ML20083N871
| ML20083N871 | |
| Person / Time | |
|---|---|
| Site: | Indian Point  |
| Issue date: | 01/31/1983 |
| From: | Levi I FRIENDS OF THE EARTH, NEW YORK CITY AUDUBON SOCIETY |
| To: | |
| References | |
| ISSUANCES-SP, NUDOCS 8302030210 | |
| Download: ML20083N871 (53) | |
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h UNITED STATES OF AMERICA CCtyETEC NUCLEAR REGULATORY COMMISSION UwRC ATOMIC SAFETY AND LICENSING BOARD Before Administrative Judges:
- g3 [ED -2 A11 '.06 James P. Gleason, Chairman Dr. Oscar H. Paris Frederick J. Shon In the Hatter of l
l Docket Nos, CONSOLIDATED EDISON COMPANY OF l
i NEW YORK (Indian Point Unit 2) 50-247-SP 50-286-SP POWER AUTHORITY O/ THE STATE OF NEW YORK (Indian Point Unit 3)
January 31, 1983 DIRECT TESTIMONY of ISAAC LEVI, Ph.D.
On Behalf Of FRIENDS OF THE EARTH, INC.
anc' NEW YORK CITY AUDUBON SOCIETY O
8302030210 930131 PDR ADOCK 0500024
f.:
6 CONTENTS OF TESTIMONY OF ISAAC LEVI pjgle_
Qualifications 1
Summary of Testimony 2
Section One Rational Choice and Nuclear Power Plants 7
Section Two On the Probability of Failure 15 Section Three Bayes' Theorem 24 Section Four Log Normal Priors 29 Section Five Assessed Intervals and Worst Permissible Priors 33 Conclusion 43 Curriculum Vitae Bibliography of Publications of Isaac Levi
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1 QUALIFICATIONS OF ISAAC LEVI I am currently Professor of Philosophy at-Columbia University in New York City, where I teach graduate level courses in probability and induction, and the philosophy of science.
I was a Guggenheim Fellow and Fulbright Research Scholar in the United Kingdom in 1966 and 1967, and a visiting scholar at Cambridge University in 1973.
From 1973 to 1976 I was Chairman of the Depart-ment of Philosophy at Columbia University.
My curriculum vitae is annexed to my testimony.
For over twenty years I have been engaged in extensive inquiry in the logic of probabilistic judgements and statistical inference, decision theory, and the application of these fields to questions of scientific knowledge and practical action.
As can be seen from the annexed bibliography, I have numerous publications in these fields, among them, my recent book, The Enterprise l
of Knowledge, MIT Press, 1980.
The appendix to The Enterprise of Knowledge presents an application of the approach developed in the book to the problem of assessing risk in the nuclear industry.
That appendix, in a some-l l
what less technical version, appeared in' Social Research in 1981 as:
" Assessing Accident Risks in U.S. Commercial Nuclear Power Plants:
Scientific Method and the Rasmussen Report".
The discussion in my testimony parallels that of the article, which critiques the Reactor Safety Study (WASH 1400).
j L
2 s
SUMMARY
OF TESTIMONY OF ISAAC LEVI 1.
Summary of Section One.
The propuncnts of nuclear power are often ready to acknowledge the possibility of dire consequences resulting from serious accidents at nuclear power plants; but they hasten to assure us that the probabilities of major accidents or long term damage to the environment are so trivially small that the risk is acceptable.
Defenders of reliance on nuclear power plants thus appeal to the principle of
" maximizing expected utility".
In other words, they take into account the possibility of dire consequences (costs) and beneficial consequences (benefits) and weight each possibility with an estimate of the probability of its occurrence.
If, however, probability assessments cannot be made numerically definite, several " risk curves" may become permissible to use in computing " expected utilities", and it may not be possible to choose between options (e.g.,
whether or not to allow a nuclear plant to operate) on the basis of expected utilities.
- Thus, the critical question to address is whether assessments of probability supported by the available data are sufficiently definite to justify a verdict one way or another in terms of " expected utility".
If assessments of probability warranted by the available data are not sufficiently definite to justify a verdict in expected utility terms one way or another, it is entirely rational
r "o '
a to appeal to minimax criteria or worst possible case analysis.
To do otherwise would be to indulge in an unreasonable form of wishful thinking.
It is widely agreed by both sides of the~ nuclear debate that the worst possible consequences of permitting nuclear power plants such as Indian Point to run are worse that the worst possible consequences of prohibiting their'use.
Hence, minimax considerations would argue in favor of refusing to permit the continued operation of the Indian Point plants.
With regard to probabilistic risk assessment at Indian Point, my conclusion is that the methodology described in the Indian Point Probabilistic Safety Study (IPPSS) for making probabilistic assessments is not adequate to justify our reposing condidence in the assessments made in that study.
2.
Summary of Section Two.
In principle, I am sympathetic to the use of event and fault tree analyses, such as in IPPSS, provided they are carefully and thorough-ly implemented with scrupulous respect for possible incompleteness due to oversight.
They must also be based on adequate estimates of the probabilities of failure rates for components of the complex system.
This discussion does not address the question of the completeness of IPPSS.
However, IPPSS goes seriously astray with regard to estimating probabilities.
Although the authors of IPPSS go to some considerable effort
r 4
e to leave a different impression with their so called i
" method two" or " probability of frequency" framework and their " level tvo definition of risk", they have in effect responded to a major criticism by the Lewis Committee of the Reactor Safety Study (WASH 1400) by stonewalling--
i.e., refusing to modify their method of reporting subjective or credal probabilities so as to give a range of distributions rather than a single one.
Since IPPSS has no basis for making non-arbitrary assignment of definite distributions, its failure to offer a range of distributions represents a serious defect in the study.
3.
Summary of Section Three.
The preceding defect would perhaps not be so serious if the authors of IPPSS could claim that they have evidence and background information sufficient to justify assigning a definite credal or subjective probability distribution over the possible values of objective failure rates.
If, on the basis of the available information, there is no good reason to pick one definite probability distribution rather than another, the choice of any one such distri-bution rather than another is arbitrary.
Rather than
.make such arbitrary judgements, one ought to regard as permissible all distributions which are not ruled out by the available evidence.
In this sense, the judgements of priors made by the authors of IPPSS are arbitrary, just like the judgements of priors made in the Reactor Safety Sttly (WASH 1400).
As a consequence, the IPPSS J
~
5 I
verdicts about posteriors cannot be trusted except, perhaps, in those cases where the plant specific data are so abundant as to swamp the impact of an arbitratily chosen prior.
What is required is a recomputation of IPPSS data against a broad spectrum of priors utilizing Bayes' Theorem.
Pending such reassessment, one should proceed as if none of the posteriors can be trusted.
4.
Summary of Section Four.
The claim made both by'the Lewis Committee and the reports of Sandia National Laboratories on IPPSS and the Zion Probabilistic Safety Study, that the use of log normal priors has negligible effect on the outcome of probabilistic assessments, cannot be trusted.
They assessed the import of one arbitrarily chosen prior (log normal) by comparing it with another arbitrarily chosen prior.
Such comparisons are deceptive and of doubtful value.
5.
Summary of Section Five.
IPPSS assumes (as did WASH 1400) that failure rates are distributed log normally, except that it assigns 60% probability to the
" assessed range" rather than 90% probability (as in WASH 1400).
This enables the authors to ascertain new S% and 95% confidence limits.
There are two components to this line of reasoning: (1) it is assumed that there is as much probability of a failure rate below the lower limit of the assessed range as there is above the upper limit; and (2) a log normal distribution is used to assess confidence intervals.
If we suppose that the prior credal probability
6 s
is indeterminate, the use of a log normal distribution is arbitrary and, by the same token, it is far from clear why symmetry should be assumed in extending upper and lower bounds of assessed ranges.,
Given the foregoing substantial and serious' defects in IPPSS, a procedure for making sensible probability
-judgements is suggested.
Tables are presented for the purpose of illustrating the difference between the arbitrary approach of IPPSS, and an approach which takes seriously the complaint that we lack a basis for making precise estimates of probability and should make assess-ments in terms of ranges of probability distributions.
It should be apparent that data from plant experience will not begin to give definitive judgements until the data become very ample.
Pending a complete reassessment of the data on Indian Point in a manner which respects the importance of reporting the indeterminacies in probability judgement, one should not rely on the analysis contained in IPPSS.
6.
Summary of Conclusion.
The conclusion reached on the' basis of these considerations is that we have thus far no rational grounds for supposing that the probabilities of serious accidents at Indian Point Units 2 and 3 are sufficiently low to justify operating these plants.
Minimax considerations, i.e., worst possible case analysis, argue in favor of refusing to permit these plants to conti-nue to operate unless and until adequate reassessment of Indian Point data results in a contrary conclusion.
7 s
SECTION ONE RATIONAL CHOICE AND NUCLEAR POWER PLANPS Assessing risks and taking decisions on such assessments in determining whether to permit the operation of nuclear power plants raise important issues concerning human knowledge and rational decision making which transcend the particular points which may be under dispute in the formulation of an energy policy.
Precisely the same kinds of issues arise in other areas of public policy making such as in the control of various forms of industrial pollution, the licensing of the use of drugs by the FDA, or in the use of military intelligence inform-ation in the design of an arms policy.
And, of course, they also appear in-deliberation about investment policy formation, the design of investigations in pure science, and in other contexts of deliberate decision making.
Opponents of the operation of nuclear power plants focus attention upon the worst possible consequences of reliance on nuclear power.
They invite us to consider the consequences of a major accident and of the possible long term damage to the environment due to such an accident or to the. storage of radioactive waste.
Proponents are often ready to acknowledge the possibility of such dire consequences; but they hasten to assure us that the probabilities of major accidents or long term damage to the environment are sufficiently small
~.
1 i
8
/
i e
to warrant the risk.
Defenders of reliance on nuclear power plants thus. appeal to the~ principle of." maximizing expected I
utility"._ In other words, they not only-take into account-l the'possiblity of dire consequences (costs)'but:the.
possibility'of beneficial consequences;(benefits) as well.
They weight each possibility with an estimate of the probability of its occurence.- Such weighting yields-an assessment of the expected benefits'and costs of reliance on nuclear power.
The expected value of allowing nuclear power plants to run is claimed to be superior to the enpected value of alternatives and, therefore, they conclude that operation of nuclear power. plants is to be 1
recommended.
From the point of view of expected utility maxi-I' mizers, those who focus on the worst possible case without taking into accqunt the probability of its occurrence are -
irrational.
The latter are invoking the so called
" minimax" criterion for rational decision making which favors choosing that option from a range of alternative policies for which the worst possible consequence (or l
" security level") is no worse than the worst possible consequence of any alternative.
They argue that the worst possible consequences of operating such plants, such as tlu3 consequences that would flow from a serious reactor accident, are much more threatening to individuals and society than would be the worst possible consequences of 4 -
9 some feasible. alternative.
Even'though the mi'nimax criterion for decision making under. uncertainty was explored and taken seriously by very eminent statisticiansl (such as A. Wald), the various versions of minimax theory (minimax loss, minimax risk, minimax regret) have come in for criticism.
The chief line of such criticism is that minimax theory counsels us to adopt an unreasonable paranoia or pessi-mism concerning what " Nature" is likely to do.
What is wrong with this view, so claim the critics of minimax, is that it leads us to assume that what Nature is likely to do depends upon our values--what we judge to be losses and gains.
If we change our values, what Nature is likely to do will change as well.
If wishful thinking is to be avoided, say the critics of minimax, so should the negative of wishful thinking.
But minimaxers should not be bullied by maximizers of expected utility into conceding their own irrationality.
There are situations where minimaxing makes very good sense.
The blanket and indiscriminate sniping at mini-t maxing in the name of Reason can only serve to give rationality a bad name.
The principle of maximizing expected utility is entirely cogent as a criterion of rational judgement when I
one can identify a precise " risk curve"(using the jargon I
of the Indian Point Probabilistic Safety Study (IPPSS))
i 1 - The locus classicus is A. Wald, On the Principles l
of Statistical Inference, Notre Dame, Indiana, University of Notre Dame Press, 1942.
l
10 which pairs with each possible " scenario" a probability of occurrence and an assessment of benefit or loss.
To do this, however, one must be in a position to make numerically definite probability and utility assessments or, at least, to make assessments sufficiently-definite so that the ranking of the policy options with respect to expected utilities-is clear.
If, however, assessments cannot be made numerically definite, several risk curves may become permissible to use in computing expected utilities.
In that event, it can happen that one option is optimal in expected utility according to one permissible assessment whereas an entirely different one is optimal according to another.
In that event, considerations of expected utility become impotent for the purpose of deciding between the options.
Thus, if it shuuld turn out to be the case that the probabilistic assessments made by various safety studies are too indeterminate to allow us to render a verdict as to the merits of operating or refusing to operate nuclear plants on the basis of an appeal to considerations of expected utility, we can no longer appeal to the argument that the probability of a serious accident is sufficiently low to warrant permitting nuclear generating plants to
' operate.
The point is not that we can claim that the probabilities are not sufficiently low.
We may not be in a position to decide whether the probabilities are low
' enough or not.
r 11 If that'should turn out to be the case, it makes, eminently good sense to appeal to another' criterion which makes no assumptions about expected utility or probability of occurrences of diverse scenarios to render a verdict.
When neither permitting nor prohibiting the use of nuclear power'is ruled out by appeal to considerations
~
of expected utility, it is perfectly reasonable to focus on the worst possible consequences of.the several alter-natives'and pick the -option for which.the vorst possible consequences of that option is better than that of any alternative.
Minimaxing comes into its own when maxi-mizing expected utility fails to render a verdict.2 When a minimax criterion is used as a secondary principle in those instances in which maximizing expected utility fails to render a verdict, the objection that minimax is a paranoid practice carries no weight.
That objection is grounded on the assumption that someone who uses a minimax solution is proceeding as if his probabil-ity judgements were those which made that solution optimal in expected utility.
That is not-the way the criterion is employed when it is used as a secondary principle.
In this latter use, the criterion is employed as a sub-stitute principle when no judgement about probabilities is sufficiently definite to allow us to make a judgement 2 - This' idea is elaborated in some detail in my book, The Enterprise of Knowledge, Cambridge, Mass., MIT Press, 1980, especially chapters 4 and 7.
r 12 on expected utility.
Appeal to worst possible case
' analysis (or to the consideration of " security levels")-
is intended to introduce a consideration distinct from expected utility in order to render a verdict when expected utility cannot do so.
No assumptions (not even "as if" assumptions) about probabilities ' are made.
Objection may, perhaps,.be made that minimax criteria are ambiguous in their application.
- Thus, i
Wald favored using what is often called a minimax risk criterion which differs from a minimax loss criterion and also from a minimax regret criterion.
If it is claimed that there must be some firm decision made between these criteria as secondary criteria as a matter of rational principle, I quite agree that the difficulties become considerable.
However, on the view outlined here, how the agent assesses security levels for the various options is a matter of ethical, political, economic, aesthetic or other value judgement just as is his assess-ment of the utility or cost of each possible " scenario".
The choice of a method for fixing security levels of feasible options ought not to be settled in advance by criteria for rational choice but is itself part of the value commitments of the decision makers or the communities whose interests they serve.
I assume that it is widely agreed that the worst possible consequences of permitting nuclear plants such is Indian Point to run are worse than the worst possible
13 consequences of prohibiting,their use.
Perhaps this assumption is mistaken.
But'it does not appear to have
- been disputed by the advocates of nuclear power.
And critics of the use of' nuclear power seem to think the assumption sound.
The main thrust of advocates of nuclear power has been to belittle the relevance of pointing to the worst possible consequences of using nuclear _ power plants.
They do so.by insisting that everything depends on which policy bears maximum expected utility.
We are urged to look at the probabilities that accidents-and other dire consequences will occur and the probabilities that they will not occur, to calculate the expected benefits and losses of operating nuclear power plants accordingly, and to compare these expectations with those associated with other options.
Opponents of nuclear power insist on the relevance of focusing on worst possible consequences.
They do not seek to show that the prohibition of nuclear power bears greater expected value than promotion.
If they could establish this, they would prove their case.
But such an argument is not necessary for the defense of their view.
If assessments of probability warranted by the available data are not sufficiently definite to justify a verdict in expected utility terms one way or another, it is entirely 4
rational to look at security levels.
Since it seems to be agreed that security levels are higher if one does not
-14 operate nuclear power plants than if.bne does, it is entirely rationalito invoke _a: minimax' argument and to recommend-prohibition of the operation ~of_ nuclear plants.
Thus, the critical. question to address is whether assessments'of probability supported by'the available data are sufficiently definite to' justify a verdict one way or anotherfin-expected utility terms.
My conslusion is that the_ methodology described in the IPPSS for making probabilistic assessments is not adequate to justify our reposing confidence in the probabilistic assessments made in that report.
Without a thorough reassessment of the data from the IPPSS and acquisition of additional data, we should' conclude that considerations.of expected utility do not warrant deciding one way or.the other whether Indian Point Units 2 or 3 ought to-be permitted to continue to operate.
To conclude otherwise is to indulge in an. unreasonable form of wishful thinking.
Without such reassessment and the determination of sufficiently definite probabilities by appropriate methods, rational decision makers ought to maximize security by refusing'to permit the continued operation of Indian Point Units 2 and 3.
1
15 SECTION TWO ON THE PROBABILITY OF FAILURE.
I shall not comment on the use of event and fault tree analyses by the Indian Point Probabilistic Safety Study (IPPSS) in deriving probability distributions for the responses of Indian Point Units 2 and 3 to diverse initiating events.
In principle, I am sympathetic to the use of'such approaches provided they are carefully
.and thoroughly implemented with scrupulous respect for possible incompleteness due to oversight.
But I lack the engineering knowledge needed to assess the extent to which the authors of IPPSS did, indeed, apply event and fault tree analyses in an effective and complete manner.
The advantage of using such analyses is that they enable us to exploit judgements as to the probability of failures of components to operate as intended in order to estimate probabilities of serious consequences--such as core meltdowns and failures of containment systems.
Data concerning the performance of the overall complex system may be too sparse while information concerning the performances of components may be better and might, given an adequate model of the function of the system, be used to derive the desired overall probabilities.
But if this advantage is to be exploited, not only must our analyses of the complex systems be adequate so that we have a good understanding of how probabilities
16 of initiating events are propagated, we must also have adequate estimates of the probabilities of failure rates for components of the complex system.
IPPSS provides an account of the methodology employed by it in making these estimates.
It purports to explain methodological improvements over the Reactor Safety Study (WASH 1400) developed in response to the Lewis Committee Report 3, In what follous, I explain by means of an illustration why their improvements are illusory.
Consider then the problem of ascertaining a probability of a given pump failing to perform as intended in the interval from time t to time t + dt for small dt.
If we assume that the pump is subjected to a regular schedule of maintenance and inspection, we may assume that there is an objective statistical probability or, as I shall call it, chance p of the pump failing to perform in an arbitrarily selected interval of time of small length 1
dt.
Suppose we then can think of the interval from time t to t + dt as selected "at random" from all such inter-vals in the history of the pump.
We are then justified in adopting as our subjective or credal probability that the pump will fail in that particular interval the value p (that is, the chance of the pump failing to perform in an arbitrarily selected interval of time of length dt).
Under the assumptions specified, the chance p identified is taken to be approximately equal to Adt where 3 - NUREG/CR-0400, Risk Assessment Review Group Report to the U.S. Nuclear Regulatory Commission, 1978..
17 h(lambda) is a parametric value characterizing the failure rate of the pump.
If the failure rate h of the pump is known to be equal to h*, then the chance is known and from that we can justify a given credal probability judgement.
Contrast the aforementioned predicament l'where the agent knows that beh*, with predicament 2, in which the agent does not know the true value of h but knows that it falls in a given range of values.
What subjective or credal probability should the agent assign to the hypo-thesis that the pump will fail in the interval from t to t + dt?
Let me distinguish three cases:
Case 2a.
Let the agent have credal probability judgements concerning the' probabilities of various values of h.
That system of judgements is characterized by a probability distribution and, if the distribution is con-tinuous, will be representable by a density function f(h),
or if discrete, by a probability function M(h).
Given such a distribution, we can then compute an expected value for h.
That will be [hf(h)dA or { hM(h), as the case may be.
Relative to that distribution and the expected value of lambda computed therefrom, the agent is then committed to a way of assigning a credal probability to the hypothesis that the pump will fail in the interval from t to t + dt.
It is equal to the expected value of lambda.
18 In case-2a, I suppose that.this expected value is equal to-h* of predicament 1.
Thus, the agent -in predicament 2a mahs the same credal~ probability judgement concerning what will happen in the interval ~from.t to t + dt as does the agent in
~
predicament 1..
The important difference between these two predicaments _ concerns the grounds on which they make' their judgements.
In predicament 1,'the agent knows the-failure rate and, hence, the objective chances of a failure-
-in an interval of length dt.
He knows-no-such thing in case 2a but has, instead, a subjective' opinion expressed by a credal, probability. distribution over possible failure rates.
Case 2b resembles case 2a except that the credal-probability distribution does not yield the' expected value for lambda equal.to h* but, say, to some other substantially different value h**. And that is used to determine f the credal-probability of failure in the interval from t to t + dt..
Case 2c also is a case where the agent does.not know the true value of A.
However, in'this case, the agent does not represent his uncertainty by a single credal distribution over the possible values of h.
Instead, it is represented by a set of permissible credal distributions (which is required to be convex).
These are the distri-butions the agent has not ruled out for use in making probabilistic assessments and computing expectations.
19 And from these distributions, he obtains an interval of expected values of h.
This interval might, for example, be the interval h* to h**.
Observe that the set of values in the interval in case 2c is not a set of unknown values of the objective 4
failure rate.
Rather, it represents the agent's indeter-minate state of subjective or credal probability judgement concerning failure in the interval from t to t + dt.
Instead of having a numerically definite credal judgement as in cases 1, 2a'and 2b, he has a numerically indeter-minate assessment.
Suppose that the agent is offered a gamble where he wins S - P utiles (or units of value) worth of prize if the pump fails in the interval from t to t + dt and receives -P utiles otherwise.
According to Bayesian doctrine, the agent should accept the gamble (rather than get nothing for sure) if S is positive and P/S is less than A* in cases 1 and 2a, and also if S is negative and P/S is greater than A* in these cases.
That is to say, there is not the slightest difference in the way the agent should make decisions in these two cases on his credal probability judgements concerning failure.
The fact that his probability judgements are grounded on different information in the two cases should not make the slightest difference in cases 1 and 2a.
The analysis of 2b is like 1 and 2a except that h**
is substituted for h*.
20 however, Bayesians can offer no analysis of case 2c; for they have nothing to recommend when probability
-judgement goes indeterminate.
To be sure, if S is positive and P/S 'is less than A*,
the expected utility of the gamble is positive no matter what permissible distribution is used; and if S is negative and P/S is greater than h**,
the same is true.
But when P/S is in the interval from h* to h**,
the gamble bears positive expected utility according to some distributions and negative according to others.
This analysis recommends refusal to gamble in such cases on the basis of the fact that refusal is the minimax solution.
This recommendation coincides with the recom-mendations of C.A.B. Smith according to the theory of upper and lower "pignic" probabilities.4 I rehearsed the similarities and differences between cases 1 and 2a, 2b and 2c in order to emphasize a critical ambiguity in the way an important observation made by the Lewis Committee Report may be understood.
According to the Lewis Committee Report "it is preferable not to try to come up with a point estimate - a single number - for a failure probability, but rather to content oneself with bounds".5 4 - C.A.B. Smith, " Consistency in Statistical Infer-ence and Decision", J. Royal Statistical Soc.
Ser. B, vol. 23 (1961), pp. 1-25.
5 - NUREG/CR-0400, pp.
8-9.
21 This recommendation may be construed as~ advice not to fix on a definite value of A as the true value in deciding on a definite numerical judgement of credal probability as in case 1, as to failure in the interval from t to t + dt.
Alternatively, the recommendation may be construed as advice not to fix on a definite numerical judgement of credal probability for failure in the interval from t to t + dt.
If one heeded this advice, one would adopt a posture rather like that in case 2c where one not only avoids making any definite judgement of the true value of A but also avoids adopting a definite credal distribu-tion over the values of A, resting content with a family of values.
A fair reading of the Lewis Committee report suggests that they did intend the recommendation in the second sense.
However, the authors of IPPSS, in responding to the criti-cisms made by the the Lewis Committee report of the Reactor Safety Study (WASH 1400), apparently have adopted the first interpretation.
Hence, the authors of IPTSS have claimed that their " method two" or " probability of frequency" approach as described in sections O.4.5 and 0.4.6 of IPPSS should be used to represent risk according to the " level two" definition of risk of sections 0.5.2 to 0.5.4 of IPPSS.
In a footnote to the opening paragraph of section 0.5, the authors of IPPSS claim that the valid point lurking behind "the major criticism by the Lewis Committee" i
22 concerns the need to resort to the-level two definition of risk to express uncertainty about risk assessments and failure rates.
The illustrations and discussion in IPPSS make it clear that the authors intend discussions of failure rates to follow the patterns illustrated by my cases 2a or 2b.
According to IPPSS, we are to desist from attempts to come up with a single number as our estimate of the true value of the objective failure rate for the pump (or whatever other component is being considered) but rather assign a credal probability to the various hypotheses possibly true concerning the true value of the unknownX.
The upshot is that even though IPPSS does desist from making a commitment as to the true value of some objective statistical probability or chance (or frequency, as the autho s of IPPSS misleadingly call it), it is still committed to a definite numerical assignment to the expected value of the failure rate h, and this expected value then becomes (or should become according to Bayesian doctrine to which the authors of-IPPSS are apparently committed) the credal or subjective probability assigned to the hypothesis that the pump will fail in the interval from t to t + dt.
As we have seen when comparing case 1 and case 2a, when it comes to deciding whether to take risks, it makes little difference whether one takes the posture in case 1 or case 2a.
23 Furthermore, it appears that the method two favored by IPPSS is already incorporated in its essentials in the Reactor Safety' Study (WASH 1400), at least when assessing failure rates of individual components.
Thus, although the authors of IPPSS go to some considerable effort to leave a different impression with their so called " method two" or " probability of frequency framework" and their " level two definition of risk", they have id effect responded to a major criticism by the Lewis Committee of the Reactor Safety Study (WASH 1400) by stonewalling--i.e., refusing to modify their method of reporting subjective or credal probabilities so as to give a range of distributions rather than a single one.
Since IPPSS has no basis for making non-arbitrary assign-ment of definite distributions, its failure to offer a range of distributions represents a serious defect in the study, regardless of the correct reading of the intent of the Lewis Committee report.
24 SECTION THREE BAYES' THEOREM The observation made in Section Two would, perhaps not be so serious--although the failure to be straight-forward would still be annoying--if the authors of IPPSS could claim that they have evidence and background inform-ation sufficient to justify-assigning a definite credal probability distribution over the possible values of the objective failure rate h.
IPPSS does describe the method-ology it uses to do just that.
It is based on the use of Bayes' theorem and is summarized in section 0.14 of IPPSS.
According to section 0.14.1 of IPPSS, there are three types of information available for the " frequency.
of elemental events"--i.e., objective chances or, in the case of our example of the pump, the objective failure rate h.
They include El General engineering knowledge of the design and manufacture of the equipment in question.
2 The historical performance in other plants E
similar to the one in question.
E3 The past experience in the specific plant being studied.
El and E2 is called " generic" information and E3 " plant specific" 3r " item specific" information.
The task is to determine the probability p(h/E E E1 2 3) for all possible values of the failure rate given the total generic and specific information.
According to Bayes' theorem, this can be characterized by the following
25.
equation:
.p(hj/E E E1 2 3) = P(hj/E Ei 2)p(E /AjE E1 2-)
3 (0.14-3)'
1 2)P(E /Aj 1 2) p(h /E E EE 3
j As IPPSS explains on page 0-92, the posterior probability distribution in the light of evidence E E 123 is then seen to be a function of the prior probability.
for h relative to the generic information E E and the 12 likelihood of the truth of Ag on the plant specific data E
relative to generic information E E 3
2' IPPSS supposes that in many cases the likelihood function can be specified with good precision and gives:
illustrations (such as equations (0.14-5) and (0.14-6)) of.
what such likelihood functions would be in typical cases.
Although one might want to examine the assumptions about a
likelihoods more closely, that is not the concern of this discussion.
I shall suppose that precise likelihoods are available.
A problem, however, still remains. 'To obtain a definite posterior-distribution for failure rates, one needs-to have a definite prior distribution relative to Lthe generic information.
If that information goes indeter-minate--i.e., if there are many permissible prior distri-butions--then the posterior probability judgement will also be indeterminate.
It is, to be sure, the case that, if the plant specific data E is sufficiently ample, the range of per-3 missible probability distributions will be narrowed down 4
considerably and, in the limit, will converge on a precise
26 posterior.
At least this will be the case when the
' likelihood functions are of.the sort considered in equations.
t (0.14-5) and (0.14-6).
~
However, the rate of convergence will depend.upon 1
the extent of indeterminacy in thefprior family of'distri-butions for failure rates.
The greater the indeterminacy, the slower the rate of convergence to precision in the posterior, and the greater the amount of data which will be required to " swamp" all permissible priors.
Furthermore, the extent to which precision is achieved will also depend upon the amount of plant specific data available in E3, which may not be very much at all.
I do not know myself the extent to which one can claim that the plant specific data yield likelihoods which swamp all permissibfe priors.
I will want to return to some aspects
~
1 of this issue shortly.
Nonetheless,.there may be many cases where plant specific data are sparse-and where it is not at all plausible to suppose that likelihoods swamp all permi-ssible priors.
In that case, posterior credal probability judgements for the failure rate may be.very indeterminate indeed.
Such indeterminacy ought to be propagated throughout the entire causal analysis in order to make a judgement of probability of serious accidents such as core meltdowns.
It is clear from the explicitly stated methodology of IPPSS that they did not-do this.
They explicitly state procedures for adopting priors for failure rates and these procedures invariably involve the adoption of a definite prior distribution.
27 Not.only does this.p~ocedure viofate wha't appears r
to have been the intent of the. Lewis Committee report--but; it entails th maki'ng of ar6itrary de'cisions about proba-bility.
,(.
Let is be n6ted here that. I am not' complaining'.that the probabilistic assessments are grounded on subjective judgements.
I quite agree that such subjectivity wil'1 be unav6idable.
The verdicts reached are g6ing to be judge-ments of-individuals and in that sens[e will be subjective.
And, as the authors of IPPSS note,' subjectivity is not the s.
same as arbitrariness.-
If one has information on thq", basis of which every i
e reasonable person ought to make the. sain6' definite credal or subjective probability judgement,)then one's endorse-
$ @ ~~
ment of that probability judgement is,7itot arbitrary.
However, if, on the basis of tIie.-available informa-tion, there is no good reason.to pick?one numerically definite probability. distribution rahher th'an another,,
the choice of any one such distribution rather than-
.,. e.
another is arbitrary.
Rather than.'mpke such arbitrary judgements, one ought to: regard as; permissible all'distri-butions which are not ruled cub byLthd available evidence.
In this sense, the judgements of: priors made by
-W theauthorsofIPPSSarearbitraryf[justlikethejudge-ments of priors made in the Reactor.' Safety Study. :As a 1
y consequence, the IPPSS verdicts abou(. posteriors cannot be trusted except, perhaps, in tilosefcases where the plant r.
~4
28
~
e specific data:are so abundant'as.to swamp'the impact of.,
an arbitrarily chosen prior.
As I have already indicate'd',.I am not in a'cpositdon to determine the ex. tent to which the plant specifiS data [
for Indian Point are sufficient to swamp t.he impact of q
arbitr&rily chosen priors.
What'is required is a recom,;.,
putation of IPPSS data acjainst a broad spectrum 'of priors utilizing Bayes' Theorem.
The authors of IPPSS have hot done this.
Consequently; we do not know the extent to which this can be done and should proceed, pending sucS!r}
reassessment, as if none of the posteriors reported in
- i.
IPPSS can be trusted.
-c.
s'
-[ I e
W 8i l
4 5.
i e
1 5
0 0h
i l
29
.c SECTI'ON FOUR LOG NORMAL PRIORS The standard procedure followed in the Reactor Safety Study (WASH 1400) in selecting prior distributions over failure rates was to identify'an " assessed range" of failure rates for the component--under scrutiny, grounded on the " generic information" alluded to in IPPSS, and then to assume that the subjective distribution of probabilities over the possible failure rates is a log-normal distribution with 90s of the probability assigned to values in the. assessed range' and tihere 9% probability is assigned to each of the tails.outside of the range in a symmetrical manner.
The Lewis Committee report complained about the arbitrariness.of this procedure and quite rightly so.
However, it did not think that the use of log normal priors of this sort would distort posterior porbability judgements by more than a factor of 2 or 3, so that
~
posterior judgements based on such priors'would not be distorted excessively.0 The Lewis Committee did not explain the basis for its passing this verdict of the relatively neglibible effect of using log normals.
One can only' surmise that they examined some of the generic data (which for the most part apparently are not sufficient to do reliable goodness of fit tests) and noticed what they thought were distributions 6.- NUREG/CR-0400, p.
9.
g which better fitted the relatively sparse data.
They then compared the impact of using such distributions as compared with the log normals to reach their conclusions.
If that is indeed the approach used by the Lewis Committee, it'is surely open to question.- If the data are sparse, there is not the slightest reason to suppose that the prior credal distribution should be represented by the curve best fitting the generic data.
Even curves which deviate wildly from such best fitting curves might yield such data with significant probability--especially if the data are not excessive.
Thus, to assess the import of one arbitrarily chosen prior by considering another arbitrarily chosen prior is deceptive.
What ene should do is to.look at the prior distributions which give the worst possible fits of the generic data and which still-could with significant probabilities yield that data and where the worst possible fits are in all directions.
In that case, the deviations s
from the log normal in some directions might have been quite significant indeed.
I am not suggesting that the prior distributions giving worst possible fits of the generic data should be adopted as uniquely permissible prior credal distributions.
My point is rather that one should begin with a set of distributions bounded by such worst possible fit distri-butions.
~31 It is just as arbitrary to pick one particular dist;ribution from the set as it is any other.
The
. reasoning of the' Lewis--Committee report appears -to make this mistake.
The import of this mistake is even more apparent in a discussion of the same issue in the report on the Zion Probabilistic Safety Study prepared.by Sandia National-Laboratories and in the similar treatment by Sandia Labs of IPPSS The practice of.IPPSS and the Zion Probabilistic
~
Safety Study (ZPSS) differed from the Reactor Safety.
Study (WASH 1400) in that they fitted only 60% of the total probability symmetrically within the assessed range-according to a log normal, rather than 90%, as in the Reactor Safety Study.
The Sandia reports ca IPPSS and ZPSS ask the question as to the effect of these prior distributions'on their estimates:of failure rates.
Sandia proceeds as follows:
They look at the plant specific data E and compute maximum likelihood 3
estimates for the failure rate and variance of the failure I
rate from'this data and compare them with'the posterior expected failure. rate computed from the log normal prior and the variance of that distribution.
i 7 - Sandia National Laboratories, " Review and I
Evaluation of'the Zion Probabilistic Safety Study", Letter Report, March 5, 1982.
8 -'Sandia National Laboratories, " Review and Eval-uation of the Indian Point Probabilistic Safety Study",
?.
NUREG/CR-2934, SAND 82-2929, December, 1982.
~.i 32
.- 7, -
. -'. y
','i, "
.h ?
.a
~
~ '.
- 9 );..
IIndffect,.as-S'andiapointsoutinsectib'n2.6of..
"~
t both reports, their procedure was to use a flat or uniform
. prior over'the assessed range,(or, strictly speaking ~, the J.-logarithmic: transformation cf that range).- As a result,
?
Sandia' concluded that for the most part, the choice of-a log normal prior would not have a marked effect.
But once more, we have a' comparison of one. arbitrarily chosen prior.with.another, and.such c6mparisons are of-
.:c:
3 i
~
doubtful value..
7, j.
t ihus,..the claim made both. irlp thd.. Lewis:Chittee -
r-
~
S-a report and'. the S ndia, reports, on.IPPSS. and' ZPSS that the ~
use of log : normal pr.iors has negligible. effect oli the out ?
l
~
come,should'not be trusted.'
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aI
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33 SECTION FIVE ASSESSED INTERVALS AND-WORST: PERMISSIBLE 6 PRIORS' 4
As already.,noted, IPPS'S follows ZPSS in broadening the' assessed ranges of:failur'e'. rates asicompared wiEh thoseusedin'theReactorSafetyStudy(HASH 1400).
- They appeal yo experime'ntal data suggesting that even experts often tend-toradopt subjec.tive probability distributions that are'"too tight";
They appeal, in, particular, to a study.b Slovic,'Fischhoff, nd Lichten-that when individ'als.give-interval stein which claims u
~
estimates with 98%-probability, somewhere between 20 and
.. s.
50 percent of true values fall-ou6 side.the limits of these estimates.
Since much'of.- the.:so ca'11ed generic information relative to which prior dist'ributions for failure rates are based seems to derive from the subjective.
testimony of experts, it.seems quitA sensible to follow the practice of IPPSS at least to this extent--to wit, in broadening the interval within which 90% of the probabiiity is to be assigned.
~
But there are.some serious difficulties involved in. determining. how this'should bel done.
When IPPSS takes generic information from the Reactor Safety Study'concerning the failure rate of some-r thing like a pump, it takes the assessed range given by the Reactor Safety Study, assumes'that with 60% probability the failure rate is in that interval :with 2G6' probability it is beyond the lower end.of the-interval,.and with 20%-
9 is~beyond the upper end.
2
a 34 Then IPPSS assumes, as di$ the Reactor Safety Study, that failure rates are distributed log normally compatible with the restrictions thus made.
This enables them to ascertain new 5% and.95% confi,dence' limits.
^
There are two components to this line of reasonings (i) it is assumed that there is as much probability of a failure rate below the lower limit of the assessed range as there is above the upper' limit; and (ii) a log normal distribution is used to asse~ss confidence intervals.
If we suppose that prior credal probability is inde-terminate, the use of a log normal is arbitrary and, by the same token, it is far from clear why the symmetry should be assumed in extending upper and lower bounds of assessed ranges.
Granted that all of this is so, how should one proceed in order to make sensible probability judgements?
To begin with, let us bracket the problem of deter-mining 95% confidence intervals.
Let us suppose that we can claim that a certain interval is with probability 1 the in-terval within which the failure rate is to be found.
My own judgement is that it is possible to specify in many
~
cases, a large finite interval for which such confidence can be expressed.
But very little in the conclusions to be drawn depends on it.
Even given such an interval, the problem remains of determining a prior credal distribution for failure rates in that interval.
If we addp> a prior credal. state which is maximally indeterminate (so that it is the " convex hull" of all distributions which assign probability 1 to some fai-lure
4 35 rate in the range'and probability O'to the rest), no
~
amount of plant specific experience vill enable likeli-hood functions to suppress the differences between the competing priors in the credal' state so that with enough experience, large indeterminacy can be reduced.
It would be as unreasonable to prevent large enough experience, even in principle, from leading us to relatively deter-minate judgements as it would to arbitrarily pick a prior l
single distribution out of a hat as IPPSS, ZPSS, and the j
l Reactor Safety Study do.
Both extremes should be avoided.
The idea is to adopt a prior credal state consisting of a broad band of distributions and,.hence, considerable indeterminacy in prior probability judgement while still allowing for the possibility that, if data obtained from plant specific experience becomes ample, posterior distri-butions will be derivable that are confined to a very narrow band.
How broad the bar.d of prior distributions should be depends on how stringent our demands are on the amount of information that will be required to reach fairly sharp estimates of failure rate probabilities on the posterior data.
There are many different ways one might proceed in attempting to implement this approach.
The arbitrariness involved here, however, can be rendered innocuous by making prior probability judgement sufficiently indeterminate, in which case there will not be much dirference between the recommendations of the different approaches.
36 For purposes of illustration, let me suggest the following approach.
Let us fix, to begin with, on a suitable sharp distribution to serve as a benchmark.
A sensible distri-bution for the failure rates would be a conjugate prior distribution for-the parameter of the Poisson distribution
--which would be a gamma distribution.
In particular, however, one might begin with the misleadingly called i
" ignorance" prior which has the density 1/A normalized to the assessed interval for h or is the uniform or " flat" l
distribution for logh over the corresponding interval for logh, The proposal is to fix a band around such an ignorance prior such that all permissible prior distribu-tions f all in that band.i. Then stable estimation theorems guarantee that with sufficient experience, posterior l
l distributions will fall in a narrow band: focusing on the maximum likelihood estimator.
However, the rate at which i
l posterior data will' swamp all priors in the prior band will be far less rapid than it would be if we started with l
l the ignorance prior as our sole distribution.
In this way, l
we guarantee that maximum likelihood estimates are not taken too seriously until we have very ample data--which is surely an appropria'e attitude to take given the t
importance of the issues which are to be settled.9 If our benchmark distribution is uniform over some 9 - for further discussion see,' The Enterprise of Knowledqe, chapter 13.
finite interval, we can view it. as' uniform over the unit
~
interval from 0 to 1 and, when desired, alter the scale by whatever factor is appropriate.
We can theit envisage.the' band [as characterized by two liness one above and para 11d1 to the uniform density of 1 and ne below.and par $iliel to'that. density.
Let the upper line; be o( (alpha) times. higher. than the benchmark (o( is greater than 1) and the lower line be g (beta) times the. benchmark (/L eingqpositive and less b
y than 1).
~
To s'implify, I shall suppose. thati these two numbers are'so chosen that it is possible to; assign an event of Lebesgue measure x for some positive number x less than i
1 a probability of
.'5 according to afdensit.y function which assigns, density equal to8 to points in x and density equal to (Ito points in the-complement of Lebesgue measure c
Thisshouldbesonomatterwhatevektshaving 1-x.
these Lebesgue measures areoselected' -This. procedure guarantees that / x = c((1-x) =
.5.
'.Given the initially specified value of x, we can then determine the values of a( and g.
Alternatively and, perhaps,.more perspicaciously, we may fix in advance a factor k (greater than or equal to 1) such that o( = kg.
Assuming that the bounds are so constrained that " W of the probability can be assigned to events of positive Lebesgue measure x, all of whose points receive density /, and the remainder of. the points have
38 density of, we can then determine the values of these two parameters and tae-value of x.
x is eqQal to k/(k + 1) so ~ that / =.5(k + 1)/k and al =
5(k + 1).
When k = 1, of course, the upper and lower lines collapse into the uniform density and we have the, classic case of an ignorance prior over the unit inter-val.
As k increases, the band within which permissible priors are permitted to lie becomes wider.
Asik goes to infinity, we may think of a case where 50% of the probability concentrated in a set of Lebesgue measure 0
~
(a finite or countably infinite set.of p6i'nts, perhaps) and 50% in the complement.
Thus, values of k index the entent to which we intend to be cautious in our initial assessments of prior probability in the' sense that we will. require a certain' amount of data before we will concede that likelihoods swamp our prior ignorance.
Assuming that we have fixed on a value of k, we can then determine a worst permissible prior.
In our case, it would consist of a distribution assigning'506 of the probability with density / to values of failure rates at the low end of the spectrum and densityc< to the rest.
Focusing on a worst permissible prior (wpp)'does F
not mean that we adopt that prior as our prior belief.
It is not any more representative of prior. belief than our best pocsible prior.
But we should ascertain whether L
39s
'the posteriors calculated with worst permissible priors are swamped or'not in such a'way as to eventually lead j-to a_ calculation of expected utility favorable to the.
l operation of the nuclear power plant.
If it does, a strong case has been made for this conclusion.
Otherwise I
p expected utility has failed to render a verdict and mini-max'becomes operative and recommends. forbidding such l:
operation.
I have spoken, for the sake of simplicity as if 1
the derivation of the. worst permissible prior was based on the unit interval as the assessed interval.- Of course, e.
in most cases to be considered here where assessed inter-vals are for failure rates, neither those assessed inter-f vals or the corresponding intervals for logarithms of failure rates are unit intervals.
So the.'" median value2-which is x for the uhit interval--must be multipiled by-i the appropriate scale. factor.
l l_
In table 1 below, I. adopt as-an-assessed range-f used in the-Reactor Safety _ Study (RSS) for " failure of air operated valves to remain open",' as reported in IPPSS I
on page 0-95.
Assuming that-with probabilityt1 all failure-I
~
rates fall in'the assessed. range from 2.8 x 10 to
-7 2.8 x 10
, I take the logarithms of these end points to obtain a range for values for the logarithm of the failure F
rate. - Relative to that_ interval, I use a uniform distri-bution for the benchmark distribution and obtain a worst i
possible probability distribution which I then transform
40 back into a distribution over the failure rates.. I report the~ median and mean values.'obtained in this way by RSS using the log normal distribution and using my approach for the uniform prior:(over logarithms of failure rates)--i.e., when k = 1 and also when k = 3, k = 19, and k = 99.
Table 1 Median Mean RSS 8.9 x'10-8 1.1 x 10-7 k=1 8.9 x 10 1.1 x 10-7
-8 k=3 1.6 x 10-7 1.4 x 10-7 k - 19 2.5 x 10-1.8 x 10-k= 99 2.7 x 10-1.9 x 10-Table 2' gives results for the s'ame problem where the assessed range is extended as in IPPSS.
Table 2 Median Mean 8.9 x 10-8 2.3 x 10-IPPSS
'k=1
.8.9 x 10-0 2.3 x 10-k=3 2.8 x 10-3.2'x 10-7 k= 19 6.7 x 10-7 4.1 x 10-7 k = 99 8.0 x 10-4'.9 x 10-7 The purpose of supplying these tables is to illustrate the difference between the approach of IPPSS to constructing priors based on generic experience and an approach which takes seriously the complaint that we
~
41
.~
~
t 15ck a basis for, making precise estimatds of probability and should make dssessments in terms o ranges'of probability distributions.
It should be apparent, however, that if we.use worst permissible. distributions as priors to calculate posteriors, sample'. data from plant experience will not begin to give definitive judgements until the da'ta become.
very ample.
If the data are scarce, it is to be expected that we shall not 'be 'able to calculate' definite probabi-lity distributions for such events as core melts.or containment failures, but will have to!Eest co'ntent'with Ci i.
interval probability assessments.
The critical i'ssue is whether it' will be possible 4
to obtain interval prob' ability assessments sufficiently definite so that the. upper probabilities calculated from the worst permissible. priors are still below the required levels.
Clearly that will depend upon how cautious we are in adopting indiced of caution k.
My own view is that given the gravity of the issues-involved, we should set k rather high.
The main criterion,. however, ought. to be that when there is controversy concerning the degree of caution to be exercised, we should choose high values of k rather than low;_for only then do'we proceed in a manner which can'r'each conclusions;a'c~eptable to all c
parties to the dispute.
The main point to emphasize, in any case, is that the authors of IPPSS, like the authors of ZPSS ar,d the Reactor Safety Study'(WASH 1400), Meport sharp distribu-
42 '
tions grounded on.the arbitrary selection of log normal priors.
Even if there were no fault to be found with the causal analysis of the various systems studied and the way failure probabilities were propagatdd, issues about.which I do not feel qualified to comment, the analysis offered by IPPSS remains faulty.
Furthermore, attempts.to make comparisons of the probabilities of major accidents at Indian Point Units 2 and 3 with such probabilities for oth'r plants will have e
to contend with the deficiencies of probabilistic safety studies for other plants of the same kind--such as the ZPSS.
Consequently, pending a complete reassessment of the data on Indian Point Units 2 and 3 (as well as for other plants) in a manner which repects the importance of reportingfthe indeterminacies~in probability judgement, one should;not rely on the analysis contained in IPPSS.
I
43 CONCLUSION The argument of this discussion rests on two main theses:
(1)
One should rely.on' calculations of expected costs and benefits in making.deci'sions only when the probabilities available are sufficiently definite to render an unequivocal verdict.
When such calculations cannot 1x3 used to decide b'ecause of indeterminacy.in the assessments of probability (hnd', hence, of expected costs and benefits or in the distribution of risks), appeal should-be made to minimax or vdrst possible case analysis.
(2)
The calculations of probabilities. contained in IPPSS gain precision by the arbitrary selection of prior probabilities for the failure rates of components and this spurious precision is~ propagated up through the entire causal analysis.
The conclusion which may be reached on the basis of these condierations is that.we have thus far no rational grounds for supposing that the probabilities of serious accidents at Indian Point Units 2 and 3 are sufficiently low to -justify = operating 'these plants.
Minimax consider-ations argue in favor of refusing to permit these plants to continuo to operate unless and until adequate reassess-ment of* Indian Point data results'in a contrary conclusion.
June 1932 ag.i Isaac Levi
- 3crn:
June 30, 1930..
i Married.
Two Children.
Collece and University Education:
3.A.
N.Y.U..
1951 Philoscphy; Minors:
Greek and Mathe=& tics M.A.
Columbia 1953
' Philosophy Ph'.D.
Columbia 1957 Philosophy Dissertation Supervisor:
Ernest Nagel Honors, Awards. Grants:
~
1951 Phi Beta Kappa 1951 Pi Mu Epsilon 1955-56 W.T. Bush Fellow, Coludbia University 1962-63 N.S.F. Grant 1965-66 N'.S.F.
Grant l
l 1366-67 Guggenheim Fellow and Fulbright Research Scholar
.in the United Kingdom i
1963-69 N.S.F. Grant 1971-72 N.S.F. Grant 1973 N.S.F. Grant Visiting Scholar, Corpus Christi College, Cambridge U.
Ep.olcirment :
1954-56
,Rutgers U.
(part time)
(lecturer) )..
1956 57 The City College
-1956-57 Columbia University lecturer l
l 1957-58 ~
Western Reserve U.
Instructor) l 1959-62
-Western Reserve U.
Assistant Professor)
(.
1961 Su==er)
Columbia.U. (Visiting Associate Professor) 1962-c(4 The City College (Assistant Professor) 196h-67 Western Reserve U.
(Associate Professor) l 1967-Case Western Reserve '.
(Full Frofessor)
U l
1968-70 Case Western Reserve U.'
(Chairman, Department of ?hiloso hy) i 1970-Columbia University (Full Professer)
~
1973-76 Chairman, Depart =ent of Philosophy, Columbia. University
l Professional Organizations:.
A.A.U.P., A.P.A., Ass 6c. of the Philescphy of Science, Board of Governors of the Ph11csophy of Science Association, 1975-76.
~
Scholarly Activities:-
In addition to publications appended to this vita, I'have read papers at several professional. meetin$s including the A.P. A.
Eastern and Western Divisions, The 3r. Association for the Philosophy of Science, and special conferences held at Sal: burg, Philadelphia, and' London, Ontario.-
I.have participated in several other conferences and. read invited papers. at many Universities including Oxford, Cambrid e, Londen School of Economics, The' S
University of Helsinki, Columbia, Chicago, Rochester, Michigan, Harvard, Bosten University, Virginia, and others.
6 6
M c
Summary.cf activities from 19S0.
~
Isaac Levi 1980 Visiting fellow at Dar.iin College, Carabridge.
Offered"a course of lectures at Cambridge.
Gave two talks at Oxf'ord, one at LSEi one at U. of Bradford and one at.U. of Warwick.
Gave a series of lectures at the. University of Helsinki and received a medal from the University 1981 Read papers at Rutgers U., Lehigh U. and at the Seminar on Bayesian Inference at Carnegie-Mellon and fl.J. Philosophy Assoc. Also at conference at Georgia Tech on Infor: nation Theory.
1932 Read papers at the Universities of. Chicago and Colorado and Washington University.
Will read paper as part of symposium at Philosophy of Science Association meetings in the fall.
1933 I am an invited speaker on the Foundstions of Probability and Induction at the 1983 Congress of the Division ~of Logic, Methodology and Philosophy of Science, International Union.of utstory end Philosophy of Science.
This congress will meet in Salzburg,'
(
i have also been informed that my niae is"un the list of cientists and scholars eligible for fellowshids at the Center for Advanced Study in the Behavioral Sciences", j ! have also been told that my "name has izacn placed on our tentat ive in,ter for" 1983-1992 But otherwise I have heard nothing.
But there is a rectote possibility that I shall request a leave tn visit the Center at Stanford for that period.
1 6
d O
t
-t V e
o BIBl.IOGR APHY OF ISA AC IIVI 4
1957 Doctoral Dissertation. The Epissemolog.r e/ Alorir: Schlu A under the setemsion of Ernest Nagel,Cohmbia Univeruey(micro 6 tan) 1998 Review of Roy llarrod, Fesmdariens af Inductise logic. Jomrmd of Phukosephi $$.
209 212.
1999 (a) 'Putnavn's Three Truth Values'. PadosophicalSoudics 19,65 69 (b) Translation of R. Carnap. 'The Old and the New Logic'.in legind P<ntsiyism (ed. by A. J. Ayer)(Free Press).
1960 (a) *Must the Scientist Make YalueJudgmentsT./nurmd affbrowphr57,345 57.
I suggest that although xientists may make value judgemcoes the safues may be characseristic of the sciensinc enterprise and, therefore, defterent from moral, econo-mic, political, prudential or other types of values.
(b) Translation of A. Meinong, *The Theory e4 Objects", in R. M. Chishbim (ed.). Realum and #Ac SarAgrasad of Phraamrnalagt (Free Pressi (with D. B. Terrell and R. M.
Chisholm).
a 1961 (a) "DecisionTbeoryand ConErmalion'.lournalef1%.losop4r58.6I4 625.
Bogdan, R J. ted i. 'llener E A)hurg, Jr. & Isaac Isri. 30s 31.t.
309 Copprught C IMI br D. ReutelPubinkmg Company.
a e
ISA AC LEVI RlR LIOGR A PilY ght Reverw of Minnesora Samars hr Philowphy of Science, l'ol.11. Journal of Philouphy gags SE,24l 248.
(c) Review of Danto and Morgenbesser (eds.) Milosophy of Scicare and E. H. Madden (a) 'On Potential Surprise *, Aarin 8,107-129.
(ed). The Structurc ofScientific Thought, Jourselof phibsophy 58, 387-390.
My Erst essay on Shackle's theory of potential surprise. l'urtlier discussion is found (d) Review of A. Rapaport, fights. Geners and Deheses, florverd Ederasional Acrirw 31, in 1%7a,1972a,1979e and 19stoe.
477 479.
(b) 'Recent Work in Probability and Induction *(retiews of lunoks by I. JJionsl,I. Ilacking, R. C. Jeffrey and H. T5rnehohm), S mihrse 86, 234-244.
1962 1967
'On the Seriousness of Mistakes *, Mibsophy ofScience 29,47 65.
I This was my Erst efices to construct decision theoretic models of scientinc inference (a) Cambling mirk Trad (A. Knopf, New York)(reissued in paperhoek without resiuon in utiliiing cognitive or epistentic utilities along the lines suggested by 1960s. Both this 1973 by MIT Press).
paper and 1960s-were written in ignorance of Hempers writings on epistemic utility.
On pp. 240 -241 of this book, I wrote," Individuals and.instituthms strise la attain, The vagaries of publication resulted in a discussion of Hempel s work (I%Is) appear, many objectives. At aimes, these ends conflict; at other times, they complenient one ing in print.before this paper. In point of fact,1968a was written after 1%3a in which another. 7.1,' as legitimately ask eguestions alwet the relatise'importance of.
i Iesplored the possebelities ofconstruing Popper's corroboration nerasures as measures
~
different wids, including the cognitive ceiectives of scienes6c ingwry. Due dnparage, of espected epistemic utility and proposed.using measures of relevance as measures ment of sognisive ends (even aihen thre are grounds for it) oughs m4 to disguise of enpected epistemic utility, itself by'sediacing these ends to practical ones. Truth, information, esplanation.
simplicity are desiderata that are different from wealth, love, security, health, peace, etc. They ought to be recognired as *uch. Such recognition is enhanced by showing 1963 how the ends of inquiry control the legiiimacy of inferences?
E in support of this view,I proposed an accown: of cognitive decision ' mal ing design-(a) ' Corroboration and Rules of Acceptance', British Journalfer she Milowphy ofScience ed to accomsnodate a limited range of problems. This account was the culminatimi 13, 307-313.
of the emphwation of accounts of crosseniec utility I had begun in 19f,0.i.
(b) Review of H. Leblanc, Statisticaland heductive Prohobilitics, Journalof Philosophy 59, (b) ' Probability Kinematics', Antish fournalfur she rhdowphr v/ & irner 68.197 2t89.
21-25.
(c) 'Information and Inference *. Syn #hric 17,369 91.
I (c) Contribution to 1/arper's Farpr/opedia ofScience.
This paper was written while I was reading proof on l%7a. It responded to proposals of Hintikka and Pietarinen. The most important technicaldesclopmentin it. homes er, is the modification of the account of epistemic utihty I propmed in 1%7a in parti-1964 cular, I no longer required escry element of an ultimate p.wemon to he as infor manisc as every other and, given this nmdelication of the model, was prepared in entertain (a)
- Belief and Action *, The Monist 48,306-316.
entending the scope of the applicability of the model to the question of reaching (b) ' Belief and Disposition *, Amerfran Philosophical Quarterly I, 221-232 (with Sidney conclusions concerning theoretical hypotheses.1%7c ought to be read along with Morgenbesser).
1967a.
This paper', wriesen in collaboration with Sidney Morgenbesser, Arnt proposes the view of disposition predicates which I subseaguently elaborated upon in 1967a and 1977b and which was adapted to furnish an account of statistical probabibty or chance of the sort proposed in 1967a,1973b,1977a,1977b and 19ttom.
i (a) Review of 3. Hintikka and P. Suppes (eds) Aircris of Ind= rsi:r.inic, ariisih /m,rnal (c) ' Utility and Acceptance of Hypotheses *, Voice of America forum Lectures, Milosophy for she Mhophy of Sciosu 19.
of Scirnec Series. No. 2.
gyp ge,;g, og w, $,gawa, yn, y,,,g,,,,,,,f 5,,,,,,,,, y,,,,,,,,, y,,,,,g,,,,,,y y,,,g,,
Philosophr ofSriener 19,259 61.
1965 1969 (a) ' Deductive Cogency in Inductive Inference *, Journal of Milosophy 62,68 -77.
(b) ' Hacking Salmon on Ind:sction'.Journolof Milosophy 63,481 - 487.
(a) 'ConGrmation Linguistic invariance and ConceptualInnovation'.S nshrse 30,48 55.
3 310 31I s
____y_
e ISA AC LEVI BIBLIOGR A PH Y l
(bj 'If Jones Only Knew More'. Britas4 Jewrnulfor the Padosophy of Sciemy 20.153 -159.
To ney knowledge, this paper contains the firse descussion of the ides that the conthct-(c) 'taduction and the Aims of Inquiry'. PMosophy. Scicere and Methed. Essays in Noner ing approaches to the Newcomb problem he viewed as invoking different principles of Erness Nagel, ed. by S. Morgenbesser. P. Suppes, and M. White (St. Martin's PressL.
ofespected utility masammassion. The idea is usually attributed ao Gibbard and Harper pp.92 Ill (d) Review of The PreMem offmkerirc Logic.ed. by 1. Labatos.Srnthese 28.143-148.
ahhough they thenmelves acknowledet that I suggested, as an alternative to the f
Bayesian approach, calculating expected utilitieming the unconditional destribution (e) 'A re Statistical )Iypotheses Covering taws 7. Symihrse 20. 297-307.
our states mhen states are cauully indepsedent of options. Gibhard and liarper This paper Wiens the widely. held view that statements of chance or sentistical appear to think their own proposal to he different inmi this. Iloweser, it is< lemons.
probabilie) cas serve as lawhke generalizations in explanatiorror that so called 'induc-trebly equivalent given the assumptions about prohobihties of conditionals they 6,e statistical explanation' can be cogently regneded to be a species of covering law adopt. To be sure there is an important difference. I showed that in the case where the esplanation.
denian is perfectly infallable the non Bayesian prescription mommends the two be-
)
solution which,in my view. is cicarly absurd Gihhasd and ll.irper accept the absusd N
iniplication with equanimity. The paper alw pinntwat that if one calculates pmhebi-lities using conditional probabslities of states on acts. there is no definite solution to.
' Probability and Fvidence'. lmiwcrkm. Acrcreence and Aarkmal 8clirf.ed. by M. Swain the Newcomb problem as stated by Norick and others. Norick thought othermiw (Reidel. Dordrecho, pp. 134 156.
Y F"
e of states given options.
1971 IM6 (a) Testainty.ProbabilityandCorrectionofEvidence'. Nous S.'299 312.
(b) ' Truth. Content and Ties'.Journalof Philosophy es,865 876.
(a) " Acceptance Revisited". in lorollmlurthm. ed. by R. Bogdan t Reidel. Dordrecht). pp.,
I-71.
f (b) *A Parados Ice the Birds' in Es:says in Mcestwy of larre Idades, ed by R. S Cohen 1972 (a)
- Potential Surprise in the Context.cf Inquiry'. in t'nrertamernadEspertariens &s Eewnnmirs. Esurrs in Jiamar of G. L S. SharAlc. ed. by C. F. Carter and 3. L Ford 1 Blackwell,. Oxford), pp.213-236.
j (b) Invited Comments on Churchman (pp. 87-94) and on Braithu aite Ipp. 56 61). Schvne.
g,79 1)es isse and l'aime, sd. by 3. Leach, R. Butts' and G. Peirce (Reket. Dordrecht).
gy. Dime Inference'. The Journslef Phiksoper 74. $.29.
This paper discusses the important issue of direct inference from knowledge of 1973 chances ce objective, statistical probahilities to judgements of credal probability Aside from the pioneering discussions of Reichenbach and Fisher, the nuist thim> ugh (a) *But Fair to Chance'. Journelof Philewph[r 70. 52-53.
st dy of disect inference had been Kyburg's i advocated an approach alternatise to I
(b> Review of D. H. Mellor. 7ne Marrerof CAsser. PAdewpedral Acricw S2. 524-530.
Kyburg's and esplored sosne of the issues involsed in the dispute. The topic is further discussed in 197tte sad in considerahle detail in 19pos.,
(b)
- Subjunctives.DispositionsandChances'.Siwr4r c34.423 455.
1974 (c) *Four Types of Ignorance'. Sersol Aricarch 44. 745 -756
~
'On Indeterminate Probabilities'. Jewrnalof Philampe r 71. 391 4 HI (d) *Epistemic Utility and the Evaluation of Emperiments'. Phdowphro/5.kwic44
)
368-386.
This is my first statement of an approach an probabehty judgenent and decision theory involving a substantial departure from the Bayesian decision theory on which I had reluctantly relied in 1967a.
1973 1975 (a) venc(. E nms sm primerms of Ikrnum thews, ed by llooker. l_cach.
and McLennen. Vol. I (Reidel. Dordrecht). pp. 263-275.
e I
'Newcomb's Many Problems'. TAcrayand /kcisiem 6.161 175.
312 313 4
)
e e
BIRLIOG R A PilY 6
(c) 'Confirmatinnal Conditionaliiation' lawnalef Philomphr 75. 730 737.
utrhty sneasures areemployed instead This idea together with an account of catmnal (d) Reprint of(1964hland of(1977h)in Drrfwerrinnt.ed. by R. Tuomela ( Reidet. Dordrecht).
choice grounded on a lexicographically ordered series of criteria for the admnsi-bility of feasible options is claterated upon in Chapters 6 9 lt responds to the boast 1979 that Bayesian theor'y offers the most general approach availahic to decision making by effering a theory of far greater scope allowing strict Bayesian theory la be a special (a) Translation of t l%7alinto Japanese (Kinohunsya Book Store. Tokyo) ng cae a u m sonw nanowly al ecqum conern 0
n (b) " Inductive Appraisal *, Current Arscarsh en Phdomper of&irme ed by P. D. Asquith probatutity and countable addithity. Chapter 10 discunes conditionaliration and irrelevance from the point of siew esplained in (1978a)TChapters il and 12 contain and 11. E Kyburg (PSA. East Lansing. Mich h pp. 339 351.
(c) erious Possibibty' Esses m Inmour of JanA Aa lhnt,A&a (Reidet. Dardrecht). pp.
the fullest account I hase offered to date of my siews on dispositionahey, aNhty and statistical probatwkty or chance and of the relations hetween these 'objersne* nmdah.
"8
' E'" '
"'"""'*I"'"
(d)
- Abduction and Demands for Information'. The Logic mad Erriormatoer of Scientife I
Change ed. by I. Niiniluoto and R. Tuomela (North floffand for Societas Philosophica Fennica. Amsterdamh pp 405 429.
revise or to select prior states of credal probability sudgement Chapter 14 dncusses Many authors have complamed about the relatmty of appraisais of inductne in-ways to rationalise Educial inference from a Rayesian pant of uew. Chapeer 15
,, gg;
.s sA msk of a Bayesian rationalussion earloiting the ferences anording to my theory to the choice of an ultimate partition of maximally-consistent potential answers and to other costicutual factors like degree of caution or
. notion of likelihood. Seidenfeld's proof that Hacking's etlert and all other efforts en boldness and appraisals of potential answers with respect to informatsonal value. I convert fiduciat inference to Bayesian enference are inconsistent nesphated to show that g,,g;
.s law of hkelihood cannot be used as a principle ofinducti c logic as HA king have repeatedly insisted that this complaint points to a virtue of my approach rather thought. Chapter 16 discusses she' ideas of Fisher on the connectwn hetneen fiducial than to a defect. Ilowever, until I had developed the apparatus presented in (1980s). -
I was not able to give a systemauc account of how conflicts in the choice of ultimate g,7,,,,,,,,,9 direct inference and K yburg's original and ingenious efforts to ela borate parhtien or in the values of other contextual parameters are to be handled. This an improveo Fisherian theory. An alternative deseloped by A P. Dempster is also paper offers such an account.
l rensidered. Chapter 17 discusses the approach to statstical theory deschiped by I
fe) ' Support and Surprise: L L Cohen's View of Inductive Probabihty'. Brrrnh fournal.
Neyman, Pearson and Wald. The deGciencies claimed to be found m these theories for the Philamphr af Science 30.279 - 292.
arc invoked in support of the approach to probahrlistic reasoning adianad in Chapter 11 Chapter 18 returns to some general themes about ob ectiuty and contest de-t pendence apphcable to the views about the seshion of knowledge descloped in 1990
~
Chapters 1-3 and the views about revision of probatulity pidgement descloped in the light of the discussion of Chapters 4 -17. The appends: on the Rasmussen Report ta} 71re Enoerprue of Snowledge: An Esser en Knowledge. Credal Prohaksirer and Chance
- "' '*"Y I #"'" '
(MIT. Cambridge, Mass )
~
'E P ' "
I "EW'""*"
T,Ns book has three objectives: to outline a view of the structure and aims ofinquiry g.,
g rd Pse'.h% W W h w wetbout seeking foundations for knowledge or the naturaliistion of epistemology, to elaborate a novel accoufrt of probability jodgement, utikty judgement and rational E. sings in hanar of R. 8. Braith=mirr.ed by D II. McHor tCambrmfgel. pp 127 140
- P dWklaRWbMm W M M W'.M m oh choice as part of this approach to en account of inquiry, and finally to exploit the rW d h L L Ch W K HMClarendon. Oxford), pp. I 27. Also rephes proposals made in a critical review of diverse cesponses to some central problems of statistica%my.
to comments by P. Teller. 81. E. Kyburg. R. G. Swinburne and L J Cohen and som-ments on papets by R. Giere.L Dorling.1 E. Adler and R. Rogdan Chapters I-3 emplain in some detail the epistemological outlook which motivated (d) *1ghaNes'. Smokse di m C7.
H%7a) as tr.odified by the explicit endorsement of epistemological infalhbilism first advanced in (19A?). These chapters contain comments on the views of Quine, This paper together with (1990b) presents a siew of Peirce based on a nmre accurate Kuhn. Feyerabend. Peirce and Popper which are further descloped in Chapter 18 and rendrag of Peirce's ideas on probabehty and statistical inference than is usually in the appendix. Chapter 4 contains an overview of my approach to probabilistic found in the philosophical hierature. In particular. (l930h) shows that Peirce had, as reasoning. This is elaborated upon in considerable detail in Chapters 5-10 and carly as 1878, elaborated the Neym n Pearson rechnique of confidence interval Chapter 11 The cen*ral feature is the relamation of the strict Bayesian requirement estimation for the binomial case and had an accurate appreciath.n of the condeseens that states of probability judgement (credal states) be representable by unique pro M in applMhy Mmm teal oide h adM in up d the %
bability encasures and states of valuation be representable by utihty measures unique (which Reichenbach himself shared) that Peirce's siew ofinduction as self correcting i
up to guetise linear transformations. Convex sets of probability measures and of was not an anticipation of Reichenbach*s own view and does not rely on any dubious
,;g 30 315 S
~
9 0
EICLIOGR A PHY ISAAC LEVI i
l I)hemmenna 1981 fa) On Assessing Accident Risks in 115. Commercial Nuclear Power Plants'. Sa.m/
Adler. J. E., *The Evaluation of Rival Inductise Logics'. m L J. Cohen and Hesse teds L
'{
PP carians of Inductive Legir (Clarendon Press. Oslord. I?t0L pp. 383 -384. 386n.
J li Ar.rierch 4.
3n7 390. 393n. 403n; and 'Cosaments'.afe ret pp 419 4'it (19 'Should Bayesians Sometimes Neglect Base RatesT. Ik #rheesaraland Draan Scirm es.
t Cardwell. C ' Gambling for Content'. J. Md. 68 (197II, see 864.
Cohen. L J. *How Empiricalis Contemporary Logical Emperitism' MJmop4m 5 (1975L 1982
- p. 359ff; The Probab/c and the ProroAle (Oxford.1977L pp 66.124. 316ff; Comnvats on Levi's 'Patential Surprine: Its Role in Inference and Decision-Making". in Cohen and (a)
- Dissonance and Consistency According to Shackle and Shafer* PSA t1979L II.
Hesse (eds.k op. cit., pp. 64 -66;*Wlat Has Inductive Logic to Da With Causahty'. Cohen (bp Arten of ThenryandEriJence by C.Glymour. Phamophical Acricm.
and Hesse (eds.h op. cit, p.151, lh.
(c) Review of Vol. 2 of St=Ars m Indurrive f.egic and Prohahdtry, ed. by R. C. Jeffrey, i
Gas.J.C
- Moral Autonomy and the Rationality of Science'. Md. Sci. 44(1977L $13- $41.
Mde phical Aereew.
Gibbard. A. and Harper. W. L. Ceunterfectuals and Two Kinds of Espected Utility'. in F8""Od8"# 8"4 APP icasmus of Drrisian Thewy ed. by C. A. Hooker. J. J. Leach and l
(d)
- Liberty and Welfare'.-to appear in Bryend Usdeteriseism, ed. by A. K. Sen and E. E Mclennen meidel Dordrec% % % H and 12 p.168.
B. Wilhams.
(c) ' Escape from Boredom: Edi6 cation According to Rorty'. Canaduur 1,wrnalef Philos,.
Giere. R.,Toundations of Probability and StatisticaHnference'. Current Arscare 4 se Mrks.
sop 4 efScience,ed. by P. D. Asquieh and H. E. Kybus3. PS 4 (1979h pp. 51N 319 5
,g,,,
(f) Review of Cham e. Acaws and Consc by A. Burks.
Goowns. K
- A Critique of Epistemic Utilities *, Loret induct==. ed. by R. J. llogdan (g) ' Direct inference and Connemational Conditionalization'. PAdosophy of Seirner.
( Reidel. Dordrecht.1976). pp. 932114.
Haciting. l..*The Theory of Probable inference: Neyman. Peirce and Braithmarte*, Sirne c.
Belief and Srharker: Essa.rs i= Armour nf A. 8. Drarsemansr. ed, by D 11. Mellne (Cambridge U. Press, Cambridge.1980L p.153.
I 198?
Hesse. M., The Structure of Sciensq#r Inference (U. of Cal. Press. Berkeley 1974). p.112 l
and 122n.
' Truth. Fallibility and the Growth of Knowledge', which le to appear in the Boston Hilpinen. R., A=/rs of Acceptance usdladertive Leric (North-4tolland. Amsterdam.1968L Colloquium volume ' Language, Logic and Method' with a discussion by I. Scheffler g3,93,,,_ gog, 4
and A. Massalit. The editor has promisad that it would appens within a year since Nintikka. J. med Pieurinen. J.." Semantic Information and Inductise Logic'. in Anpre en 1975 when it was initially submitted to him.
I of hearrese Logic, ed. by J. Hintikka and P. Suppes (North-Holland. Amsterdam,1966).
The paper itself was first written and delivered orally in l971.
pp. 96,107 408.
This paper is the nrst expression of an important mod,6 cation of the epistemo-Hutchison.T. W *Pemte Eranomete and Polia y Ohmmer ( Ahn ar* Unwm, London, kigical outlook I had advanced in (L%7a) and had elaborased upon in (1970) and 1964L p.103n.
(197ta). I draw a distinction between the corrigibility of knowledge (which I accept)
Jeffrey R. C., "Dracula Meets Wolfman: Acceptance ss Partial Behef'. i*i Induction, and its falkbehty (which I denyt I emplain why Peirce and Popper must reject the Acevrance and Reeknes18 clef. ed. by M. Swain. (Reidel Dordrecht. 3970t pp 157 185.
distinction as I understand it because of their shared outlook concerning the uhimate Kyburg. H. E *Recent Work in Inductive Logic'. 4PG I (19ML p. 9;-Conjuntinied. in aims of scientific inquiries. Elements of the point of view of thispaper are presented m I
M. Swain. op. cit., pp. 191 215;' Local and GlobalInduction'. in Lo.at Imhaik e. ed.
(1976a) and Il977b). (19 mon) claborates upon it in detail-by Bogdan, pp. 191 215;' Chance'.1. of PAdosep4iral Logec 5 (1976L pp 363. 365. 366, la prorrss: Papers on decision making under unresolved conflict and collective decision 371-376. 389-392 ' Propensities and Probabilities'. in lhtfootams, ed by R. Tuomels makeng-(Reidel. Dordrecht.1978), pp. 277. 284-285. 289. 295 299; Randomness and the Right Reference Class'. J. pad. 74 (1977) 504 321; 'Conditionalization'. J. Ped. 77 (19eren
'98-104, 113-114.
C' Leach, James.' Explanation and Value Neverahty* 81PS 1911968L93-los Lehrer. K., ' Induction. Consensus. Catastrophe'. m R. Briedan of. ret., pp 138 143 :
Reviews of Gamhang with Truth (l%7): I. Hacking. S)nterse 17 (l%7). 444 -448; R. C.
Ehe ad h Gmnm on miin N ad Heue W e eA JefIrey. /. pad. 65 (1968) 313 322; K. lehrer. Neins 3 (1969h 255-297; J. Mackie. 81PS
- "* Y '"*EP 19 (196ML 261: D. Miller. JSL 36 (1971) 318-320.
Reviews of The Enterprisc of Knowles%c (1980): D. V. Lindley. Nature (Nov. 6.1980);
R. Swinburne. Temrs th 4rr Ederation SmPplement (Oct. 3,1900); A. Margalit. Tiners Lucrary Supplement (Feb. 27.1981) 237.
316 l
0
-Continuation of bibliography for Isaac Livi 1931 (a) 'On Assessing Accident Risks in".U.S. Commercial Nuclear Power Plants',
Social Research 48, pp.395-403.
(b) 'Should Bayesians sometimes neglect base rates?'
The Behavioral and Brain Sciences 4, 342-343.
(c) Comment on 'On some statistical paradoxes and noncongicmerability
by Bruce Hill, Trabajos de Investicacion Operativa y Estadistica 32, 135-141.
(d) 'Olrect Inference and Confirmational Conditionalization,' Philosochv of Science 48, 532-552.
(e) ' Escape from Scredom: Edification according to Rorty,'
Canadian Journal of Philosophy 11, pp.589-601-1982 (a) Revie.1 of Theory and Evidence by Clark Glymour, Philocochical Setic.4 91, pp. 12a-12d.
(b)ProfilesofHenryE.Kybure,dr.&IsaacLevied. by R. Bogdan, Dororecnt: D. Reicel. x1,322 pp.
This volume censists of intellectual autobiograp' hies by Kyburg and by me tooether with four essays, two devoted to Kyburg's work and two to mine,tagether with our replies and bibliographies of our wcrk.
The Profiles series is a series of such vulua:es designed to raview tne work of contemsorary philosophers in n'id career.
(c) ' Dissonance and Consistency according to Shackle and Shafer,' P5A 1978, 2.
(d) 'Cor.flict and Social Agency,' Journal of Pjulosotahy 79, (e) 'A hoto en Ne.,ccm:; mania,'
Journal of Philosaghyv 79, (f) '!.iberty and '.iol f are. ' in Beyond U,t_i,lp ar s_.r,.,ij,3 ed. Dy A.K. Sen and B. Williams, t.ambr idge: Camarioge U. Pres.
(9) ' Truth, Fallibility and the Graw:h or.<nowledge.' which is to apperir this jaar in Len tuaus. Locic anJ.%; hod ed. by R. Cohen and M..iartof sky Oordrecht:, P.c i aa l.
(h) en.crar.co..a c ability an: Rasional Choice.'
Sy n t h3j.5,.,
r i
e 4
_