PHL 3000 Lecture Notes - Lecture 10: Modus Ponens, Modus Tollens, Logical Form
Module 10
Lecture 10.1: Common Argument Forms
Modus Ponens – the method of putting
• Argument form:
o If P then Q
o P
o Therefore Q
• Make a truth table for it
P
Q
P u Q
Q
T
T
T
T
T
F
F
F
F
T
T
T
F
F
T
F
• Valid
• Use: proves that something follows from something we already know to be true. Pointing
out the consequences of what the audience already accepts.
• Examples of Modus Ponens
o P u Q
▪ P
▪ Q
o (P v Q) u (R v D)
▪ (P v Q)
▪ (R v D)
o ((P = R) * S) u (T u V)
▪ ((P = R) * S)
▪ (T u V)
• Look for: main operator of one premise is a horseshoe; other premise is the antecedent of
the conditional; allowed to write down consequent
• Examples of Modus Ponens
o If it is wrong to cause humans pain in order to satisfy trivial desires, and if
animals can feel pain, then it is wrong to raise and the kill animals in factory
farms
▪ It is wrong to cause humans pain in order to satisfy trivial desire, and
animals can feel pain
▪ Therefore, it is wrong to raise animals and then kill animals in factory
farms
Modus Tollens – the method of taking
• Argument form:
o If P then Q
o Not Q
o Therefore not P
• Make a truth table for it
P
Q
P u Q
~Q
~P
T
T
T
F
F
T
F
F
T
F
F
T
T
F
T
find more resources at oneclass.com
find more resources at oneclass.com
F
F
T
T
T
• Valid
• Use: prove that some statement is mistaken because it leads to a falsehood. Presenting a
counter example.
• Look for: main operator of one premise is a horseshoe; other premise is the denial of the
consequent; can conclude that the denial of the antecedent is true.
• Example of Modus Tollens:
o If NCR is correct, then the only way to resolve a moral disagreement is by taking
a poll.
o However, taking a poll is not a way of resolving a moral disagreement
o Therefore, NCR is not correct.
Formal Fallacies That Use Horseshoes
• Denying the Antecedent
o If P then Q
▪ Not P
▪ Therefore, not Q
o Truth Table
P
Q
P u Q
~P
~Q
T
T
T
F
F
T
F
F
F
T
F
T
T
T
F
F
F
T
T
T
o Invalid
o Example:
▪ If it is raining, then the streets are wet
▪ It is not raining
▪ Therefore, the streets are not wet
• Affirming the Consequent
o If P then Q
▪ Q
▪ Therefore, P
P
Q
P u Q
Q
P
T
T
T
T
T
T
F
F
F
T
F
T
T
T
F
F
F
T
F
F
o Invalid
o Example:
▪ If it is raining, then the streets are wet.
▪ The streets are wet
▪ Therefore, it is raining
Disjunctive Syllogism
• Argument form:
o Either P or Q
▪ Not P
▪ Therefore Q
find more resources at oneclass.com
find more resources at oneclass.com
P
Q
P u Q
~P
Q
T
T
T
F
T
T
F
T
F
F
F
T
T
T
T
F
F
F
T
F
o Valid
• Use: demonstrate only one of two apparent options is correct
• Examples:
o P v Q
▪ ~P
▪ Q
o (P v Q) v (R v D)
▪ ~(P v Q)
▪ (R v D)
o ((P = R) * S) v (T u V)
▪ ~((P = R) * S)
▪ (T u V)
• Look for: main operator of one premise is a wedge; other premise is the denial of one of
the disjuncts; allowed to write down the other disjunct.
• Example of Disjunctive Syllogism
o It is either permissible to perform painful experiments on humans who are not
capable of giving consent, or else is it wrong to perform these experiments on
animals.
o It is not permissible to perform painful experiments on humans who are not
capable of giving consent
o Therefore, it is wrong to perform these experiments on animals
Formal Fallacy that uses Wedge
• Disjunctive Fallacy:
o Either P or Q
▪ P
▪ Therefore not Q
P
Q
P v Q
P
~Q
T
T
T
T
F
T
F
T
T
T
F
T
T
F
F
F
F
F
F
T
o Invalid
• Example:
o Either Atlanta is in Georgia or else Dallas is in Texas
o Atlanta is in Georgia
o Dallas is not in Texas
▪ Incorrect
Hypothetical Syllogism
• If P the Q
o If Q then R
o Therefore if P then R
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Modus ponens the method of putting: argument form, if p then q, p, therefore q, make a truth table for it. F: valid, use: proves that something follows from something we already know to be true. It is wrong to cause humans pain in order to satisfy trivial desire, and animals can feel pain: therefore, it is wrong to raise animals and then kill animals in factory farms. Modus tollens the method of taking: argument form, if p then q, not q, therefore not p, make a truth table for it. T: valid, use: prove that some statement is mistaken because it leads to a falsehood. Formal fallacies that use horseshoes: denying the antecedent, if p then q, not p, therefore, not q, truth table. If it is raining, then the streets are wet. It is not raining: therefore, the streets are not wet, affirming the consequent, if p then q, q, therefore, p.
