Basic Argument Forms
Keith Burgess-Jackson
9 October 2016
An argument form is the skeleton of an argument. It is what remains of
an argument after its flesh (content, substance, matter) has been removed. In a zoology or anatomy course, you might be expected to distinguish between raccoon, skunk, ringtail, opossum, wolverine, coati, and
badger skeletons. What makes this task difficult, and what leads some
students to fail to accomplish it, is that these species are similar as well
as different. In this course, I expect you to be able to distinguish between
the following four argument forms, which, as in the case of real skeletons,
are similar as well as different:
Affirming Mode
Denying Mode
Valid
If p, then q1
p
 q2
Invalid
If p, then q
q
p
Modus Ponens (MP)3
Fallacy of Affirming the
Consequent (AC)4
If p, then q
Not p
 Not q
If p, then q
Not q
 Not p
Modus Tollens (MT)5
Fallacy of Denying the
Antecedent (DA)6
Do you see why each of the valid forms is valid (i.e., truth-preserving)?
1 Propositions of the form “If p, then q” (known as conditionals) have two parts.
The “if” part—in this case, “p”—is known as the antecedent (part that comes before); the
“then” part—in this case, “q”—is known as the consequent (part that comes after). In the
conditional “If q, then p,” “q” is the antecedent and “p” the consequent. The letters “p” and
“q” stand for propositions, such as “It is raining” and “The ground is wet.” Thus, someone
might utter the conditional, “If it is raining, then the ground is wet.”
2 The symbol “∴” means “therefore.”
3 The term “modus ponens” is Latin for “affirming mode.” Modus ponens says,
in effect, that anything implied by a truth is true. (Strictly speaking, it says that anything materially implied by a truth is true, but we can ignore this complication for the
time being.)
4 The second premise affirms the consequent of the first premise.
5 The term “modus tollens” is Latin for “denying mode.” Modus tollens says, in
effect, that anything that implies a falsehood is false. (Strictly speaking, it says that
anything that materially implies a falsehood is false, but we can ignore this complication
for the time being.)
6 The second premise denies the antecedent of the first premise.
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Do you see why each of the invalid forms is invalid (i.e., not truth-preserving)? For each invalid argument form, give an example—a counterexample—in which the premises are true and the conclusion false. Is it
possible to do this for the valid argument forms? If not, why not?
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