BASIC DEDUCTIVE ARGUMENTS
There are five main deductively valid argument forms and two main
deductively invalid argument forms. Some use an "If/then" statement,
known as a CONDITIONAL (because it states that on the condition that
one statement is true, another is). There are two parts to a
conditional. The statement which goes with the "if" is called the
ANTECEDENT, the statement that goes with the "then" is called the
CONSEQUENT. With conditionals it's important to remember which
statement is the antecedent and which is the consequent--mixing them
up can make the difference between making a valid and an invalid
argument. This is because, depending which is which, the conditional
can have different true values. "If I get an A, then I'll pass this
class" is true. But "If I pass this class, I'll get an A" is false.
One could get a "B" or a "C" and pass as well.
Others of these arguments use "either/or" statements known as
DISJUNCTIONS. In these there is no antecedent and consequent. Each
part of the disjunction (called DISJUNCTS) can be switched with the
other with no change in true value. "Either you're a Democrat or
you're a Republican" has the same truth value as "Either you're a
Republican or you're a Democrat." (By the way, if the you is a
general you as in “every U.S. citizen,” what is that true value?)
MODUS PONENS (Valid)
If p, then q
p
Therefore, q
MODUS TOLLENS (Valid)
If p then q
Not q
Therefore, not p
DENYING THE ANTECEDENT (Invalid)
If p then q
Not p
Therefore, not q
ASSERTING THE CONSEQUENT (Invalid)
If p then q
q
Therefore, p
HYPOTHETICAL SYLLOGISM
If p then q
If q then r
Therefore, if p then r
DISJUNCTIVE SYLLOGISM (Valid)
Either p or q
Not p
Therefore, q
Because either disjunct may be denied, this form is also valid:
Either p or q
Not q
Therefore, p
DILEMMA (Valid)
Either p or q
If p then r
If q then s
Therefore, either r or s