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of type A and an action of type D, and in a choice between an action
of type C and an action of type D, to choose either. Suppose then that
the main consequence of choosing an action of type B over an action
of type A will be the loss of two hundred dollars, and that the main
consequence of choosing an action of type A over an action of type B will
be a month of very bad depression.14 If one has a reasonable income, it
would be irrational to suffer such a depression merely to save two hundred
dollars. Thus S(RA ) + X < S(RB ). Now suppose that the choice is not
between saving money and being depressed, but between being depressed
and dying rather painfully. The strength of the reasons in favor of avoiding
depression is still S(RB ). Let us call the action that avoids the painful death
an action of type C. It is irrational to die painfully merely to avoid a month™s
depression. Thus S(RB ) + X < S(RC ). Now for the action type, D. Let
us suppose the reasons in favor of an action of type D are that by doing so,
one will prevent serious malnutrition, with attendant risk of sickness and
death, in forty children for four months. In a choice between saving the
children and saving oneself from a painful death, it is rationally permitted
to decide either way. Thus, |S(RD ) ’ S(RC )| ¤ X. But in a choice to save
the children or to save two hundred dollars “ a choice which most readers
are now in a position to make “ it is also rationally permitted to decide
either way. Thus, |S(RA ) ’ S(RD )| ¤ X. And that, plus the assumptions
of a single-value view of the strength of reasons, is enough to generate the
contradiction.
One of the assumptions I have made on behalf of an adherent of the
single-value view is that RA (the reasons in favor of or against doing an
action of type A) can be ˜separated™ from an action of type A, so that RA
could also be the reasons in favor of or against some other action. In such
a case, the strength of the reasons in favor of the two actions would be, in
both cases, S(RA ). There are, for example, many different actions that will
cause one to lose one™s arm. All of these actions have, as a reason against
them, that one will lose one™s arm. And that reason is always quite strong,
although of course there may sometimes be other reasons that outweigh it
(for example, in the case in which one™s arm is gangrenous). That the same
reason can occur in many different contexts, and that it always bears the
same weight, seems true to me, and I offered some arguments in favor of
such a view in chapter 4. But whether it is true or not, it is an indispensable
premise for someone who holds the single-value view. Unless the same
14 Not, however, so bad as to make suicide likely, or the loss of one™s job. In such a case,
additional reasons, which I do not want to consider, would favor B over A.

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Accounting for our normative judgments

reason, RA , can occur in different contexts, where it has the same strength,
it makes no sense to talk about S(RA ) at all. The notion of the strength of
a reason is like the notion of the weight of an object, or the length of a
stick. If the regularities in the behavior of objects placed on a scale did
not allow one to assign weight values to objects “ values that remained
constant from occasion to occasion “ then we would not have the concept
of ˜the weight™ of an object, and could not make appeal to the weights
of objects in explaining why one side of a scale went up, and the other
went down.15 Similarly, the single-value view of the strength of reasons
presupposes both that one can re-identify the reason when it occurs in
different contexts, and that it bears the same relations of ˜weaker than™ and
˜stronger than™ to all the other reasons with which it can be compared.
This is why the transitivity of the strengths of reasons can also be assumed
in criticism of the single-value view.16
In the above example, we chose action types A, B, and C so that S(RA ),
S(RB ), and S(RC ) were 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. That is, there is clearly a very
great difference between the strength of the reason in favor of an action
that will save one two hundred dollars, and the strength of the reason in
favor of an action that will save one from a month of extreme depression.
Because we wanted the intervals between S(RA ), S(RB ), and S(RC ) to
be so great, we chose an action A with relatively weak reasons in favor
of it. Because of the weakness of S(RA ) it is more plausible (but not, I
think, actually plausible) that one is in fact irrational to choose an action
of type A over an action of type D. But given that it is irrational to spend
two hundred dollars today simply to save one hundred dollars tomorrow,
it seems that any plausible X must be rather smaller than the difference
between S(RB ) and S(RA ) in the example. This suggests that we could
have chosen action types A, B, and C so that S(RA ), S(RB ), and S(RC )
were much closer together. This would have allowed S(RA ) to be much
higher, making it still more plausible that it would be rationally allowed
to choose an action of type A over an action of type D.
Of course one can still deny the normative judgments made in the
above example. One could claim that we are all acting irrationally when
we decide to save two hundred dollars rather than donate it to a charity
that we believe will use it to prevent serious malnutrition in a large number
15 See Wittgenstein (1953), §142.
16 See Darwall (1983), pp. 67“73 for a different sort of argument for the same conclusion.

97
Brute Rationality

of children. I do not think very many people seriously hold this belief.
But the point of the two-gap argument is not to argue against this belief.
Rather, it is to show that the single-value view cannot accommodate our
normal intuitions about the rational status of many actions, even using
a margin of practical indifference, X, which allows many actions to be
labeled ˜rationally permissible.™ Of course one is always free to deny that
our normal intuitions are correct. But one should realize when one is
committed to doing so. And holding the single-value view does so commit
one.


The equal justi¬cation argument
Suppose we have action types A and C. And suppose that in an either/or
choice between an action of type A and an action of type C, it is ratio-
nally permissible to choose the action of type A. The equal justi¬cation
argument starts from the premise that if the choice of the action of type
A is permissible in virtue of self-interested reasons RA , then it is possible
to construct an action type B, which is also rationally permissible, but in
virtue of altruistic reasons, RB . These reasons RB are to be understood
as involving exactly the same types and quantities of harms or bene¬ts as
do reasons RA , except that while the harms or bene¬ts involved in RA
are harms and bene¬ts exclusively for the agent, the harms and bene¬ts
involved in RB are harms and bene¬ts exclusively for someone other than
the agent. Call this premise “ that RA and RB have the same justifying
strength “ ˜the agent-neutrality of justi¬cation.™ Here is an example of
what the agent-neutrality of justi¬cation amounts to. Suppose it is admit-
ted that, in situation S, it is rationally permissible to risk a terrible injury
in order to try to save one™s life. Then, according to the agent-neutrality
of justi¬cation, it would also be rationally permissible, in a suitably similar
situation S— , to risk the same injury in order to try to save someone else™s
life. Here ˜suitably similar™ only means that no reasons other than RB are
introduced by the change in situation, and no reasons other than RA are
eliminated.
Recall that the single-value theory of reasons and rationality holds that
if, in an either/or situation, the balance of reasons favor C1 over C2 by
a margin in excess of X (the margin of practical indifference) then it is
rationally required to choose C1 over C2 . Further, the single-value view
holds that if the balance of reasons favors C1 over C2 , but only by a gap
smaller than X, then either choice is rationally permissible. The equal

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Accounting for our normative judgments

justi¬cation argument will ¬rst show that reasons of equal justi¬catory
strength must, on the single-value view, have equal requiring strength.
This should come as no surprise. If it were false, then the single-value
view would in fact be allowing the central point for which this chapter
is arguing: the logical separability of the requiring and justifying strength
of reasons. Then the equal justi¬cation argument simply points out that
there are reasons that we do not think of as having the same requiring
strength, but which the agent-neutrality of justi¬cation asserts must have
the same justifying (and, hence, according to single-value views, requiring)
strength.
In order to show that the single-value view of reasons and rationality
cannot use the margin of practical indifference, X, to explain our intuitive
judgments, we will need action types A, B, and C that have the following
properties. Actions of type A and actions of type B must be favored by
reasons RA and RB that differ only in the following respect. The harms
and bene¬ts involved in RA accrue to the agent, while the harms and
bene¬ts involved in RB accrue to someone other than the agent. But it
must be irrational to choose an action of type C over an action of type A,
while it is not irrational to choose an action of type B over an action of
type C. If we can ¬nd such action types, then the following will be true.

(∀y)((S(RA ) + X > S(Ry )) ⊃ (S(RB ) + X > S(Ry ))). (1)

1 simply asserts that whenever it is rationally permissible to choose an
action of type A over an action of type y, it is also rationally permissible to
choose an action of type B over an action of type y. This is true in virtue
of the agent-neutrality of justi¬cation, and our stipulation that RA and RB
differ only in respect of the person to whom bene¬ts and harms accrue.
But we also have, because of our stipulation about actions of type C, the
following.

S(RC ) + X < S(RA ). (2)
S(RC ) + X > S(RB ). (3)

2 claims that it is irrational to choose an action of type C over an action of
type A, while 3 claims that it is rationally permissible to choose an action
of type C over an action of type B.
Now choose action type D, such that

S(RD ) = S(RC ) + 2X. (4)

99
Brute Rationality

Solving for S(RC ), we get
S(RC ) = S(RD ) ’ 2X. (5)
From 1 we have
(S(RA ) + X > S(RD )) ⊃ (S(RB ) + X > S(RD )). (6)
From 2 and 5 we have
(S(RD ) ’ 2X) + X < S(RA ). (7)
Simplifying, we get
S(RD ) ’ X < S(RA ). (8)
Adding X to both sides we get
S(RD ) < S(RA ) + X. (9)
This is the same as
S(RA ) + X > S(RD ). (10)
From 10 and 6 we get
S(RB ) + X > S(RD ). (11)
But from 3 and 5 we have
(S(RD ) ’ 2X) + X > S(RB ). (12)
Simplifying, we get
S(RD ) ’ X > S(RB ). (13)
Adding X to both sides we get
S(RD ) > S(RB ) + X. (14)
This is the same as
S(RB ) + X < S(RD ). (15)
But this contradicts 11.
As in the two-gap argument, this contradiction will only cause troubles
for the single-value view of reasons and rationality if we can ¬nd actual
action types A, B, and C that have the required properties. But again,
we can ¬nd many such examples. Suppose that actions of type A involve
saving my own index ¬nger, and actions of type B involve saving someone

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Accounting for our normative judgments

else™s index ¬nger, and actions of type C involve saving myself the now
familiar sum of two hundred dollars. If the agent-neutrality of justi¬cation
is true, then premise 1 is true. If it is irrational to sacri¬ce one™s index
¬nger merely to save two hundred dollars, then premise 2 is true. And if it
would not be irrational to refuse to spend two hundred dollars to save a
stranger™s index ¬nger, then premise 3 is true. Again, even with the aid of
the margin of practical indifference, X, the single-value view of reasons and
rationality cannot accommodate our intuitions here, as long as one grants
the premise I have called ˜agent-neutrality of justi¬cation.™ In assessing the
independent plausibility of the agent-neutrality of justi¬cation, one should
not be misled by the name. It is not the strong premise that it makes no
difference to any question about the rationality of an action, whether the
relevant bene¬ts or harms are going to accrue to the agent or to someone
else. That is a much more controversial claim, and it should already be
obvious that according to the view on offer here, it is false. Rather, the
agent-neutrality of justi¬cation only involves the following claim: that if
it is rationally permissible to make a certain sacri¬ce for one™s own sake,
it would also be rationally permissible to make that same sacri¬ce for
someone else™s sake. That does not mean that, rationally speaking, one
should make the sacri¬ce. In only means that if one chose to do so, one
would not be choosing irrationally.
As with the two-gap argument, one can avoid the conclusion of the
equal justi¬cation argument if one is willing to reject one or more of the
premises. Thus, if one is enamored of a single-value view of reasons and
rationality, one can claim that the agent-neutrality of justi¬cation is false.
Or one can hold that any cost that I would be rationally required to pay
in order to save my own index ¬nger I would also be rationally required
to pay in the interest of saving the index ¬nger of a complete stranger.
But if one does not want to make either of these concessions, then one
cannot continue to hold that the strength of a reason can be represented
by a single value, and that rational action is action favored (within some
threshold) by the balance of reasons.


oth e r s olut i on s
Even if the preceding arguments have successfully demonstrated the inad-
equacy of single-value views, this by itself does not provide very strong
support for the justifying/requiring distinction. For there may be better
ways to account for the intuitions that caused trouble for single-value

101
Brute Rationality

views. This section will brie¬‚y present and criticize two alternate solu-
tions, both defended by Joseph Raz: widespread incommensurability, and
exclusionary permissions. In the case of incommensurability, it will even
turn out that the requiring/justifying distinction can help explain how
certain normative phenomena might have led Raz and others to embrace
such a troublesome and paradoxical concept.


Widespread incommensurability
Joseph Raz explicitly endorses the commonsense view that the normal case
of decision-making is one in which the relevant reasons make a number
of options eligible, but do not require any of them. He calls this claim
˜the basic belief,™ and he is suf¬ciently strongly committed to its truth to
hold that, despite dif¬culties in seeing the theoretical position it expresses,
it should be maintained unless it can be shown to be incoherent.17 One
way in which Raz expresses the basic belief is by saying that the primary
function of practical reasons is to render options eligible, rather than to
require them. This sounds very much like the claim that the primary
function of reasons is to justify actions, and not to require them. Indeed,
at points one might even think that Raz endorses the position defended
in this chapter. But although Raz is one of the very few philosophers who

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