How to Criticize (and Defend) a Normative Ethical Theory
Keith Burgess-Jackson
14 January 2016
A normative ethical theory is a statement of necessary and sufficient conditions for moral rightness. It purports to tell us what it is
that makes right acts right—and, by implication, what it is that makes
wrong acts wrong. Theological voluntarism, for example, says that
“Act x is right if and only if x conforms to God’s will.” Act-utilitarianism
says that “Act x is right if and only if x is optimific.”1
In philosophy, as in science, theories are criticizable—both in the
sense that they are capable of being criticized and in the sense that
they are worthy of being criticized.2 A critic of a theory tries to show
that the theory is false (or otherwise unacceptable). One way to do this
is to show that the theory has a false (or unacceptable) implication, for
(1) anything that implies a falsehood is false and (2) anything that implies something unacceptable is unacceptable. The critic’s argument
has the following form:
1. If theory T is true, then proposition p is true. (In other words,
T implies p.)3
2. p is not true.
Therefore,
3. T is not true.
This form of argument is known as modus tollens (Latin for “denying
mode”). Modus tollens is not to be confused with modus ponens (“affirming mode”), though both forms are valid. See my handout entitled
1
See the Appendix for an elaboration of statements of the form “x if and only
if y.”
2 The word “desirable” is similarly ambiguous. Depending on the context, it
means either “capable of being desired” or “worthy of being desired.” Some things, such
as horse manure, are capable of being desired but not—to most people, at any rate—
worthy of being desired. Some things, such as friendship, are both capable of being desired and worthy of being desired.
3 An “if . . . then” sentence is called a conditional. It has two parts, each of
which is itself a sentence. The sentence that follows the word “if” is called the antecedent; the sentence that follows the word “then” is called the consequent. A conditional
says that, as a matter of fact, it is not the case that the antecedent is true while the
consequent is false. If you conjoin a conditional with a true antecedent, therefore, you
get a true consequent, and if you conjoin a conditional with a false consequent, you get a
false antecedent. As we will see shortly, these correspond (respectively) to the valid inferences known as modus ponens and modus tollens.
1
“Basic Argument Forms” for the difference between these argument
forms.4
What does it mean to say that an argument form, such as modus
tollens, is valid? Validity is a formal (structural) feature of argument.
To say that an argument is valid (as opposed to invalid) is to say that
its conclusion follows logically from its premises, i.e., that it is logically
impossible for its premises to be true while its conclusion is false.5 The
following arguments are valid, though the first has true premises and
the second false premises:
1. All dogs are mammals.
2. All mammals are animals.
Therefore,
3. All dogs are animals.
1. All dogs are cats.
2. All cats are birds.
Therefore,
3. All dogs are birds.
These arguments share the following (valid) form:
1. All Xs are Ys.
2. All Ys are Zs.
Therefore,
3. All Xs are Zs.6
A sound argument is a valid argument all of whose premises are true.7
Thus, the argument about mammals is sound, while the argument
about cats is unsound. All sound arguments are valid, but not all valid
4 The handout contains, in addition, a discussion of two invalid argument forms
that are often confused with modus ponens and modus tollens, namely, the fallacy of
affirming the consequent (which is often confused with modus ponens) and the fallacy of
denying the antecedent (which is often confused with modus tollens). A fallacy is an
argument that seems to be correct but is not. Do you see why the fallacies just mentioned
seem to be correct? In other words, do you see the source of the confusion?
5 To say that an argument form is invalid is to say that its conclusion does not
follow logically from its premises, i.e., that it is logically possible for its premises to be
true while its conclusion is false. Valid arguments are truth-preserving; invalid arguments are not truth-preserving.
6 Any argument with a valid form is a valid argument.
7 It may help to remember the following “equation”: S = V + T.
2
arguments are sound. Note that all sound arguments have true conclusions. (Do you see why?) Thus, if a particular argument has a false
conclusion, then it is unsound—either because it’s invalid or because it
has a false premise, or both. It follows that if you reject the conclusion
of an argument, you must either deny the validity of the argument or
reject one of its premises, or (in some cases) both.
Suppose someone produces a modus tollens argument, the conclusion of which is that your favorite theory (act-utilitarianism, for example) is false. (In other words, someone is criticizing your theory.) Since
modus tollens is a valid argument form, there are only two ways for
you to reply:

Reject the first premise (the one that says, “If theory T is true,
then proposition p is true”). This is called grasping8 the bull
by the horn. If you adopt this strategy, you are saying that
your theory does not, in fact, have the stated implication. You
are saying that the critic either misunderstands or misapplies
your theory.

Reject the second premise (the one that says, “p is not true”).
This is called biting the bullet. If you adopt this strategy,
you are saying that you accept, rather than reject, proposition
p. (Rejecting “p is not true” is equivalent to accepting “p is
true.”) This may be painful to do, so it will be like biting on a
bullet while one of your limbs is being amputated. To bite the
bullet, philosophically speaking, is to stick by your theory,
come what may.9
Other terms are “grabbing” or “taking.”
“If a theory has counterintuitive implications, then this is prima facie evidence against the theory. But if we decide that this counterintuitive implication of the
theory is a more or less isolated phenomenon and that the theory accounts for a great
many of our particular value judgments, and especially if it seems to explain more of our
value judgments better than alternative theories, then this initial evidence against the
theory will be overridden and we should revise the particular value judgment that conflicts with the theory.” David O. Brink, Moral Realism and the Foundations of Ethics,
Cambridge Studies in Philosophy, ed. Sydney Shoemaker (New York: Cambridge University Press, 1989), 218.
In case you’re wondering, it’s not possible, with regard to the same argument,
to both grasp the bull by the horn and bite the bullet. The reason for this is that, while
the premises of a modus tollens argument can both be true, they can’t both be false. (In
technical terminology, they’re subcontraries.) So you can either grasp the bull by the
horn or bite the bullet, but not both.
8
9
3
To defend a theory is to ward off criticisms of it, just as to defend a
fortification is to ward off attacks on it. A successful defense of a theory
doesn’t show that the theory is true; it merely rebuts the critic’s claim
that it is false. The effect is to leave the theory standing. By the same
token, failure to breach the walls of a fortification during a siege
doesn’t show that the fortification is impregnable;10 all it shows is that
this particular siege failed. For all we know, some future attack (siege)
will succeed in breaching the walls.
Appendix
Shelbie gets a treat if and only if Shelbie is good.
Shelbie gets a treat if Shelbie is
Shelbie gets a treat only if
good.
Shelbie is good.
Shelbie’s being good is sufficient
Shelbie’s being good is necesfor Shelbie’s getting a treat.
sary for Shelbie’s getting a
treat.
If Shelbie is good, then Shelbie
If Shelbie is not good, then
gets a treat.
Shelbie does not get a treat.
False if: Shelbie is good but does
False if: Shelbie is not good but
not get a treat.
gets a treat.
10 “Impregnable” means “(of a fortified position) unable to be captured or broken into; resistant to attack or criticism” (Oxford American Dictionary and Language
Guide, 1999).
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