself, however, must be scrutinized further because some counterexamples are imaginable. See Hitchcock (2002), p. 16.
Incidentally, Twardy and Korb (2003) are worth noting in connection with this topic, since
they propose a new strategy of probabilistic causality by offering the refined notion of'Objective Homogeneity', at the basis of which contextual unanimity is defined. They also
try to combine this notion of objective homogeneity with Bayesian Nehvorks . Their argument might influence my 'Points about Bayesian Networks. But Tneed time to reflect on that,
so I want to make it my next task to consider how to evaluate their arguments.

BA YESlANlSM AND RESPONSIBILI1Y

23

However, such an assertion does not erase at all the fact that e1 is supposed to confirm h, & h, by BCOND. Thus, unless Bayesians introduce
some other idea that can consider the relevance of evidence to a background theory like Glymour's bootstrapping strategy, it does not seemthat BCOND could avoid this absurdity."

4. The Problem of Old Evidence
Well, let's move to the second difficulty concerning BCOND. That is to say,
I3COND cannot describe a confirmatory process in which P pJE) = 1, because
in that case, Ppri(H I E) is equal to Pp'i(H), so it comes to Ppm(H) = Pp'i(H),which means that evidence has nothing to do with confirmation ls Of
course, if no confirmatory process occurs when P pri(E) = 1, there is no problem. That case is simply irrelevant to confirmation, therefore harmless to
BCOND. For example, probabilities of logical truths in the form of a tautology like modus pones or the law of excluded middle must be 1 (in fact
this is usually included in the axiom of probability calculus), no matter
when we estimate them. However, P pri(tautology) = 1 causes nothing inconvenient to BCOND, since we do not carry out any confirmatory reasoning
conditional upon logical truths, although we can make a deductive inference by them. Another harmless case is that we propose a hypothesis inorder to explain evidence which we have already had. In this case, although
I' pri(this evidence) = 1, we have no problem with regard to BCOND,
because we do not expect this evidence to confirm the hypothesis. Thisevidence is rather the basis of the hypothesis, so it is logically entailed
by the hypothesis. In other words, this evidence isn't regarded from thestart as contributing to confirmation. If we illustrate this in the blueberry
17. The same absurdity was pointed out by Glymour regarding the hypothetico-deductive,lCcount of confirmation (i.e., the deductive strategy), See Glymour (1980), p. 135. As to an,lpplication of this absurdity to Bayesianism, see Pennock (2004), section IV.
18. This can be proved eaSily. According to the definition of conditional probability,(1) P,,(H IE) = P,,(H&E) I P,,(E).
So, general addition rules of probability tell us that
(2) P,'i(H&E) = P,,(H) + Ppo(E) - Pp,(HvE) .
Then, by presupposition,(3) Pp'i(E) = 1.
So, since E logically entails HvE, P pri(HvE) can't be less than Pp,/E). Therefore,(4) PpJHvE) = 1.

Then, by applying (3) and (4) to (2),(5) P,,(H&E) = P,, (H) + 1 - 1= P, ,(H).
Consequently, by apptying (3) and (5) to (1),(6) Pp,(H IE) = Pp,(H) .

24

BA YESIAN ISM AN D RESPON SIBILITY

TIlE PI II LOSOPI IY OF FAC INC UNChl< I " IN I Y

example, this evidence correspond s to the post d oto .lbou t the causal
effect of blueberries on eye function tha t probab ly the ocu list has alreadyobserved. Those data compose the hypothesis h, rather than confirm it.
However, we have to pause here. Are those cases with probability 1
always harmless to BCOND? What should we think of the case in which
we subjectively feel that those things with probability 1 play the role ofevidence and confirm the hypotheses? In questioning this way, we comeacross the so-called problem of old evidence. This problem was initiallyraised by Glymour, who describes it in an unmistakable way like this:
Newton argued for universal gravitation using Kepler's second andthird laws, established before the Principia was published. The argument that Einstein gave in 1915 for his gravitational field equations wasthat they explained the anomalous advance of the perihelion of Mercury, established more than half a century earlier . . . . Old evidence canin fact confirm new theory, but according to Bayesian kinematics it
cannot. 19
The gist of his point is very obvious. Old evidence about the perihelion of
Mercury had already had probability 1 at the time of 1915 when Einstein
proposed his theory of gravitational field equation, therefore, following
the situation in the case of P pri(E) = 1 which I mentioned above,
P!9!,(GFE I PM) =P!9!,(GFE & PM)
P (PM)
1915= P I9I ,(GFE)

where GFE stands for the gravitational field equation and PM is old evidence about the perihelion of Mercury. That is to say, this old evidence
has no confirming power. Nevertheless, as a matter of fact, the old evidence actually confirmed his theory. Thus, BCOND can't deal with thisfact appropriately. This seems to be a very serious criticism against
BCOND and Bayesian epistemology. Could Bayesian epistemology solve
the problem of old evidence? Or should we flatly reject Bayesian ideas
because of this problem?

25!'(old evidence) '" 1. 'This response would be the most effective pOSSible, itwould remove the problem altogether'. (2) Second, when saying that theold evidence confirms the hypothesis, 'we make reference not to our present actual epistemic state but to some alternative(s) thereto'. That is to say,we are considering such a counterfactual conditional that if the old evidence had been established sufficiently later than it actually was, it would
have confirmed the hypothesis. (3) Thirdly, 'the phrase "E confirms H"
may well be used in the speech of the vulgar, but attention is being drawn
to something else that has to do with E, and really does confirm H for us'.
To put it another way, the problem should be interpreted as rather concerning our subjective state of belief beyond the relation between evidence and hypothesis simpliciter.
The first response claiming P(old evidence) '" 1 is quite attractive inorder to eliminate the problem of old evidence altogether. For example,
Ma rk Kaplan suggests that probability 1 could be assigned only to logicalor mathematical truth.'! Timothy Williamson also maintains that evidenha l probability cannot always keep 1 by denying a tacitly presumed
claim about evidential probability, that is, MONOTONICITY, which says,'once a proposition has evidential probability 1, it keeps it thereafter' .22
Williamson finds BCOND to allow propositions to acquire probability 1,
but not to lose it, which leads to monotonicity. But he refuses this idea byemphasizing the factor of our forgetting, and claims that evidential probnbility could go down to less than 1 as time passes, saying, 'Bayesians
have forgotten forgetting' .'3 If that is the case, the problem of old evidence
will instantly vanish, since this problem stems entirely from the situationof P(old evidence) = 1. 24
However, this response against P(old evidence) = 1 is not perfectly reasonable, for if we restrict probability 1 to logical or mathematical truth,
the concept of evidence seems to lose a foothold. If obvious data of observa tion we have here and now, which is typically taken to be evidence,
have only less than probability 1 in any sense, it is difficult to talk about
evidence. Williamson's argument avoids this defect, since he allows thecase in which evidence has evidential probability 1 for some time before
21. Kaplan (1996), pp. SQ.-SI.

19. Glymou1 (1980), p. 86.

22. Williamson (2000), p. 218.
23. Ibid.; p. 219.
24. I am fully aware that we have to take into account Jeffrey Conditionalisation as well inthis context of questioning whether evidential probability is always 1 or not, since the main
point of Jeffrey Conditionalisation is to seriously consider the pOSSibility that probability of
l'v idence is not 1. But I think that focusing my attention on scrutinizing BCOND is not off thepoint because that is definitely still the very core of Bayesian epistemology. See Jeffrey

20. van Fraassen (1988), p. 154.

(1983), Chapt.,]].

5. Three Responses to the Problem
Bas van Fraassen neatly presents three possible responses to the problemof old evidence.20 (1) First, no one is certain about the old evidence, namely,

26

BA YESIANISM AND RESPONSIBILITY

T il E 1'1 ll LOSOl'l lY OF FACiNC UNt I '" A IN I Y

we forget it. Yet.. how about the case where Wl' Hl'I ,) P~)l' li c lll a r observa-

tional datum, and then happen to stumble upo n 0 particu lar hypothesis
independently of the datum immediately after the datum (the refore keeping evidential probability of the datum 1), and then come to realize thatthe datum confirms the hypothesis (which is not so rare actually, as I will
mention later)? In that case, the problem of old evidence seems to appear
again, as far as the term' old' is used in a loose way, as in our ordinary life.
However, in spite of that, I want to think of much of this response from a
bit different point of view, which I shall mention later.
Let us glance at the second response, namely the one to avoid the problem by introducing counterfactual conditionals. Howson and Urbach givea typical argument of this reaction. They say that in the formulation of the
problem of old evidence against Bayesian theory, 'it is clear that the theory
has been incorrectly used. It is equally clear where the mistake lies, namely,
relativising all the probabilities to the totality of current knowledge. They
should, of course, have been relativised to current knowledge minus e'."Then, there are the usual objections against this reaction. How can we go
about having a uniquely determined set of background knowledge minusthat particular old evidence? How should we treat propositions logicallydeduced from the sentence of evidence? As far as those counterfactual
conditionals involve many fictitious suppositions about the history of science, we should ask how we could verify the truth of those counterfactual
conditionals.26 In short, all of those objections point out that those counterfactual suppositions are too unclear to be enough to clarify and solve
the problem of old evidence. I think those are absolutely right. But so
what? The fact that counterfactual conditionals are hard to verify cannot
be the reason at all to exclude them from our analysis of BCOND, since
any theory of confirmation must involve some counterfactual analysis intheoretically analysing the relation between evidence and hypothesis, orin making predictions. When predicting something, we have to makecomparisons between several future possibilities by taking into accounteach probability, which is definitely the process of counterfactual analysis. Actually, such a sort of counterfactual consideration is alreadyembedded in the initial formulation of BCOND, for BCOND offers thedevice of analyzing a confirmatory process by supposing the situation
before we get the evidence even though we have actually had it.
Well, how about the third response? This type of response is represented by Garber's argument, whose substantial idea is succinctly
expressed by this:
25. Howson and Urbach (1993), p. 404ff. See also Ho rwich (1982), p. 52.

26. See van Fmassen (1988), pp. 155-56, and Glymour (1980), pp. 87-91.

27

If old evidence can be used to raise the probability of a new hypothesis,
then it must be by way of the discovery of previously unknown logicalrela tions. In the cases that give rise to the problem of old evidence, weare thus dealing with circumstance in which hypotheses are confirmed
not by the empirical evidence itself, but by the discovery of some logicalrelation between hypothesis and evidence"
tf this is the case, the problem of old evidence would be solved, because
the discovery of logical relations between hypothesis and old evidence ismade now, before which the old evidence hasn't been regarded as evidence. As it were, that is newly discovered evidence which has old history. As is the same with the two previous responses, some philosophers
have already raised an objection against this response, whose kernel,eems to be very simple. For example, John Earman says, 'The original' luestion was whether the astronomical data F confirmed GTR [the genl'ral theory of relativity] (for Einstein if you like). Garber, Jeffrey, andNiiniluoto replace this question with the question of whether Einstein's
learning that TI-E raised his confidence in the theory. Not only are thetwo questions not semantically equivalent; they are not even extension.llly equivalent'.211 In other words, the gist of this objection is that
responses like Garber's concern not the issue of confirmation properly,
hu t just the psychological process of belief of a person who studies the
Cilse in question.
I think that this objection isn't fair to the Bayesian theory of confirmation. It seems to me that there is a highly doubtful presupposition in theobjection, namely that confirmation is a sort of objective relation between
da ta and hypothesis independent of the human process for dealing withheliefs. However, we cannot deny at all that confirmation is primarily,lCcomplished regarding our belief, or to put it another way, regarding
our epistemic process, as Bayesian epistemology takes for granted. I completely agree with Bayesians in that they correctly accept the intrinsic connection between confirmation and our epistemic process. This could bemade quite explicit if we adopt a deterministic view, since in that caseconfirmation in the form of raising probability obviously has nothing to
do with objective reality."
27. Garber (1983), p. 120.
28. Earman (1992), p.l30. See also van Fraassen (1 988), p.l63.

29. Certainly what is called objective Bayesianism thinks much of objective factors in,I.,sessing confirmatory power, but such objective facto rs are only concerned with determinItlg prior probability in some impersonal way. In particular, a sort of a principle of indiffervnce is often relied on to determine that, but apparently the principle is hopelessly difficult
tu clearly formulate. See Talbot (2001), section 5.1.

BA YESIANISM AND RESPONSIBILITY

6. D ecision- Lad en Aspects of Con firmalion

For my part, I want to assert that all of the three responses to solve theproblem of old evidence are somehow plausible, or that none of them are
mistaken. However, I don't think that they are perfectly satisfactory, since
they are just responses to the problem, so they don't seem to reach the systematic analysis of how a viewpoint supporting each response could contribute to the theory of confirmation. In addition, if those responses aim to
defend Bayesianism, they are insufficient in that respect as well, because
it isn't clear how they could cope with the difficulties of evidential relevance that I discussed before mentioning the problem of old evidence.
Therefore, I will propose an idea to break the deadlock. I will try to do it
by taking up the issue of medical cases. Actually, medicine is, I think, themost appropriate subject for verifying some philosophical theories about
empirical knowledge obtained through induction or confirmation, since
medicine is definitely a genuine empirical science. In my opinion, when
we discuss the philosophy of science, it is an unrealistic one-sided view tofocus on physics or evolutionary theory and ignore other areas, particularly relating to our practice of such as dietetics, exercise physiology, or
ethology, as well as medicine, for actually science comprises immense
fields of research. Furthermore, medicine is especially suitable to examine
Bayesian theory which appeals to degrees of belief and subjective probability, because in medicine subjective belief essentially matters. For
instance, subjective impressions that a physician receives from or gives topatients at the clinical scene is often crucial for diagnosis or treatment, or
subjective belief can be an object of medicine in the case of psychiatry.
Now, let us consider the next situation as a typical example.
A patient comes to the emergency room of a community hospital withsigns and symptoms that the chief resident calls equivocal for appendicitis. He decides to consult with the chief of surgery, who agrees thatthe symptoms and signs are equivocal. She knows that patients withsuch symptoms and signs often have NSAP (i.e., nonspecific abdominalpain) and, if an operation is performed, will have had unnecessary surgery. Some such patients, however, have an inflamed appendix which
may perforate by the time of surgery. She wonders if it might be beneficial to hold this patient for six hours in the emergency room to see
whether the symptoms improve or worsen (or remain the same) before
deciding whether to operate. 30

This is quoted from a famous textbook about clinical decision, so someone
rna y doubt how relevant this decision problem of whether to perform an"pe ration is to our context of discussing problems of confirmation. Of
course, for the time being, decision problems about medical treatment
should be outside my argument. However, what I focus my attention onis the uncertainty of medical diagnosis, as in the example the chief resident describes as 'equivocal'. Apparently diagnosis and treatment are two
major tasks in medicine, which are supposed to be distinguished but actu.l ll y are interconnected in a complicated way. Then, nobody denies that
diagnosis is nothing but a theoretical task of confirming a hypothesis (e.g.,
Ihis patient suffers from appendicitis), while treatment is corresponding
to a practical application of the theory. In this sense, I can connect medicall·xamples with problems of confirmation by specifically putting the caseof medical diagnosis into question.
Well, how do phYSicians or clinicians confirm their diagnoses? I am.]sking this question from a descriptive point of view, although I know thatlJayesian theory of confirmation is proposed in principle as a normative
theory, as I said earlier. The reason why I intentionally do so is that any
Ilormative theories must be based on understanding actual matters of factwhich empirical descriptions provide, otherwise they would not be persuasive. In this sense as well, it is highly beneficial to scrutinize medical
diagnosis in order to solve problems of confirmation, since there has beenplenty of empirical data already accumulated in the course of the study of
ev idence-based medicine (EBM). Anyway, we have to check how physicians or clinicians make their diagnoses. First of all, it should be noted that
.It the clinical scene evidence or data to confirm a hypothesis or diagnosis
is not simply given but should be collected on purpose. Collecting these isIIsually done with consideration of what sort of diagnostic tests should be
l'.1rried out and what kinds of risk is taken to conduct such tests. Undoubtl'd ly, this is nothing but the process of decision-making. As a matter of
1.ICt, confirming diagnosis is basically regarded as one of the processes of
rli nical decision. According to Weinstein and Fineberg, ' . .. most clinicaldecisions fall into one of two categories, namely, (1) decisions regardingwhether to seek additional information (and, if so, how), and (2) decisions
n lllcerning which treatments, if any, are to be employed'.31 Or, Chapman.lIld Elstein say, ' ... the patient and physician must decide whether thehenefits of a treatment outweigh the side effects or whether the risks of ad iagnostic test are worth taking, given the information it will provide'.32~ !. Weinstein and Fineberg (1980), p. 23.

30. Weinstein and Fineg erg (1980), p. 13 .

29

~ 2 . Chapman and Elstein (2000), p. 189.

30

TilE PIIILOSOPII Y OF FAU NC UNL H~ I AIN I'

In fact, even computer-based clinical diagnostic decision support systems
have already been developed " In connection with the appendicitis example above, to hold this patient for six hours in the emergency room is asort of diagnostic test to collect additional clinical data, which is actually,as the example clearly shows, involved in their deciSion-making. If so, we
can say that confirmation of diagnostic hypothesis intrinsically includes a
decision-laden aspect.
This decision-laden aspect could be recognized from a different angle.
That is concerned with how to determine prior probabilities of a particular disease or a particular symptom, and how to determine the likelihoodof a particular disease given a particular symptom." How do physicians
determine those? Usually they initially try to find relevant primary studies in the medical literature. However, this task itself involves probabilistic situations, because, for example, there might be publication bias (i.e.,
positive studies are more likely to be published than negative studies),"or because data published in those studies are not necessarily applicableto the patient at hand. 36 In other words, if they stick to such objective harddata, they have to choose or make a decision among them. This is also theappearance of a decision-laden aspect. But actually, physicians often facea clinical case in which it is not possible at all to get objective hard data .
Nevertheless, 'decisions must be made and are implicitly based on judgment about probabilities of uncertain events'." That is, phYSicians often
rely on subjective probabilities, which make clinical cases fit Bayesiananalysis. Yet, unfortunately, 'Information obtained by physical examination or a diagnostic procedure may be intrinsically ambiguous and may
thus be interpreted differently by different observers.... Observers may
differ in their ability to detect these signs and in their propensity to record
them'.38 Some psychological factors to produce cognitive bias when
physicians determine basic probabilities have been pointed out; for example, representativeness, availability, or anchoring," which are generally
called 'confirmation bias'.'" Of course, according to the Bayesian idea,
such bias could be revised into an approximate agreement as evidence is
33. See Miller and Geissbuhler (1999), pp. 3-34.
34. Even generally speaking, many philosophers regard the problem of how to determine
prior probability as a fundamenta l difficulty about Bayesianism. See Hesse (1975) and
Swinbume (2002).
35. Hunink and Glasziou (2001), p. 225.
36. Ibid., p. 232.
37. Weinstein and Fineberg (1980), p. 172.
38. Ibid., p. 2.
39. Tve;sky and Kahneman (1974), pp. 1124-3l.
40. Chapman and EIstein (2000), p. 187-88.

BAYESIAN ISM AND RESPONSIBIUTY

31.lccumulated. But this is not the case with medicine, since clinical diagnosis and treatments are more or less urgent, with no time for collecting plentyo( sufficient evidence. Thus, in order to reduce such bias properly and to be.IS precise about probability assessment as pOSSible, even a method of decision by groups of experts, which is called the Delphi method, has been
proposed." In any case, these circumstances strongly suggest that there is,1 decision-laden aspect lurking in the clinical confirmation process.
Those considerations thus far help us to find that there is the samedecision-laden aspect at a deeper level. That is to say, we have to make adecision about which background theory must be relied on to give a satis(.lctory diagnosis. As to the appendicitis example again, presumably clinidans of Chinese herbal medicine will have a completely different way of
Ihinking to arrive at a diagnosis; for example, they may judge the cause as.1 strained abdominal muscle. If so, a phYSician who has been educated inho th Western medicine and Oriental medicine (such physicians are cur'l'ntly not so rare) ought to make a decision about which system it wouldh" more appropriate to apply. Mercury, which I took as an example (h,) earlier, is well known to have been thought to be actually good for the health in'\lrly modern times although no one adopts such a system nowadays. Here
we find a case in which a choice of theories must be made. Similar points,.111 be raised at a less radical stage. Let's go back to the eye fatigue exampie. Symptoms classified as eye fatigue can equally appear in the case of ahrain turnor or psychosomatic illness. Therefore, a phYSician seeing a
I'.ltient with this symptom, exactly speaking, must make a decision about
which department of medicine should treat her: ophthalmology, brainsurgery, or psychosomatic medicine. This could be regarded as a sort ofI hoice of theories. If we probe deeply into this idea, it seems that decisions"hout how to collect diagnostic data or how to assess probability as I havedisc ussed could also be taken to be a sort of decision about theories.
I\s a matter of fact, the same thing could be corroborated by the case ofphysicists as well as of physicians. Different reactions experienced by
I.orcntz and Poincare to the Michaelson-Morley experiment could be one" I Ihe typical examples in which differences (i.e., different decisions) abouth.lckground theory deeply influence the confirmation relation. Lorentz,,·ga rded the result (i.e., the null result) of the experiment as evidence of the,,,ntraction hypothesis by sticking to the theory of aether, while Poincare
I, 'ok it to be evidence of the principle of relativity by questioning the the,' ry of aether" To put these points another way, evidence or data to supI'" rt a diagnOSiS is inseparable from a background theory, which precisely
11. Hunink and Glasziou (2001), p. 237-38.
12. Cushing (1998), pp. 202-4.

32

TilE PI II L050PII Y OF FACiNC UNCH { I AIN I \BA YESIANISM AND RESPONSIBILITY

33

corresponds to what J noted earlier by mentioning C lyrnour's basic idea
and his bootstrapping strategy" In fact, the same circumstance lurks inmedica l decision analysis is supposed to be linked with confirmation relalion by noting the decision-laden aspect in the process of confirming a

the idea of Bayesian Nets as well. When we construct networks, we haveto 'choose' a variable as a root" and 'determine' the prior probability ofthe variables." Obviously a process of rational decision-making lies,
although unconSCiously, at the bottom of those situations. Additionally,'prior knowledge of causal relationships' is needed in order to construct
Bayesian Nets," which suggests that we have to make some decisions
about causation in advance, particularly when we apply networks to thecase in which there is an etiological controversy, such as a case about
improving our physical condition. Therefore, we must say again, evidence or data to support a hypothesis or diagnOSiS is inseparable frombackground knowledge, i.e., from selecting particular knowledge rather
than others.

diJgnosis.

7. Decision-Oriented Aspects of Confirmation

Thus, we have to consider a decision process for confirming a hypothesis
in order to understand the problems of confirmation, at least as far as
medical cases are concerned. This suggests that we must take into accounta reCiprocal relevance between a philosophical decision theory and a clinical decision analysis for the sake of establishing an adequate theory of
confirmation. Actually, Chapman and Sonnenberg give the following significant suggestion: ' ... the study of medical decision making should be a
two-way street: decision theory should benefit medical practice, and medicine should advance the study of decision making .... Medicine can contribute to decision theory because medical decisions sometimes pose
unique challenges that spur advance in both decision analyses anddescriptive decision theories" 7 My argument so far happens to have thesame way of paying attention to medical decision analysiS from a descriptive point of view to examine philosophical problems, but in my case
43. My argument here might correspond to Christopher Hitchcock's argument about cau·sation, as well as to Glymour's. Hitchcock stresses that causation should be studied not as abinary relation between cause and effect, but as a ternary one of cause, effect, and an alternative cause inferred from the context or background information. However, I am moreinte rested in how we choose the context. That question is not seriously posed in Hitchcock's
argument. See Hitchcock (1996), pp. 267-82.
44. Pearl (1988), p. 122.
4S. Williamson (2005), p. 128.
46. Ibid., p. 49.
47. Chapman and Sonnenberg (2000), p. 7.

•

In any case, next we ought to question a normative form of the decisionI"dcn aspect of confirmation beyond the descriptive examination that 1h"ve been engaging in, insofar as my argument is related to decision
lheory." What is absolutely necessary first to address such a question.. dcq uately is to clarify what sort of utility or value should be considered
hl're. But, for the time being, tJ:>e answer to this question is very simple in,'n official sense. That is to say, whether in diagnOSis or treatment, a good
qunlity of life of the patient at hand is the very utility to which a medical,Ic-cision is directed . That can be just a life in contrast to death, longer
Yl'olrS of life, or longer quality-adjusted life years (QALYs)," depending\I ll the situation. However, I want to point out some additional factors
Ih"t are rarely mentioned in this context. 1 raise three additional factors orv,lilles to be considered, which could be deduced from the quite prag1lI"tic standpOint of regarding confirmation of diagnosis as a physician's
I"",ctical action to make clinical records or to inform a patient of the diagnosis. First, as a matter of fact, physicians have to take into account the
Ill'rsuasiveness (perhaps gained through clarity and intelligibility) of theird",!;noses, because currently physicians ought to go through the process
01 informed consent at the clinical scene. Second, a physician shouldoll1ehow consider how Significant giving each diagnOSiS is to the physi, 10111 herself or the clinical institution she belongs to as regarding her or its"'I>l,tation. This will be particularly essential when a patient has a very
"pl'cial social status or is suspected of having a very rare infectious dis,',lSe. Third, a sort of psychological effect that patients receive from being
IlIlmmed of a diagnosis (I am not sure whether to call it the placebo effect"" not) must be counted when a diagnosis is recorded or given. In reality
1I1,lIly patients would be relieved at being given a particular name for
Ihl'ir disease in contrast to the situation in which they are anxious about
whnt disease they have. Or they might be healed by the fact that a profes" "nal physician explains a diagnosis based on detailed tests, perhaps inill<' form of a considerate chat. In these respects, giving a diagnosis to ai',llient has a certain clinical value by itself. If those factors or values,
It\. As to the distinction betvYeen 'descriptive' and 'normative' in the context of decision
Ih,'\u'y. I learned a lot from Melior (2003), which stresses the important role of descriptive.m.l \lbjective aspects in decision theory in contrast to the standard trend to think much of
III Irll1(l tive and subjective aspects.
PI, Crisp (2004) directed my attention to the theory of QALYs, which is currently becomIlIg Important in the context of medical ethics.

34

Til E I'II ILOSOPII Y 01' FACING UNCFR I AI N I Y

which must involve careful decision-makin g, ar' Ii nlc.1l1 y relevant to diagnoses, we have to say that confirmation o f a diagnosis leads to decisions
about such values. In other words, confirming a diagnos is is a decisionladen process as I discussed (where the value to be considered is simply
the patient's good quality of life), but ultimately it is also oriented to deCIsions about those additional values or utilities.
Well, then, how can we think about the difficulties of confirmation I
examined earlier by exposing the decision-theoretic (i.e., decision-ladenand decision-oriented) aspects of confirmation? I think that those difficulties will be simply solved, or at least we will have a deeper understandingof the difficulties. As to evidential relevance, it comes to that such relevance must be simultaneously determined as decisions are made about
what sort of diagnostic tests should be conducted. In a certain sense, decisions about diagnostic tests are nothing but decisions about the relevanceof evidence to background theories, although such decisions could bechallenged and revised later by new data. Then, how about the problemof old evidence? In reality, confirmation through old evidence is not rareat the clinical scene. Remember the appendicitis example. In the example
two hypotheses corresponding to the particular symptoms are considered, namely, it is appendicitis or NSAP. But, according to Weinstein and
Fineberg, ' ... the patient with acute abdominal pain may be diabetic'."'. If
so, and if some clinical test of the blood, for example, suggests qmte
strongly the hypothesis that the patient suffers from diabetes after thephysician has been wondering whether the patient has appendiCllls or
NSAP, then evidence of acute abdominal pain is nothing but old eVidence
which confirms the new hypothesis that the patient suffers from diabetes.'! Nevertheless, no theoretical problem occurs here, although thephysician may be forced to change her strategy.
It is not difficult to understand what is going on here if we take into
account decision-theoretic aspects included in confirmation of diagnosis.
Confirmation of the new hypothesis by old evidence is based on decision
making that is performed by considering both (1) a newly proposed relevance between old evidence and the new hypothesis through backgroundtheory and assessment of probabilities and likelihood, and (2) utility that
SO, Weinstein and Fineberg (1980), p. 26.
51. In the process of confirming a new diagnosis of diabetes like this, the next case does notseem to be so rare: a physician recognizes the patient's abdominal pain again, and thenlearns the result of a blood test from which she reaches the diagnOSiS of diabetes independently of abdominal pain, and a few seconds later she finds the abdominal pain to be further
evidence to confirm the diagnosis . In this case, even if we accept Williamson's denial ofmonotonicity, the problem of old evidence appears.

•

BA YESIANISM AN D RESPONSIBIUTY

35

I, newly questioned by the newly proposed relevance. In other words, so•.1lied old evidence appears not as genuinely old evidence but as presentt'vidcnce as it were in connection with newly proposed relevance and,wwly questioned utility in the course of decisions made now. This solu111111 I offer seems compatible with three classical responses to this probh·rn . My solution could be consistent with an idea that the probability ofIIld evidence can be less than 1, because probability of evidence is supposed to be assessed in relation to the particular hypothesis through ap.!rticular background theory, so under a different theory, probability 1 oflitt' evidence could not work as such probability, or simply may not matter.
N.'xt, as far as confirmation is based on a sort of decision making, counh·rf.1ctual analysis is indispensable, since a decision is usually made con. Idcring several possible (counterfactual) results. Finally, Garber's appeal
it, Ihe discovery of logical relations is very similar to my solution as
tqi.u ds having such an idea that we enter a new stage when we confirm a
I"'W hypotheSiS by old evidence.
Ilowever, two crucial questions might be raised. First, my argument is
IIllly concerned with the medical situation of confirming a diagnOSiS, so it
I dou btful whether my proposal can be applied to any confirmation relaIIIIn in general. I admit that this is still an open question, although [ tendh' Ih ink that my proposal is ultimately applicable to any confirmation
1I 'I.lI ion, since, as a matter of fact, any confirmation should be made in theIII' Ill of a sort of speech act directed to other people. Therefore, decisionlill'oretic aspects must be embedded there.52 Second, someone may say that
11 I, not clear whether my proposal of a decision-theoretic approach toI'".blems of confirmation results in reinforcing Bayesian theory or underIlIlning it. My argument, on the one hand, tries solving difficulties Bayesianlill'ory faces, which seems to defend Bayesianism, but on the other hand,lilY proposal seems to virtually destroy Bayesianism in the end by funda 1I,,'rr 10 Ily changing the structure of Bayesian theory. Presumably we have
III I.!ke Bayesian decision theory into account rather than Bayesian confir"",lion theory, for my proposal is decision-theoretic. Actually, as far as
lilY ,! rgument is decision-theoretic, I have to face the problem of what sort
" I dt'cision theory I should adopt. Is it possible to adopt Bayesian decision,," 'pry? If it is pOSSible, my argument would eventually come around to'I.' /\ccording to Howie (2002), subjective inte rpre tation of probability has always been
1"IIIIIl,lnt in the history of natural science from the eighteenth century up to now as a matter
1111.1, I, ,llthough officially frequency of interpretation of probability has been appealed to. If
111\ "Illposal, like Bayesian theory, is based even partially on the empirical fact that we usenl,,"1 live probability in confirming a hypothesis, Ho w ie's argument might suggest that my1.1" 1'.'....11 could apply to other fields of natural science than medicine .

36

BA YESIANISM AND RESPONSIBILITYT H E PH ILOSOPI IY OF FI\ClNG UNCERTI\ INTY

the defense of Bayesianism. But what is Bayesian decisio n theory? Whatshould be noticed about this at least is that Bayesian decision theory as
explanatory is a theory which explains action in terms of degrees of belief
and desirabilities, as Eells stipulates. 53 For if so, it seems to me that Bayesian
decision theory takes over all the difficulties of Bayesian confirmation
theory in that it accepts subjective probability, which leads to BCOND."
Furthermore, it is well known that Bayesian decision theory is puzzled bysome paradoxes like prisoners' dilemma or Newcomb's problem, in which'the probability matrix can be expected to change in one way or another as
and when one act or another is chosen'.55 Giving a diagnosis seems tohave the same structure as those paradoxical cases according to my proposal, because it sometimes has a sort of placebo-like effect. Of course,
Bayesians tried to cope with those paradoxes. For example, they invented
a skillful strategy called ratifiability. Ratifiability requires us to make adecision with conSidering the probability matrix the agent would have if
she finally decided to perform that act, on the supposition that it is possible for her not to perform the act she finally decides to perform. 56 Perhaps
introducing ratifiability might make it possible to treat those paradoxes
appropriately in the Bayesian framework to a certain extent. However,even this strategy doesn't seem to work well on a medical decision about
diagnosis. If a physician does not perform the act of informing her patientof her diagnosis at the end of the day despite having finally decided to doso, a whole circumstance of diagnosis and its probability matrix would bechanged as regards its placebo-like effects. At the clinical scene everything must be practical, so the supposition of ratifiability is not realistic.
Thus, it seems that my proposal is undermining Bayesian confirmation
theory or Bayesian epistemology rather than reinforcing it, at least as far
as a simple application of BCOND is concerned.
8. Logic of Responsibil ity
In any case, the next task I should tackle must be to investigate what sortof non-Bayesian decision theory could clarify those decision-theoretic
aspects of confirmation. However, that is so huge a task that I could not
and should not do it here. Instead of that I will briefly discuss how possi53. Eells (1982), p. 41.
54. Actually Bayesian decision theory is often criticized for not taking into account the
problem of causal relevance (Le., one of the problems of evidential relevance) adequately,
from which so-called causal decision theory arises. See Resnik (1987), pp. 112-15.
55. Jefhey (1983), p . 16.
56. Ibid., pp. 15-20. §ee also Skyrrns (1990), pp. 44-56.

37

ble it is to put Bayesian epistemology to some practical use regardless of
Ihose difficulties that I have mentioned thus far, because I don't think that
IS.lyesian theory should be abandoned altogether. Undoubtedly Bayesian
Iheory is an excellent and simple formulation of our reasoning, if decision
making has been already performed concerning evidential relevance andUl il ity. Therefore, if we apply Bayesian ideas to such cases in which such" decision has already been made, Bayesian theory is expected to show its
IIwn ability. What is such a case? What about the case in which we takeIh" issue of past events?" lt seems that when we retrospectively question
I'."t events like people's previous behaviour, relevance and utility have
Ill'cn established precisely by questioning them. Rather, we could say thatqoestioning them arose from recognizing their relevance and utility. In
Ihis sense, responsibility is a promising subject to which Bayesian theory,ni~ht appropriately apply. I conclude my argument by briefly sketching
my (although more or less provisional) idea about this, which hopefully
wo uld lead to a logic of responsibility.
First, I would like to offer a formulation of a function of expected harm(li ll) rather than expected utility. That can be given in a parallel way to a
. l.lI1dard formulation of expected utility. I illustrate it by the appendicitis,·•.lmple. Suppose that, when I decided to hold (i.e., hold the patient with"",ne abdominal pain for six hours in the emergency room), there were
Ihree possible results, i.e., improvement (im), worsening (ws), or suddend'·.Ith (sd), whose probabilities were assessed at that time at 0.5, 0.4 and11.1 respectively, and whose amount of harm (AH) was, for example, 0, 10,,,,d 90 respectively. AH can be assigned arbitrarily, but in principle AH
III Ihe case of benefit or improvement, namely positive utility, should"qual zero altogether, no matter how much positive utility is gained, since
111 1 ha rm comes. However, AH in such cases might be negative rather thanI ,'m if the result is so valuable that it is really worth risk or possible harm
III Iry it. This corresponds to the case in which a physician dared to perillnn a hard emergent operation with very small probability of success(,,,,.1 with high probability of generating death) when the condition of theI'.,lient was very dangerous and would lead to early death without treatIIll'nl'. AH of the operation could be assessed negatively if successful in
Ih, ,' case, and if unsuccessful, AH could be reduced compared with AH of
Ih,,' .<impliciter. Anyway, EH at time t in the past of holding the patient for.1, hours in the appendicitis example can be expressed in this way:'·7. It is not strange to apply probabilistic strategy to past events. Actually, for example,~ h ( ullngh discusses the issue of how to apply Bayes's theorem to statistical inference in his-

It It \' Sl'e McCullagh (1984), pp. 57--64.

38

Ti lE PI ll LOSOP l lY OF FACING UNCc lHA IN I Y

EH ,(hold) = AH, (imJP, (illl) + AH, (WSJP, (1115) + All , (sd) P, (sd)= 0 x 0.5 + 10 x 0.4 + 90 x 0.1=l3
Let act; denote a particular action based on a decision (whether confirmation or physical action), r its possible result, then my idea could be generalized in this way under the condition that there are only n possible
results from r1 to rn:
EH, (act) = AH, (r])P, (r]) + AH, (r,JP, (r,) + ..... + AH, (r,JP, (r,,)(P, (r]) + P, (r,) + ..... + P, (r,,) = 1)
Each probability could be calculated perhaps by applying BCONO normatively and retrospectivelySS That is to say, for instance, this physician
ought to have had or updated such subjective probability about such andsuch results given such and such data. In this respect, my idea seems to fit
Bayesian theory very well."
Finally, I propose a formulation of degrees of responsibility (OR) in
terms of EH. Let (mah) denote maximum amount of harm in an absolute
58. Hugh Melior kindly read an early draft of this article and asked me a very insightfulquestion: is expected harm no more than the in".'erse of expected utility (like, for example,
loss of function)? That is to say, he wonders whether an idea of expected hann is conceptu~
ally different from that of expected utility. This is a very natural question. But as my argu~
ment might show, at least two differences between them can be noted. First, expected harmshould be counted only in a retrospective way, while expected utility (or average loss corresponding to it) is usually assessed in a prospective way, as it is used for decision making
about the future action. Second, utility is not inversely proportional to harm . As I said, positive
utility is not equivalent to negative harm, because expected harm about positive utility
should be zero altogether. However, this is true of loss function, for no matter how posi~
tively the products that reach the desired quality are evaluated, their loss is zero. But per~haps negative utility or loss might not always be corresponding to positive harm if an initialcondition as a standard to assess utility is extremely fortunate. For example, if a very richperson whose income is one million pounds a month happens to reduce his income to three~quarter million pounds a month, we should say that no harm comes, although utility isassessed as negative, i.e., a loss, from his initial point of view. Thus, the concept of harm
depends on such complex factors as norm or context in comparison with concepts of utility
or loss which are relatively simple and objective to express numerically, so it seems that
expected harm should be formulated independently of expected utility and loss function. I
wish some suggestion would be given from experts as to how to refine this idea as a statisti~
cal formulation.
59. In fact, Bayesian theory has been already used in the context of jurisprudence, in which
responsibility matters of course, in order to understand the relation between hypotheses
about crime and DNA gVidence. For example, see Dawid (2002).

BA YESIANISM AND RESPONSIBILITY

39

sense (like, perhaps, harm caused by a brutal murder), suppose that r m,
onc of all rs, has actually happened in the end, then OR when an agent has
pe rfo rmed act; at time t in the past and rmhas actually happened can befo rmulated in this way:

OR(act; & rm) =IEH,(act;)AH(rm)1(mah)'

xw(,) is an intention-weight whos;, value can move between 0 and 1. w = 0
means that the agent is thought to have performed act;mechanically withuut any choice, and w = 1 means that the agent is thought to have perI"rmed act,fully intentionally (which could indicate in the case of OR that
It was performed from a selfish motive or mens rea). This formulation isr.'"ched by thinking analogously to a logical conjunction. It is obvious thatI ) I~ moves between 0 and 1, which enables this system to work steadily,h respective of different values that are arbitrarily assigned to AHs. If an
Ilgent fully intentionally committed a brutal murder from a selfish motive
with a completely certain method like decapitation, then EH, (this murder)(IIIGh ), AH(this death) = (mah), and w = 1, therefore OR (this murder & thisI/m/h) = 1, which is the maximum. On the contrary, if an agent killed
IlI10ther person through a process that the agent could not physically avoid
II I " 11, then, no matter what value EH and AH have, OR (this killing & this"m /h) = 0, which is the minimum, because w = O. Perhaps in order to makethis formulation more persuasive, we should consider how to deal with
11.., case of an attempted action that wasn't accomplished, since the caseo,','rns to suggest that AH (the attempt) = 0, which would automatically
10 '1 1.1 to no responsibility. That is counterintuitive. My opinion is if we take
1,110 account harm (for example, fear or anxiety) caused by only attempted,11 I,on when counting EH, then it would come to AH (the attempt) > O.
I'<Thaps OR is neither equivalent to degrees of guilt nor straightfor1Y" ..dly contributive to the assessment of culpability. Questions of law
1," llId ing medical malpractice suits are judged by examining various
tllll<' '' factors, such as an agent's ability to be responsible,'" social or family, I" IIlllstances that cause the agent to act in such and such a way, and so'''' 1\ 11 that I hope is that my proposal about OR could be at least one
d"I"I"" to sort out issues of responsibility at the starting point, probably
f,O In particular I think that the problem of criminal behaviour performed by mentally
III .,'oIl'd people must be carefully scrutinized, since this problem is extremely difficult to

1,1,111' III the traditional philosophical context of debating freedom and responsibility. As to
Ihl_ I" 'lplcxi ng problem, see, for example, Schopp (1991) .

40

BA YESlANISM AND RESPONSIBILITY

T I lE 1'1 "LOSOPII Y OF FAClNC UNCmn AIN 1Y

following Bayesian ideas. In summary, in a ny case, I have argued thatphilosophical problems of confirmation raised in the context of probabilistic strategies must be investigated through considering the decisiontheoretic aspects, which suggested a peculiar way that could preserve
Bayesian theory in a certain sense, that is to say, a decision-theoretic formulation of degrees of responsibility from a retrospective viewpoint, or alogic of responsibility. If that is the case, Bayesian theory would still
remain powerful.

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Is a Decision-Theorist a Friend or
Foe of a Bayesian -Theorist?
Comments on Professor Ichinose's Paper

Daisuke Kachi

III hi , paper Professor !chinose effectively described the ways of medical
1IIIIflnosis and its confirmation, in which the processes of confirmation
1lIlIllI'dia tely affect the life of patients. Since doctors are responsible for
Ih" II'Stil ts, they have to make confirmations with maximum intensity andI h11Isness. Through his analysis Professor !chinose has made it clear that
I1 hould take hypothesis-confirmation as a type of action that includes
1I III1IS decision-theoretic aspects in each step of confirmation. He insists
1",l llhose aspects are not only seen in medical examples but also seen in,lIuII' sciences, since every confirmation is a kind of speech act directed to,,1111' 1' people. I totally agree with him in that respect. Moreover, he has
I 1IIIIIded me that confirmation is a kind of incessant and critical action
110 /'I lIrviving in a severe environment, which sometimes behaves unpre0110 I.. hly. He has succeeded in evoking the most fundamental features of
I II llth'll1a tion that are easily forgotten in theoretical analysis.
I 'I!"pa red with his persuasiveness and clarity as to the importance of
011 I I' I! ",-theoretic aspects in confirmation, a little difficult to understandI
such aspects are related to Bayesian confirmation theory, espeI," ll \' III th e problem of old evidence. He says that the problem of old
I Idl 'nee will be simply solved by adopting a decision-theoretic view of,," lIlInation, because 'so-called old evidence appears not as genuinely
1II II 'v idence but as, as it were, present evidence in cormection with newly
IIIIII'llsl'd relevance and newly questioned utility in the course of a deciIII I1 Ill ,lde now'. Moreover, he insists that his way of solution is consistent
Ilh ,I ll three classical responses to this problem.
11111 <',lch response more or less includes criticism of the other posi111111, h>r example, Williamson, who proposed a solution by noticing the
1\1111 n\onotonicity of evidence, showed that we would have to admit a""w•

43