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Knowledge-based decision theory and the new evil demoni am grateful to davide fassio and errol lord for substantial help in working through the ideas of this paper, and to charity anderson and, again, davide fassio for detailed comments on an earlier draft. thanks also to matt benton, john hawthorne, maria lasonen–arnio, clayton littlejohn, nico silins, jacques vollet and tim williamson, members of the new insights for religious epistemology group in oxford and the audience at a 2013 new evil demon workshop in geneva.
The idea that being rational is doing what is best in view of what one
knows has some intuitive appeal, fits nicely with attractive views of evi-
dence, reasons and the application of decision theory, and promises to bring
some theoretical unity to epistemology. However, it has hardly ever been
seriously considered, because it appears to fly in the face of what episte-
mologists call the New Evil Demon problem. There is a loophole in the
problem, however. While I show that it cannot be exploited by the most
straightforward implementation of the view — Knowledge-based Decision
∗I am grateful to Davide Fassio and Errol Lord for substantial help in working through the
ideas of this paper, and to Charity Anderson and, again, Davide Fassio for detailed comments onan earlier draft. Thanks also to Matt Benton, John Hawthorne, Maria Lasonen–Arnio, ClaytonLittlejohn, Nico Silins, Jacques Vollet and Tim Williamson, members of the New Insights forReligious Epistemology group in Oxford and the audience at a 2013 New Evil Demon workshopin Geneva.
alternative implementation — the Two-Step account — that shows more
Being rational is, roughly, doing the reasonable, intelligent, smart, sensible thing;
being irrational doing the senseless, stupid, idiotic, crazy thing 33).
Being rational is not doing what is best. Some smart decisions are disastrous and
some idiotic ones turn out good. Rather, being rational is, roughly, doing what is
best as far as one can see. What is best as far as one can see is what appears best
in view of the information one has. But the information one has is just what one
knows. Thus being rational is, roughly, doing the best in view of what one knows.
The idea may sound like a platitude but it is rejected by all currently dominant
theories of rationality. Subjective Bayesians take rationality to be a matter of
doing what is best in view of one’s (graded) beliefs. Many philosophers take it to
be a matter of doing what is best in view of one’s internal evidence, which consists
in various internal mental states — seemings and Others take it to be a
matter of one’s action or beliefs being the output of reliable cognitive processes
or virtues, where the relevant processes are internal to one’s It is thus
worth mentioning a few considerations that make the knowledge view attractive
illustrates both views. On the one hand he says that it is rational to believe,
want or do something when “what we believe would, if it were true, give us [decisive] reason” tobelieve, want or do it (111). When giving a more fine-grained account, however, he says that therationality of some of our beliefs does not depend on our other beliefs (as the above suggested)but on our “evidence” (129).
2Along the lines of what says about justification. Goldman himself distin-
guishes justification from rationality. He doubts the latter turn captures any well-defined or usefulnotion (27). His stab at a positive characterization of it — being rational is reasoning well (317–8)— indicates that he takes rationality to be an internal matter.
and explaining why it is widely rejected. That will lead to the topic of this paper,
namely, whether the rejection is warranted.
Two disclaimers are in order, to set aside irrelevant issues and to clarify why
the view under consideration is that being rational is only roughly doing what is
First, what “best” amounts to will not matter much here. Perhaps rationality is
a matter of doing what is sufficiently good rather than what is best — satisficing
rather than maximizing. Perhaps it is matter of doing what is expectably best
rather than what is best: for there are cases in which we know that an option
does not have the best result and yet it is still rational to take it because it has the
best expected results 159–60). There are plausibly different flavours
of best: personal, moral, aesthetic and so on. These will yield corresponding
flavours of rationality. There are also various localized notions of best: what
is best in view of a certain goal or norm alone — which may or may not be
best in a wider perspective. These will yield correspondingly localized notions of
rationality. On some views, what counts as “best” for the purpose of evaluating
an person’s rationality also varies with what that person desires, prefers, wants
and so on. Most importantly for us, a person’s desires and like states may also
affect what appears best to that person, for instance by affecting how they rank
alternative state of affairs. To reflect that, we may have to say that being rational
is, roughly, doing what appears best in view of what one knows and of what one
desires. The precision would have no impact on the present discussion, however.
Second, some would prefer to say that being rational is doing what is best in
view of what one is in a position to know. Others that it is doing what is best in
view of what one knows by observation, directly or some similar restriction. The
differences between these variants of the view are interesting but lateral to our
The paper proceeds as follows. Section 1 states five considerations in favour of
the knowledge view. Section 2 states one main reason for its rejection: it appears
to have blatantly false consequences in cases of non-culpable error. The problem
is a version of what is known as the New Evil Demon problem in epistemology.
Section 3 argues that it is not yet clear whether the view has such consequences.
To progress on that score, section 4 spells out a straightforward implementation of
the view: Knowledge-based Decision Theory. Sections 5–6 prove that the version
does have the unpalatable consequences. Section 7 introduces a less straightfor-
ward implementation of the view: the Two-Step account. While that version is in
better shape, it cannot yet be said to avoid the problem altogether.
Here are five considerations in favour of the idea that rationality is, roughly, doing
what is best in view of what one knoThe first comes from ordinary folk
appraisals 571). Claims about what is rational are
routinely backed up by claims about knowledge. Explicitly so when we make such
3The claim is intended to cover both what is rational ex ante and what is rational ex post.
Roughly, rationality ex post would require not merely doing what is best in view of what oneknows but doing it in the light of (relevant aspects of) what one knows. See section 3 below onthe distinction.
claims as “It wasn’t sensible for Hannah to get so much food since she didn’t know
how many people would come”. Explicitly, but indirectly so when we use instead
knowledge-entailing constructions such as “seeing that”, “remembering that” and
so Implicitly so when we make such claims as “It was silly for Hannah to
buy bonds since the market was about to collapse” which arguably presuppose that
Hannah knew or was in position to know that the market was about to collapse.
One symptom of the presupposition is that challenges such as “How would she
know that? All agencies gave the bonds stellar ratings!” are perfectly natural. Of
course, some appraisals are instead backed up with claims about desires and the
like. But as said above, we are not concerned with how rationality depends on
those. Some appraisals are backed up by claims about reasons: “Hannah had no
reason to think that the bonds would not be repaid”. But these may be a matter of
knowledge as well, as will be seen shortly. Some are backed up by claims about
what it is reasonable to think: “It wasn’t silly for Hannah to buy the bonds; in
fact, it was perfectly reasonable for her to expect that they would be repaid”. But
that leaves open the possibility that what is reasonable to think is itself, roughly,
believing what seems true in view of what one knows. Better counterexamples
are appraisals backed up by mere claims of belief : “it was sensible for Hannah to
get a lot of food, for she thought that many people would come”. However, it is at
least arguable that these presuppose that the belief in question was reasonable. If
Hannah’s belief that many people would come was wholly irrational, one would
4See chap. 1) for the view that these entail knowledge. The view is fairly
orthodox but not uncontroversial 27–34).
feel at least reluctant to accept that it was sensible for her to get a lot of food
because she thought that many people would come. If it is presupposed that the
belief is reasonable, then again its being so may be a matter of what one kno
The second consideration involves a principle linking rationality to evidence:
being rational is doing what is best in view of one’s evidence. Something along
those lines is commonly endorsed in decision theory, formal epistemology and
philosophy of science. As we noted, many philosophers take one’s evidence to
consist in internal mental states (or their contents). However a case can be made
for the idea that one’s evidence is just what one knows chap.
9). And though few decision theorists or philosophers of science seem to accept
the idea that all one knows is evidence, they typically assume that one’s evidence
consists in a subset of what one knows: what is known by observation, for in-
The third consideration involves a similar principle framed in terms of reasons:
being rational is doing what is best in view of the reasons one has. Talk of reasons
is notoriously flexible. There are marginal uses of “having a reason” on which
5A few more things can be said here. First, “ought” and “should” are sometimes used to talk
about what is rational for one to do. When they are, they receive the kind of back up discussedabove. See 571–3) for relevant examples — though note that someof their cases involve a use of “ought” on which one may reasonably (“excusably”) do somethingwhat one “ought” not to do. Second, these ways of talking are not restricted to the folk. Theyare also widespread in disciplines dealing with rationality, such as decision theory, game theory oreconomics — though admittedly, “knowledge” and “information” are there often used in ways thatdo not sharply distinguish knowledge and belief. Third, claims of rationality are rarely backed upwith claims about what one experiences unless the latter indicate a reasonable belief. For instance,suppose that Hannah knows that a pair of gold sticks are of the same length though due to someoptical illusion one looks longer than the other. “It was sensible for Hannah to take the left onesince it looked longer” is bizarre if not outright false in such a scenario.
a “reason one has” may be something unknown to one. Two bankers talk about
Hannah; one asks: “does she have any reason to pull her money out?”, the other
replies: “yes, her stock’s value is about to collapse”. That may be felicitous and
true even though Hannah has no idea of the impending But that is
not a use on which the principle is plausible. If Hannah pulled out now, her
doing so would not be made rational by the impending collapse. That being said,
central uses of “reasons one has”, “one’s reason” and “reasons for which” appear
to require knowledge. On their salient reading, “Hannah had a reason to complain:
the banker lied to her”, “Hannah’s reason to change bank was that the banker had
lied to her”, “The reason for which Hannah changed bank was that the banker
lied to her” all presuppose or entail that Hannah knew that the banker lied. They
are intimately related to the reading of “Hannah left her bank because her banker
lied” that presupposes the same. A case can be made for the principle stated with
The fourth consideration is one of systematic unity. The line of thought is
due to For decades, epistemologists have taken justification
or rationality as their central notions and tried to account for knowledge in their
terms. The project has not been That leaves us with three alternative
pictures. The first is a two-headed epistemology, where knowledge and rational-
ity are independent notions. Knowledge would belong to a group of interrelated
6See 31–2), though see for a contrary view.
is paradigmatic. The programme is carried out in the literature of “unde-
feated justification” accounts of knowledge, which boomed in the 70s but was superseded by ac-counts of knowledge that used wholly different primitives in the 80s, such as relevant alternatives,reliability or sensitivity.
notions — including perhaps safety, sensitivity, modal stability, causal connex-
ions between world and mind — and rationality to another — including perhaps
reason, justification, defeat, epistemic norms, reasoning, reflexive access. The
second is an epistemology with one trunk and two branches: knowledge and ra-
tionality are both explained in terms one third primitive — the current contenders
are reliability and virtue. The third is a knowledge-first epistemology, where ratio-
nality and justification are accounted for in terms of knowledge. Those who find
the first option theoretically unsatisfactory and the second unsuccessful are pulled
towards the third. In recent years, knowledge-first accounts of justification have
been actively devKnowledge-first accounts of rationality are the obvious
next step. The knowledge view — the idea that rationality is, roughly, doing what
is best in view of what one knows — is not the only way to go this route.
The fifth consideration has to do with how to apply decision theory in particu-
lar cases 77-82). We leave it aside for the moment but return
Each consideration is debatable. The point here is not to establish the knowl-
edge view conclusively. It is, after all, a controversial view. The point is rather to
show why it would be very natural to consider it. That makes more striking the
fact that, with few exceptions, theorists hardly give it a single thought.
One major reason for theorists to dismiss the knowledge view is that it appears
incompatible with some obvious facts about rationality. The facts in question have
to do with what epistemologists call “the New Evil Demon problem”
Consider a pair of cases. In the Good case, Sarah remembers — and thereby
knows — that her car is parked in front of the office. Her workday is over and
she decides, reasonably, to walk towards that spot. In the Bad case, everything
seems to Sarah as it does in the Good case but her car has been stolen. She does
not know that her car is parked outside — it is not —, but she takes herself to do
so. She decides to walk towards the same
Sarah’s decision is rational in the Bad case just if it is rational in the Good
case. That is obvious or at any rate extremely hard to deny. As
349) puts it, “when the word “rational” is used in the way that is most common
among philosophers, [that] intuition is compelling”.
The intuition appears incompatible with the knowledge view. What it is ratio-
nal for Sarah to do in the Good and the Bad cases is the same. Yet her knowledge
differs from one case to another. That does not entail, but strongly suggests, that
rationality is not a function of knowledge. Rather, rationality appears to be a
function of what remains constant across the cases: how things look to Sarah or
9The Good case / Bad case terminology comes from 150).
The version of the problem familiar among epistemologists is more dramatic.
In that version, the Good case is an ordinary case of knowledge, but the Bad case
is one of massive deception: Sarah is the victim of a Cartesian Evil Demon, or she
is a brain in vat stimulated to have experiences similar to the ones she would have
in the Good case. Again, the claim is that her decision is rational in both cases.
(As the case is more outlandish, the claim is perhaps less unassailable.) Since the
cases differ drastically in terms of what is know, rationality does not seem to be a
The Old Evil Demon problem was for certain views to explain how one knows
in the Good case even though one does not in the Bad case. The New Evil Problem
is for certain views to explain how one as rational and justified in the Bad case as
one is in the Good case despite lacking relevant knowledge and failing in various
While the New Evil Demon intuition is robust about many pairs of cases, it is
not trivial to find a suitable generalization of We call case a centred world,
that is a possible world with a designated subject and time. When talking of a
case we refer to its subject as one or the agent and to its time by using tenseless or
present-tensed constructions. Conditions such as being seated, raising one’s arm,
believing that there are rocks obtain at We predicate rational of some
conditions at cases: it is rational to intend to sell one’s stock in some given case.
10In the dramatic scenario, not only Sarah knows little, but she also forms her beliefs in ways
that are unreliable relative to the environment she is in. That is why epistemologists — whoseoriginally targeted reliabilism about justification — focussed on the dramatic version.
11Thanks to ***Timothy Williamson for pressing this point.
12The terminology comes from 52).
Now we may initially try to generalize the intuition as follows:
NED-generalization — physical. If the agents of two cases are phys-
ical duplicates, then something is rational in one if and only if it is
The generalization is mistaken. First, it captures too few cases. It is not essential
to the pairs that they involve physical duplicates: some involve a healthy human
being on one side and a brain in a vat on the other. The problem is not fixed
by replacing “physical duplicates” by “cerebral duplicates”: the intuition does
not require that the two subjects are atom-per-atom duplicates. Second, it fails
insofar as the contents of one’s mental states do not supervene on the physical. It
is rational for me to believe that water is wet, but it is not rational for my physical
duplicate on Twin Earth to believe that water is wet. Similar problems arise if we
replace “physical” by “intrinsic”.
A second attempt is to say that mental states duplicates are rational duplicates.
That does not capture the intended cases if knowledge is among the mental states
chap. 1). For in the Good case one knows while in the Bad
case one does not. The idea should rather be that duplicates in internal or non-
factive mental states are rational duplicates. But again, that will capture too few
cases. First, their are pairs of cases that differ on irrelevant mental states: the
verdicts on any of the foregoing pairs are unchanged if we make one case so that
one believes that the number of stars is even and the other so that one believes that
it is odd. Second, many pairs involve different though analogous mental states
that rationalize different but analogous beliefs or intentions. In the Good case I
see a dog d jumping around — it is my first encounter with it. In the Bad case
I have a corresponding hallucination. On a standard view I am able to entertain
thoughts about d in the Good case but not in the Bad case. Hence in the Good
case it visually seems to me that d jumps around; not so in the Bad case. In
the Good case it is rational for to believe that d jumps around; not so in the Bad
case. Still, the intuition goes, in the Bad case it is rational for me to have an
analogue belief (or belief-like state) that I would express by saying “that dog is
jumping And in both cases it is rational for me to believe that there is a
dog jumping around. A NED-generalization framed in terms of duplicates is too
We can better recast the NED generalization with the help of two primitives.
The first is relevance (to rationality): in a given case only some of one’s mental
states are relevant to whether a given belief or intention is rational. In the parked
car cases Sarah’s beliefs about the number of stars are irrelevant, for instance.
The second is that of counterparts of internal mental states. My belief that water
is wet and my Twin Earth counterpart’s belief that twater is wet are counterparts.
My belief that d is jumping around and my belief (or belief-like state) that “that”
is a dog in the Bad case are internal counterparts. Similarly, my intention to catch
d in the Good case may have an intention (or intention-like state) to catch “that
dog” in the Bad case. We do not provide necessary and sufficient conditions for
counterparthood, but the notion has a fairly intuitive application in the intended
13The state is not indisputably a belief since (on Russellian accounts) there is no singular propo-
NED-generalization — internal counterparts. For every pair of be-
liefs or intentions F, G and every pair of cases a, b, if F and the F -
relevant mental states in a are counterparts of G and the G−relevant
mental states in b, then it is rational to F in a iff it is rational to G in
Summing up, overwhelmingly plausible facts about NED pairs appear incompat-
ible with the view that rationality is, roughly, doing the best in view of what one
knows. In the NED pairs two cases are identical in some respect of rationality
even though they differ in relevant respects of knowledge. That suggests that ra-
tionality is not a function of knowledge. This is one of the main reasons why the
knowledge view has long been left off the table
There is a loophole, however. Suppose that one’s pay is a function of one’s job; it
is still possible for two different jobs to pay the same. Similarly, rationality may
be a function of knowledge even though some people differing in knowledge do
not differ in rationality. The knowledge view can advert the New Evil Demon
problem if it is shown that what is known in the Bad case, though different from
the Good case, makes the same choices rational.
pursues just such a strategy. On his view, whenever one knows p
in the Good case, one knows that it appears that p in the (dramatic version of the)
Bad He argues that that knowledge plays an equivalent role in rationalizing
one’s actions and choices. In the Good case, it is rational for Sarah to walk towards
the parking spot because she knows that the car is there. In the Bad case, it is also
rational to do it, but because she knows that the car appears to her to be there.
At this point we need to distinguish two concepts of rationality: ex ante and
ex post. What is ex ante rational is what it is rational for one to do, irrespectively
of whether one does it or not and of why one does it. What is ex post rational
is what one does rationally; that requires that one did it and depends on why
one did The two come apart when one does the reasonable thing for wrong
reasons. Suppose it is reasonable for Sarah to buy health insurance but that she
does so only because she has the pathological conviction that she caught a deadly
disease. Is her action rational? Yes and no. It is (ex ante) rational for her to buy
health insurance. But she did it (ex post) irrationally. The common wisdom is that
rationality ex post requires doing the ex ante rational thing on a proper basis, that
is, doing it in the light of what makes it ex ante rational.
As stresses, the distinction raises a double New Evil Demon prob-
lem for the knowledge viewThe primary New Evil Demon problem is to ex-
plain why one is ex ante rational in the Bad case. The strategy here is to find
pieces of knowledge in the Bad case that make the relevant action rational. Sup-
pose that is done. Still, there is a secondary New Evil Demon problem, which is
14The proposal develops a suggestion made by 199–200).
15That is an analogue of the epistemologists’ distinction between “propositional justification”
and “doxastic justification”. The labels “ex ante” and “ex post” are used by
16Not so for reliabilists, for instance.
to explain how can one act ex post rationally in a Bad case. For even if there is
some knowledge in the Bad case that makes one’s act ex ante rational, one does
not appear to act on it. Rather, one acts on the basis of a state that does not con-
stitute knowledge, e.g. a false belief. So we would have to say, implausibly, that
actions in Bad cases are always ex post irrational. (And similarly for intentions,
In broad outline, Lord’s answer to the secondary problem is this. In the Bad
cases in which one is ex post rational, one is sufficiently sensitive to the relevant
pieces of knowledge for her action, intention or belief to count as based on them.
Of course the action, belief or intention is also and more saliently based on a state
that does not constitute knowledge, such as false belief. But that does not prevent
it to be based on items of knowledge that rationalize it. The answer seems to me
on the right track. At any rate, nothing will be added to it here. Our main focus is
the primary problem, which raises more pressing concerns.
To see whether the loophole can be exploited, I focus on a more specific version
of the knowledge view. I call it knowledge-based decision theory. It has been sug-
gested, if not endorsed, by 577–80) and endorsed
17Showing that endorse the view requires a bit of exegetical
work. They explicitly present their view as an alternative to dominant theories of rationality (571,577 and other places). Yet when they state their view they do not use “rational” and cognates butinstead “ought”, “should”, “appropriate” and “excusable”. While they call the norm “treat p as a
A choice situation — choice, for short — is a case and a set of mutually
exclusive and exhaustive options between which one must choose. In any concrete
case we typically face several concurrent choices. Suppose Hannah stops at a
coffee shop on her way to the bank: she faces the choice of what drink to have
and the choice of whether to carry on with the plan to go to the bank. Typically
we only give thought to one choice at a time, but that does not mean that we
do not concurrently face several. There is a worry that concurrent choices are
hardly ever independent: what to choose on one is always at least dimly relevant
to what to choose on another. If that is so, any concrete case really is just one
big choice between a myriad of highly specific options. Be that as it may, we
will not worry much about the individuation of choice situations here. We assume
that in the cases we will discuss, the individuation we use is at least an acceptable
reason for acting only if you know p” a “norm of practical rationality” (577), it is unclear whetherfailing to comply with the norm entails being in any way irrational. This depends on whether“excusable” violations are always rational; but they stay silent on this — see 573, 577, 582, 586.
Whichever way they go on this, they must endorse the idea that practical rationality is a function ofthe relevant types of appropriateness and excusability. If not, it is hard to see how their proposal isa theory of rationality. Since they think that appropriateness and excusability in the relevant senseare a function of what one knows, they endorse the generic knowledge view. More specifically,they take themselves to “gesture at” a type of decision theory in which knowledge delivers epis-temic probabilities (580). It is very natural to assume that that knowledge is also meant to deliverepistemic possibilities, as in Weatherson’s more explicit proposal.
The same page (580) misleads some readers into thinking that Hawthorne and Stanley distancethemselves for the proposed decision theory. They write that while “[they] are by no means op-posed to a perspective in which claims of practical rationality [. . .] are grounded in a decisiontheory of the sort [they] gestured at”, “the need to integrate such a theory with reasons for action isstill vital”. The point of this, however, is not to distance themselves from the proposal; rather, it isto stress that the proposal only covers rationality ex ante. That is made clear in the next sentence:“For one thing, there are cases where one does one ought to do but for the wrong reasons, and thisphenomenon needs explanation”. The idea is not that knowledge-based decision theory is false; itis that it fails to cover rationality ex post.
A decision table is an abstract object consisting of a set of options, a set of
states — and sometimes a probability distribution over them —, a set of outcomes
that are functions of possibilities and options and a ranking of outcomes. A de-
cision theory is a set of principles that selects options on decision tables. We
assume that the selection sorts out options at least into acceptable and unaccept-
able ones. We say that a decision table adequately represents what is rational in a
given choice just if what is acceptable on the table matches what is rational in the
choice. We sometimes write simply that a table “adequately represents a choice”.
We say that a table reflects one’s knowledge in a choice if and only if the table’s
options match those of the choice and (a) all states on the table are compatible with
what one knows in that case and (b) every possibility compatible with what one
knows obtains in at least one state. If we represent one’s knowledge as a set of
possible worlds — the ones compatible with what one knows —, that amounts to
saying that the table’s states are a partition of one’s knowledge.
Knowledge-based decision theory is the following view (compare
(KBDT) If a decision table reflects one’s knowledge in a choice, then
that table is a rationality-table for that choice.
Some necessary refinements are left The view straightforwardly imple-
18Not every way of partitioning one’s knowledge will do. A gang of street kids threaten to
scratch your car unless you pay them. If you divide the options compatible with what you knowinto they will scratch the car and they will not then paying will be dominated and hence deemedirrational no matter what. The table is wrong, however, because it fails to take into account thefact that your paying makes the former state less likely to obtain. A suitable partition should usestates that are evidentially — on some views — or causally — on others — independent of youroptions.
ments the idea that it is rational to do what is best in view of what one knows.
Decision-theoretic principles tell what options are “best” in view of the informa-
tion provided in a decision table. When the information matches what one knows,
the selected options are the best in view of what one knows. On the knowledge
view, these are just the rational options.
The view is motivated by cases like the following 79).
Lucy chooses to put $1000 token down on 28 on a fair roulette with extremely
poor returns: she merely wins double if her number comes out but looses if any
of the 37 other numbers comes out. She is irrationally convinced that 28 will win,
and in fact it will. We could represent her choice with a table like the following:
On that table the selected option is to put the token down. The table may be an
adequate representation of what Lucy will do, since it reflects her beliefs. It may
also be an adequate representation of what option is in fact best, since it reflects
the facts. But it does not adequately represent what is rational for her to do. For
it is clearly irrational for Lucy to put the token down. On the knowledge view this
is because she does not know that 28 will come out. In view of her knowledge,
it is possible that other numbers come out and there is only 1/38 chance that 28
comes out. The following table reflects her knowledge:
On standard decision-theoretic assumptions putting the token down is not se-
lected. Knowledge-based decision theory thus predicts that it is irrational to do
further argues that of all the relations that one may bear to
the information encoded in a decision table — such as knowledge, justified true
belief, knowing that one knows, and so on —, knowledge is the most natural one
that correlates with tables that represent rational choice adequately. That is the
fifth consideration in favour of the knowledge view. It tells more particularly in
favour of its implementation as knowledge-based decision theory
A proof that knowledge-based decision theory vi-
Knowledge-based decision theory is well-motivated and simple. But it can be
shown to violate the New Evil Demon intuition. Consider the following pair of
cases. You are home and you need to grab a bottle of water to go on a bike trip.
19Surprisingly, does not consider justified belief (in a sense of justified dis-
tinct from knowledge) or reasonable belief. The following suggests that they would have beenbetter candidates.
b: there is a full bottle of water in the basement.
g: there is a full bottle of water in the garage.
Further details are as one would expect. You know that there is no other bottle
of water in the house. You know that if there is a bottle in the basement and you
go there, you will have a bottle; and that if there is a bottle in the garage and you
go there, you will have a bottle. You know that it is good to have a full bottle —
no matter which — and bad to have one. You also know that going down to the
basement or the garage is a negligible cost. We claim that:
(1) In the Good case, the following table reflects your knowledge:
In the Bad case, everything is as in the Good case, except that under excep-
tional circumstances, your partner has taken the bottle in the garage without warn-
ing you. So in the Bad case, you do not know that g. We claim that:
(2) In the Bad case, the following table reflects your knowledge:
We further assume that our decision theory contains two principles. Let us
say that an option is unsurpassed on a table iff its pay-offs are at least as good as
any alternative at all states. For instance, in the first table above, the two actions
are unsurpassed; in the second, the first action is. And let us say that an option is
weakly dominated iff there is some option whose pay-offs are at least as good as
any alternative at all states and even better for one or more states. For instance, in
the second table, the second action is weakly dominated. Now our two principles
(3) Unsurpassed options are acceptable.
(4) Weakly dominated options are unacceptable.
Both principles are uncontroversial dominance principles. Dominance principles
do not apply to tables whose states are causally or evidentially dependent on one’s
actions. But nothing of the sort is going on here.
(5) It is rational to decide to go to the garage in the Good case if and
only if it is rational to decide to go to the garage in the Bad case.
The claim is, of course, an instance of a New Evil Demon intuition.
(1)–(5) are inconsistent with (KBDT). By the decision-theoretic principles
(3)–(4), going to the garage is selected on the first table but not on the second.
By (1) and (2) the first table reflects what one knows in the Good and Bad cases,
respectively. Hence by (KBDT) it is only rational to decide to go to the garage in
the Good case, which contradicts (5).
Hence knowledge-based decision theory violates the New Evil Demon intu-
ition. The result is not surprising but it is worth establishing. The argument can
be used against one way of spelling out Lord’s view, for instance. Even if we
add it appears that g in all columns of the Bad case table, going to basement still
dominates going to the garage. So the view makes the wrong prediction that go-
ing to the garage is irrational in the Bad case. Hence if Lord’s view is spelled out
along the lines of Knowledge-based decision theory, it fails to avoid the New Evil
A few attempts at blocking the proof are worth considering.
Attempt 1: scepticism. One may flat-out reject the claim that you know that b
and g in the Good case, arguing that nothing is known of the external world.
Answer. External-world scepticism easily reconciles knowledge-based ac-
counts of rationality and the New Evil Demon world intuition. It does so by
holding that in Good cases one cannot know things that are not know in Bad
cases, thereby removing asymmetries in knowledge between the cases. The dif-
ficulties for scepticism lie elsewhere: it is highly implausible, and when paired
with a knowledge-based account of rationality, it has a hard time explaining why
certain choices are rational (see chap. 4, who argues that sceptics
must claim that none is). A discussion of scepticism is beyond our scope, how-
ever. The knowledge views we are concerned with are embedded in a resolutely
Attempt 2: in the Bad case, you do not know that b. One may try to argue that
in the Bad case, you lack knowledge of b as well as g. Contra (4), the proper table
for Bad would thus be along the following lines:
Going to the garage is not weakly dominated on the table, so the proof fails.
Answer. The strategy is untenable for some variants of the case. Suppose you
are currently standing in the basement, staring at the full bottle of water. The
unusual happenings in the garage can hardly deprive you of your knowledge that
Attempt 3. Either you do not know b in the Bad case or it is irrational to
go to the garage in the Good one. The attempt uses the previous one as part
of a divide and conquer strategy. Variants of the pair are divided in symmetric
and asymmetric ones. Symmetric ones are those in which b and g stand and fall
together. For instance, you learnt about both bottles from the same source. Since
the source is misleading in the Bad case, you fail to know both b and g in the Bad
case. These case are dealt with along the lines of Attempt 2. In the other cases, it
is now said, your standing to b is better. After all, your knowledge of b is retained
in the Bad case. Because your standing to b is better, it is somewhat irrational
to go the garage in the Good case. So it is not a problem that we classify it as
Answer. First, the decision theory needs revision in order to integrate “quality
of knowledge” considerations. That is not trivial. Second, it is dubious that when-
ever one’s standing to b is slightly better than one’s standing to g, it is somewhat
irrational to opt for the garage. Third and mainly, it is simply false that in asym-
metric cases, one’s standing to b is better. Consider the following. In the Good
case, you are standing in the garage and looking at the bottle. You only know of
the basement bottle by a fairly distant memory. In the Bad case, highly unusual
circumstances have forced your partner to refill the water bottle you are looking
at with petrol. The case is asymmetric, in the sense that the unusual happenings in
the garage do not affect your knowledge of the basement. But it is not such in the
Good case your standing to b is intuitively better than your standing to g in a way
that would make it somewhat irrational to opt for the garage. If anything, your
standing would make it somewhat irrational to opt for the one in the basement.
Attempt 4: in the Bad case, you do not know that the basement is at least as
good as the garage. In the Good case, you know that the garage is no better and
no worse than the basement. In the Bad case, you loose knowledge that the garage
is no worse — for in that case it is worse. Perhaps you also loose knowledge that
it is no better. You may fail to know that there is not more water or a fancier drink
in the garage. If so, the proper table for Bad is something like:
Where r stands for the proposition that the garage is no better than the base-
Answer. Again, that is highly implausible for some versions of the case. Un-
usual happenings deprive you of some knowledge of the garage’s contents, but
not all of it. You retain knowledge that it does not contain a dozen elephants, for
instance. You may equally well retain knowledge that the garage has at most one
Attempt 5. Zero Probability. Since knowledge entails truth, actuality is always
compatible with what one knows. In the Bad case, this forces us to introduce a
state that reasonably believes not to obtain: b&¬g. But everything else the agent
knows (misleadingly) indicates that it does not obtain. So we could argue that
the state receives a probability 0. And since the state has a zero probability, the
fact that going to the basement is better in that state should not be taken into
consideration. Hence we reject weak dominance (4): weakly dominated options
are acceptable if they are only dominated in virtue of zero-probability states.
Answer. First, one has to motivate the probability function. If it is obtained
by conditionalizing on knowledge, for instance, it requires a prior probability of
1 to there is a bottle conditional on there appears to be a bottle. That may appear
implausible — especially if similar assignments must be made for all NED-style
pairs. Second, the strategy faces a dilemma. Either it treats probability 0 as equiv-
alent to leaving a state off the table or it does not. If the former, the strategy in
effect gives up knowledge-based decision theory. If the latter, weak dominance
Consider the latter horn first. Probability 0 and impossibility are thought to
come apart in cases involving infinite sets of possibilities. A point-sized dart is
randomly thrown on a disc; it has equal chance of falling on any point. The chance
that it hits the point-size bull’s eye cannot be a real number greater than 0 — for
the chances of each point is the same and they would add up to more than 1. So it
must be 0. Still, it is possible that the dart falls on the bull’s eye. Hence probability
0 is not impossibility; rather, it indicates that the ratio of positive cases to all cases
is infinitely small. When probability 0 and impossibility are thus distinguished,
weak dominance appears correct. It is not rational to prefer a bet that pays $1000
unless the dart falls on bull’s eye to a straight offer of $1000. (If you doubt that,
consider instead a huge but finite number of points scattered on the disc, say a
trillion. It is not rational to prefer a bet that pays $1000 unless the dart falls on
one of those to a straight offer of $1000. Yet the probability that the dart fall on
To this, one may be tempted to reply that the infinite case and the Bad case
differ. In the infinite case, it may be said, the probability is not 0 but infinitesimal
— where infinitesimal numbers are (non-real) numbers whose infinite sums can
add up to a finite number. By contrast, in the Bad case the true state should receive
a proper probability 0. And here dominance does not apply.
If one goes this route, then for all intents and purposes one treats probability
0 as impossibility — that is, as equivalent to leaving a state off the table. But that
is tantamount to reject knowledge-based decision theory: the true state is left out
even though it is compatible with what one knows.
Attempt 6. Reject the decision principles. Finally one could object to the
dominance principles (3) and (4), arguing that they fail in some cases.
Answer. The cases in which dominance principle appear to fail are well-
delimited: when the states are causally or evidentially dependent on one’s choices
or when reiteratively eliminating dominated strategies in game settings. Our case
involves none of those. Those applications aside, the principles are perhaps the
less controversial ones of decision theory. Rejecting them is a high cost.
Attempt 7: restrict the knowledge base. One may endorse a version of the
knowledge view on which rationality depends on a subset of what one knows:
what is known by observation, “directly” or some such restriction. The subset
may suitably be called one’s evidence. (KBDT) is revised accordingly: a table
adequately represents rationality in a choice if it reflects one’s evidence in that
choice. Moreover, one’s evidence in the same in both cases. Hence what is rational
Answer. If evidence includes things observed, it is easy to produce pairs on
which a structurally similar proof goes through. In the Good case, one may ob-
serve both that there is a bottle of water on the bar (b ) and one on the ground (g ).
In the Bad case, the ground bottle has been filled with petrol or one hallucinates
it. So one does not have evidence g but one still has evidence b . The rest goes as
before. Now the more evidence is restricted, the more contentious the pairs are.
If evidence is restricted to propositions about one’s presently occurring narrow
mental states, it becomes less obvious that one can be mistaken about them —
hence a convincing Bad case is harder to find. But with evidence so restricted, the
20We can say more. Since one’s evidence is compatible with b&¬g in the Bad case, it must
be so as well in the Good case; since going to the basement does not dominate in the Good case,one’s evidence must be compatible with ¬b. Hence the table for both cases should like the one inAttempt 2.
view, like scepticism, makes it harder time to explain why it is rational to act.
Knowledge-based decision theory is not the only way to spell out the idea that
rationality is, roughly, doing the best in view of what one knows. In this section,
an alternative is sketched, the Two-Step account. Like Knowledge-based Decision
Theory, it makes what is rational a function of what is known. But unlike it, it
does not directly uses one’s knowledge as input to decision theory. Rather, it
proceeds in two steps. First, one’s knowledge determines what is supported by
what one knows. Second, what is supported in turns determines what is rational
to do. For belief the second step is straightforward: it is rational to believe just
what is supported by what one knows. For intentions and actions, what is rational
is what is justified in view of what is supported by what one knows.
If what is supported by what one knows just is what one knows, the view boils
down to knowledge-based decision theory. However, if what is supported is more
than what one knows, the view has some hope of solving the New Evil Demon
problem. The suggestion would be that what is supported by one’s knowledge in
the Bad case is the same as, or a counterpart of, what one knowledge supports
in the Good case. In the basement / garage Bad case, for instance, even though
you do not know that there is a water in the garage, what you know supports that
there is one. Hence the one-column table of premise (1) would reflect what is
supported in both cases. If rational choice is a matter of what is supported rather
than of what one knows, it will be the same across both cases.
On the proposed view what is rational is still a function of what is known, for
it is a function of what is supported, and what is supported is itself a function of
what is known. If what is supported is the same (or analogous) across Good and
Bad cases, the New Evil Demon problem is averted.
It is useful to contrast the proposed view with Lord’s On Lord’s view
what rationalizes actions are known facts; they differ across Good and Bad cases.
On the present view what rationalizes actions are supported propositions; they are
the same across Good and Bad cases. On Lord’s view, what ultimately rationalizes
action in the Bad case is a known fact about appearances. On the present view,
it is whatever knowledge supports the relevant propositions. Lord’s view requires
a psychological state of appearing that p; the present view only requires that p
is supported by what one knows. Note, however, that the proposed view cannot
plausibly wholly avoid appeal to known appearances. In the dramatic Bad cases,
one’s relevant knowledge is limited to propositions such as it appears to me that p
or the present situation is like one in which p holds 199). If p
is supported, it will have to be supported by such propositions. The crucial differ-
ence between knowledge-based decision theory and the two-step view, however,
is that in the former only it appears that p makes it way into decision tables, while
in the latter p itself does. What Lord says about his own view does not adjudicate
One could call what is supported “the evident” — with an eye towards Chisholm’s
use of the term. The evident is what is made evident by one’s evidence,
namely what one knows. What one knows itself is evident, but the evident is
not restricted to what one knows — see below. The term strains ordinary usage,
however, because some things that are “evident” in that sense are false.
If we call what is supported one’s reasons, the proposed view would yield
the result that one’s reasons are the same (or analogous) in the Good and Bad
cases. However, that would require that in some cases one’s reasons are false
propositions. That strains ordinary usage.
Let us call what is supported the scaffolding. We can list some properties that
the scaffolding must have for the view to succeed.
The scaffolding supervenes on knowledge. What is supported in a
case is a function of what is known in that case.
The scaffolding includes knowledge (reflexivity). If one knows p, p is
The scaffolding goes beyond knowledge (ampliativity). For some p,
one does not know that p (and p does not follow from what one
knows) but p is supported. For instance, in our Bad case it is sup-
ported that there is a bottle in the garage, though one does not know
The scaffolding is indistinguishable from knowledge. If p is sup-
ported, one does not know that one does not know p. Equivalently,
21Thus the view entails that if one knows p, it is reasonable to believe that p. That has been
if one knows that one does not know p, then p is not
The scaffolding is less than the “unknown unknowns”. For some p,
one does not know that one does not know p, but p is not supported.
For instance, if p is a proposition that one cannot even conceive, one
does not know that one does not know p. Yet p is not
The first four properties can be summed up as follows: the scaffolding lies be-
tween the known the “unknown unknowns” but cannot be identified with either
New Evil Demon compatibility. The scaffoldings in Good cases / Bad
cases pairs are counterparts of each other
Some further properties that are not mandatory but desirable are consistency (the
scaffolding never entails both p and not-p), deductive closure (the scaffolding
is closed under logical entailment), non-monotonicity or defeasibility (strict in-
creases in what is known need not preserve what is supported). To illustrate the
latter: if in the Bad case you learned that the neighbour asked your partner some
water in emergency, the proposition that there is a bottle of water in the garage
22That entails that if one knows that one does not know p, it is not reasonable to believe that p.
That is challenged by those who think that it is reasonable to believe that a lottery ticket will looseeven though one does not know it.
23I do know that I don’t know facts that I cannot conceive. But that does not make it the case
that I know that I don’t know p, where p is a particular fact that I cannot conceive.
24“Between” makes sense because the known is necessarily a subset of the “unknown un-
knowns”: if you know p, it is not the case that you do not know p, so you do not know thatyou do not know it.
25Strictly speaking, our counterpart relation applies to internal mental states. We may extend it
to propositions by saying that p in case a is a counterpart of q in case b if and only if a belief thatp in case a would be counterpart of a belief that q in case b.
would cease to be supported. Non-monotonicity is required if the scaffolding
function is reflexive, ampliative and A further property is cut: what
supported propositions would support if known is itself
The notion of support generalizes to supported probabilities. Some associate
an evidential (or epistemic) probabilities with what one knows
chap. 10). Supported probabilities would be a function of those. The simplest
proposal is that supported probabilities are obtained by conditionalizing evidential
ones on supported propositions. Supported probabilities — rather than evidential
ones — would then be fed in decision tables that represent what it is rational for
It is far from trivial to build a scaffolding function that has the required prop-
erties. But that does not show that there is none. One simple refutation one would
26By ampliativity, there is a body of knowledge X that does not entail p but that supports p. By
reflexivity, ¬p is apparent on X ∪ ¬p. By consistency, p is not supported by X ∪ ¬p. So a strictincrease in knowledge fails to preserve a supported proposition.
27The idea is this: suppose that a body of knowledge, K, supports p. And suppose that taken as
a body of knowledge, K and p together would support q. Then q is supported by K itself. Thatmay seem intuitive. Some word of warnings are in order, however. Cut is notoriously violated inprobabilistic settings — it may be that given p, it is likely that q, and given p and q, it is likely thatr, and yet given p alone, it is not likely that r. And, as argues, failures of Cutseem precisely to be what appears to go wrong in “bootstrapping” reasoning. So one may rejectCut if one invokes some probabilistic machinery to account for the scaffolding function and onemay need to reject it anyway to classify “bootstrapping” reasoning as irrational. We do not explorethese issues here.
28On the view just sketched, a lot of things get (apparent) probability 1: everything you know
and then some more. Many philosophers think that it is irrational to assign probability 1 to any-thing except a highly restricted group of propositions. They are worried, first, that assigningprobability 1 to a proposition means that one will be disposed to bet on it at any odds. And, sec-ond, that assigning probability 1 to a proposition means that one is disposed to remain certain of itwhatever evidence comes. With respect to second problem, it should be clear from the above thatgiven the non-monotonicity of supported propositions, increases in one’s knowledge can demote asupported probability of 1. The first is beyond the scope of the present paper. See 589) for some discussion.
be to exhibit a pair of cases which are identical in knowledge but differ in ratio-
nal belief, in violation of the supervenience claim. But none seems forthcoming.
Furthermore, as long as the New Evil Demon property is not well specified, it is
difficult to prove that no such functions exists — just as it is difficult to prove that
The idea that rationality is, roughly, doing the best in view of what one knows
has some intuitive and appealing features. But it appears to fly in the face of the
New Evil Demon intuition. The intuition is that rationality is similar across cases
that differ in knowledge but that are suitably similar in internal mental states.
That suggests that rationality is not a function of knowledge. It does not entail
it, however. For it is in principle possible that different bodies of knowledge
The most natural way to spell out the idea more rigorously is knowledge-based
decision theory. That is the view that what is rational to do is determined on a table
whose states are a partition of one’s knowledge. We have shown that the view does
violate the New Evil Demon intuition. To many, that definitely disqualifies it as a
That is not the end of the knowledge view, however. For one may retain the
idea that what is rational is a function of what one knows without plugging knowl-
edge directly onto decision tables. The Two–Step view we introduced does exactly
this. On that view, what one knows determines what is supported in one’s case,
and the latter is what gets onto decision tables. The view avoids the problem of
the simple knowledge-based decision theory approach. We have delineated the
properties that a notion of the supported must have for the view to work. We have
not built one, however, and it remains to be seen whether a suitable notion exists.
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