affirming the consequent
f p, then q. If the cat is on the mat, she is asleep.
q. She is asleep.
Therefore, p. Therefore, she is on the mat.
DENYING THE ANTECEDENT
f p, then q. If the cat is on the mat, she is asleep.
Not p. She is not on the mat.
Therefore, not q. Therefore, she is not asleep.
The first part in a conditional statement (the if part) is known as the
antecedant
conditional statement
if then statement
the second part (the then part) is known as the
consequent
disjunctive syllogism
Either p or q. Either we light the fire or we will . freeze.
Not p. We will not light the fire.
Therefore, q. therefore, we will freeze.
Hypothetical Syllogism
f p, then q. If Ajax steals the money, he will go to . jail.
If q, then r. If Ajax goes to jail, his family will . . suffer.
Therefore, if p, then r. Therefore, if Ajax steals the . money, his family will suffer.
Implicit premise
a premise that is not
explicitly stated in an argument but is a
crucial part of the argument. Also
called suppressed premise and hidden
premise
Modus Ponens (Affirming the Antecedent)
f p, then q.
p.
Therefore, q
Modus Tollens (Denying the Consequent)
If p, then q.
Not q.
Therefore, not p.
syllogism
a deductive argument made up of three
statements–two premises and one conclusion
deductive argument
intended to
provide logically conclusive support for
its conclusion
inductive argument
is intended to provide
probable support for its conclusion.
valid argument
A deductive argument that succeeds in providing conclusive support for its conclusion.
invalid argument
A deductive argument that doesnt succeed in providing conclusive support for its conclusion.
sound argument
A deductively valid argument that
also has true premises.
unsound argument
A deductively valid argument that has a false premise.
A strong argument is
An inductive argument that succeeds in providing
probable support for its conclusion
weak argument.
An inductive argument that fails to provide probable support
cogent argument
An inductively strong argument with true premises
uncogent argument
An inductively strong argument witha false premise
truth preserving
The argument’s form is good; if the premises are true, the conclusion must be true.
fallacious appeal to authority.
The fallacy of relying on the opinion of someone deemed to be an expert who in fact is not an expert.
Background information
The large collection of very well supported beliefs that we all rely on to inform our actions and choices. It consists of basic facts about everyday things, beliefs based on very good evidence (including our own personal observations and excellent authority), and justified claims that we would regard as “common sense” or “common knowledge.