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by the prospect of saving one™s ¬nger.8 Indeed, in a very important and
intuitive sense, given by FA1 in chapter 4, the reason provided by the fact
that one™s action can save forty children from malnutrition is a stronger
reason than the reason provided by the prospect of saving one™s ¬nger. For
7 Graduate students and adjunct professors should modify the amount in these examples.
8 Of course, one is rationally required to save one™s ¬nger at this price only in the context
of af¬‚uent societies, in which the sum of two hundred dollars is relatively easy to come by.

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Brute Rationality

the very same altruistic reason would justify acting in ways which would
be ridiculously irrational otherwise, and which would not be regarded as
justi¬ed by the mere prospect of saving one™s ¬nger. For example, suppose
that it is wartime, and that one is the sole adult in charge of an abandoned
orphanage of forty ˜enemy™ children. One has gone to the supply base to
get the next forty days™ rations of food and medicine. There, a report comes
that much of the route back to the orphanage is now within shelling and
sniper range. Orders come that one is not to risk one™s life bringing food
to these children. Would it be irrational to disobey these orders, risking
one™s life and one™s career, in order to save these children from starvation,
sickness, and serious risk of death? No. Indeed, it would not be irrational
to help these children even if one were virtually certain that it would cost
one one™s life. And yet to risk the same thing merely to save one™s index
¬nger would be the height of irrationality. Nor is this case made special
by the context of wartime. In cases in which one can save forty children
from serious malnutrition for four months, if there is no way of doing so
without risking death, it is rationally permissible to risk one™s life in order
to save the children, and it is rationally permissible not to risk one™s life.
A naive reading of the above example, in line with a single-value view of
the strength of reasons, would suggest that saving forty children provides a
reason of roughly the same strength as does saving one™s career and life. But
this cannot be the whole of the story, if it is also true that one is rationally
allowed either to donate, or not to donate, two hundred dollars in order to
save the same number of children from the same kinds of harms. For one
is certainly rationally required to spend two hundred dollars to save one™s
career and life. Indeed one is rationally required to spend two hundred
dollars to save one™s index ¬nger. The naive view that the rational status
of an action is a matter of the balance of reasons “ a view expressed by R2
and R3 above “ leads to the following claims.

(1) Saving forty children is roughly as important as saving one™s career
and life, for in a choice between the two, either option is rationally
permissible.
(2) Saving forty children is roughly as important as saving two hundred
dollars, for in a choice between the two, either option is rationally
permissible.
(3) Saving one™s career and life is clearly more important than saving two
hundred dollars, for in a choice between the two, one is rationally
required to spend the two hundred dollars.

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Accounting for our normative judgments

Admittedly, these three claims do not involve any formal contradiction.
But they do suggest that there may be a contradiction lurking somewhere,
for there is a signi¬cant failure in transitivity in the relation ˜is roughly as
important as.™ At pp. 94“98 I will try to show where that contradiction
lies.
A more sophisticated reading of the above cases suggests that the deter-
mination of the rationality of actions is not simply a matter of weighing the
univocal strengths of the relevant reasons for and against the action. Rather,
the principle that uni¬es our judgments of all the cases is something more
like principle P of chapter 3:
P It is irrational to do anything that you believe will cause you
harm, unless you also believe that someone (perhaps yourself )
will thereby be spared at least as signi¬cant a harm, or that
someone (perhaps yourself) will thereby receive at least as
signi¬cant a bene¬t.
Surely many will ¬nd P inadequate. Indeed, chapter 7 will point out a
number of signi¬cant problems with it. One reason some philosophers
will object to P is that they wish to give altruistic reasons some measure
of requiring strength, and so would favor something more like Q. But for
most everyday cases, P is an adequate approximation of Q. For it remains
true that it is only when harms to others are disproportionately great that it
becomes irrational to cause them (or to fail to prevent them) without some
reason. In less extreme cases, actions that harm others for some negligible
bene¬t to the agent are not irrational. Rather they are, depending on
the magnitude of the harms involved, thoughtless, sel¬sh, mean, cruel, or
heinous. On the other hand, if an action involves any foreseeable nontrivial
harm to the agent, then that action requires a rational justi¬cation. And
the rational justi¬cation of such agent-harming actions must involve the
avoidance of harms, or the getting of bene¬ts, of at least a comparable
magnitude, either for the agent or for someone else.9 P allows one to
see, in a bold relief that Q may obscure, the logical difference between
the power of a reason to require action, and the power of a reason to
9 This may seem to make it irrational, for example, for parents to make comparatively large
sacri¬ces so that their children will receive comparatively smaller bene¬ts. But real life
cases of this kind are very complex. It would be a mistake to think that a parent who
spent ten thousand dollars in order to get three thousand dollars to her adult daughter was
acting irrationally simply because ten is greater than three. There are many more reasons
involved in such cases than simple economic ones, and even economic reasons are not best
measured in dollars.

91
Brute Rationality

justify actions that stand in need of justi¬cation. But if one moderates P
to accommodate the intuitions that may make it seem too extreme, this
difference in logical space remains. For even Q implies that the justi¬catory
strength of altruistic reasons greatly exceeds their requiring strength. And
this is enough to falsify the claim that one is rationally required to act on
the stronger reason, no matter which sense of ˜stronger™ one chooses.
In the examples here, the reasons provided by the prospect of saving
forty children from serious malnutrition have a great deal of justifying
strength, but no (or not much) requiring strength. This is why one would
be rationally justi¬ed in undertaking a suicide mission aimed at saving
children from these harms, but why one would not be rationally required
to do so, and why one would not even be required to donate two hundred
dollars to produce the same effects. In contrast to this, the reasons pro-
vided by the prospect of saving two hundred dollars have a small justifying
strength (they cannot justify risking the loss of one™s index ¬nger, much
less the risking of one™s career and life). But the prospect of saving two
hundred dollars also has nontrivial requiring strength, since it is irrational
to throw two hundred dollars away without any reason. The justifying
strength of the prospect of saving two hundred dollars is in fact at least as
great as the requiring strength of the altruistic reasons in favor of donating
two hundred dollars to a good charity. This is why it is rationally permis-
sible to keep the money. But the justifying strength of the altruistic reasons
is far greater than the justifying strength of the reasons to save the money.
This is why it is rationally permissible to risk one™s life for these altruistic
reasons, but it is not rationally permissible to risk one™s life, or even (if the
risk is genuine) one™s ¬nger, to save two hundred dollars.

two arg um e nt s aga i n st s i ng le - value v i ews
This section provides two technical arguments that the strength of a reason
cannot be represented by a single value. Although such a single-value view
is not typically explicitly endorsed by philosophers, it is implicit in all current
accounts that identify reasons with the desires that an agent would have
under some sort of ideal conditions.10 Stephen Darwall makes this point
explicitly about the de¬‚ationist informed desire account of normative
reasons, writing that:
10 The quali¬cation ˜current™ is necessary, because, as chapter 6 will argue, such views could
accommodate the distinction between justi¬cation and requirement by interpreting the
theoretically important counterfactual in a more reasonable way.

92
Accounting for our normative judgments

as a de¬‚ationist view, it holds that the normative force of reasons is fully consti-
tuted by the motivational pull a consideration exerts when considered in light of
knowledge and experience.11

In fact, the same point goes just as well for non-de¬‚ationist ideal desire
accounts of normative reasons. In Darwall™s words, such accounts hold that

p is a reason for S to do A if, and only if, were S to consider p in the right way he
would be given some motivation to do A.12

The only difference between such an ˜ideal desire™ view and the de¬‚a-
tionist view is that the phrase ˜in the right way™ in the ideal desire view
is replaced, in the de¬‚ationist view, by conditions that can be speci¬ed in
nonnormative terms. This difference, though important in other contexts,
is not relevant to the question of whether such views imply a single strength
value for any given normative reason: both views have this implication.
Therefore, if Darwall is right in his claim about de¬‚ationary informed
desire accounts, and if the suggestion is right that the point goes just as
well for nonde¬‚ationary ideal desire accounts, then the single-value view
of the strength of reasons is extremely widespread.
Against the single-value view, this chapter presents further arguments
that at least two values will be required to characterize the normative
capacities of practical reasons. Until one has done the math it is very
tempting to suggest that, with the aid of a ˜fudge-factor™ X “ let us call it
˜the margin of practical indifference™13 “ a single strength value can do the
required work. Or one may think that the job can be done by appeals to
vagueness in the measure of the strength of reasons. That is, it is tempting
to suggest that the above examples only show that the particular altruistic
reasons discussed are strong enough to put their respective actions into the
˜rationally permissible™ category, but are not strong enough to put them
into the ˜rationally required™ category. Recall the troubling claims that a
naive interpretation of some of the previous examples seemed to commit
us to:

11 Darwall (1990), p. 262. The view of reasons as related to ideal desires explains the nat-
uralness of using the word ˜force™ to describe the normative capacities of reasons. But
this terminology lends itself too easily to an interpretation of the normative capacities of
reasons based on an analogy with physical forces, and the consequent idea that, given the
relevant reasons, there is only one rational way to act. Esther Gert™s preference for the
term ˜force™ here seems to me a rare mis¬ring of her philosophical intuitions.
12 13 This label comes from a suggestion by Paul McNamara.
Ibid.

93
Brute Rationality

(1) Saving one™s career and life is roughly as important as saving forty
children.
(2) Saving forty children is roughly as important as saving two hundred
dollars.
(3) Saving one™s career and life is clearly more important than saving two
hundred dollars.

These claims were troubling partly because of a striking failure in transi-
tivity in the relation ˜is roughly as important as.™ But failures of transitiv-
ity are a commonplace where thresholds or vague concepts are at issue.
And surely the strengths of reasons do not admit of precise measurement.
Because of this, advocates of a single-value view may believe that appeals
to a threshold like the margin of practical indifference, or to vagueness,
will be able to explain away any apparent inconsistencies in their view. In
order to dispel this illusion, this section offers two arguments showing that
a single-value theory cannot, even with the help of a margin of practical
indifference, capture the strength of a reason without systematically going
against our intuitions about the rationality of certain types of actions. The
simplifying assumptions made throughout these arguments are, admittedly,
not completely insigni¬cant. But even the schematic arguments provided
here should convince an open-minded reader that it is unlikely that a more
nuanced single-value theory of normative strength will fare any better.


The two-gap argument
First some remarks about notation. Let us use uppercase letters to label
action types. We will call the reasons in favor of an action of type A ˜RA ™,
the reasons in favor of an action of type B ˜RB ™, and so forth. And let us
abbreviate ˜the strength of reasons RA ™ with the symbol ˜S(RA )™. For our
purposes, action types are individuated only by the number and type of
reasons that favor or oppose them.
The single-value theory of reasons and rationality holds that an action is
rationally required if and only if the balance of reasons in favor of the action
exceeds the strength threshold X “ the margin of practical indifference.
The single-value theory holds that if the balance of reasons favor a given
choice, but favor it by a gap smaller than X, then the choice is rationally
permissible but not rationally required. In such a case other options are also
rationally permissible, as long as the accumulated strength of the reasons in
favor of them is within the margin X of the strength of the reasons in favor

94
Accounting for our normative judgments

of doing the ˜best™ action. What we need, in order to raise troubles for the
single-value view of the strength of reasons is a set of either/or decisions
that have the following properties. In deciding between an action of type
A and an action of type B, one is rationally required to choose the action
of type B. In deciding between an action of type B and an action of type
C, one is rationally required to choose the action of type C. In a choice
between an action of type A and an action of type D, either is permitted.
And in a choice between an action of type C and an action of type D,
either is permitted. If we can ¬nd action types A, B, C, and D, as described
above, then the following will be true.
S(RA ) + X < S(RB ). (1)
S(RB ) + X < S(RC ). (2)
|S(RA ) ’ S(RD )| ¤ X. (3)
|S(RD ) ’ S(RC )| ¤ X. (4)

We can diagram 1 through 3 as follows:

Org Org+X Org+2X Org+3X Org+4X Org+5X
““|“““““““““““|“““““““““““|““““““““““|““““““““““|““““““““““|““““““““““|
S(RA) S(RD) S(RB) S(RC)

And we can diagram 1, 2, and 4 as follows:

Org Org+X Org+2X Org+3X Org+4X Org+5X
““|“““““““““““|“““““““““““|““““““““““|““““““““““|““““““““““|““““““““““|
S(RA) S(RB) S(RD) S(RC)

By inspection of the diagrams, we can see the problem. 3 and 4 assert
that S(RD ) must be within the margin of practical indifference, X, both
of S(RA ) and of S(RC ). This means (because of 1), that S(RD ) must be
less than S(RB ), while (because of 2) S(RD ) must be greater than S(RB ).
But S(RD ) cannot be both greater and less than S(RB ).
Can we ¬nd actual action types A, B, C, and D that have the properties
required to generate this contradiction? We can ¬nd many such examples.
What we need are action types A, B, and C so that S(RA ), S(RB ), and
S(RC ) are clearly at suf¬ciently wide intervals so that it would be irrational
to choose an action of type A over an action of type B, or an action of
type B over an action of type C. And then we need an action type D,
such that it is rationally permissible, both in a choice between an action

95
Brute Rationality

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