Philosophy 103Linguistics 103
Yet, still, even further more, expanded,
Introductory Logic: Critical Thinking
Dr. Robert Barnard
Last Time:• Definitions
– Lexical– Theoretical– Precising– Pursuasive
• Logical Form• Form and Validity
Plan for Today
• Deductive Argument Forms• Formal Fallacies• Counter-Example Construction
Validity and Form• Deductive Validity – IF the premises are true
THEN the conclusion MUST be true.• Deductive Soundness – the deductive
argument is valid AND premises are all true• Form - The structure of an argument. Validity
is a Property of Form.
Common Deductive Logical Forms
• Modus Ponens• Modus Tollens• Disjunctive Syllogism• Hypothetical Syllogism• Reductio Ad Absurdum
Common Logical Forms
• Modus Ponens
If P then Q, P --- Therefore Q
• Modus Tollens
If P then Q, Q is false --- Therefore P is false
Modus Ponens Example
If P then Q, P --- Therefore Q
If Peter is from Ohio then Peter is an AmericanPeter is from Ohio --- Therefore Peter is an American.
Modus Tollens ExampleIf P then QQ is false
Therefore P is false
If Paul is a potter then Paul has worked with clay Paul has not worked with clay. Therefore Paul is not a potter.
Common Logical Forms• Disjunctive Syllogism P or Q, P is false --- Therefore Q
• Hypothetical Syllogism
If P then Q , If Q then R --- Therefore If P then R
Disjunctive Syllogism Example
P or QP is false
Therefore Q
Pizza is yummy or Quiche is manly.Pizza is not yummy.Therefore Quiche is manly.
Inclusive OR vs Exclusive OR
Assume: Tom is a Lawyer or Tom is a Doctor
If Tom is a Lawyer does that require that he is not a Doctor?
Inclusive-OR: No - (Lawyer and/or Doctor)
Exclusive- OR: Yes - ( Either doctor or lawyer, not both)
Hypothetical Syllogism Example
If P then QIf Q then R
Therefore If P then R
If Pigs fly then Cows kiss.If Cows kiss then Otters sing.Therefore If Pigs fly then Otters sing
Common Forms• Reductio Ad Absurdum
(Reduces to Absurdity)
a) Assume that Pb) On the basis of the assumption if you can prove ANY contradiction, then you may infer that P is false
Case of : Thales and Anaximander
Thales and Anaximander
• Arché - Table of Elements
- Thales: Water - Anaximander: Aperion
The Presocratic Reductio1. Everything is Water (Thales’ Assumption)2. If everything is water then the universe contains an
infinite amount of water and nothing else. (From 1)3. If there is more water than fire in a place, then the
water extinguishes the fire. (observed truth)4. We observe fire. (observed truth)5. Where we observe fire there must be more fire than
water. (from 3 & 4)6. Therefore, everything is water and something is not
water (Contradiction from 5 and 1)7. Thus, (1) is false.
Common Formal Fallacies
• Affirming the Consequent• Denying the Antecedent• Illicit Hypothetical Syllogism• Illicit Disjunctive Syllogism
Common Formal Fallacies
• Affirming The Consequent
If P then Q, Q --- Therefore P
• Denying the Antecedent
If P then Q, P is false --- Therefore Q is false
Affirming the Consequent
If P then QQ is true
Therefore P
1. If it rained last night then the grass is wet
2. The grass is wet.3. Therefore, it rained last night.
Denying the Antecedent
If P then QP is false
Therefore Q is false1. If Tom is not hungry then Tom ate lunch2. Tom is Hungry3. Therefore Tom did not eat lunch.
Common Formal Fallacies
• Illicit Disjunctive Syllogism -P or Q, P is true -- Therefore not-Q
-P or Q, Q is true -- Therefore not-P• Illicit Hypothetical Syllogism(*)
If P then not-Q , If Q then not-R --- Therefore If P then not-R
* - there is more than one form of IHS
Illicit Disjunctive Syllogism
P or QP is true
Therefore not-Q
John is Tim’s father or Sally is Tim’s mother
John is Tim’s FatherTherefore Sally is not Tim’s mother
Illicit Hypothetical Syllogism
If P then not-QIf Q then not-R
Therefore If P then not-R
1. If I like fish then I won’t eat beef2. If I eat beef then I won’t eat cheese3. Therefore, If I like fish then I won’t eat
cheese.
Testing for Validity
The central question we ask in deductive logic is this: IS THIS ARGUMENT VALID?
To answer this question we can try several strategies (including):
a)Counter-example (proof of invalidity)b)Formal Analysis
Counter-Example Test for Validity
1) Start with a given argument2) Determine its form
(Important to do correctly – best to isolate conclusion first)
3) Formulate another argument:a) With the same formb) with true premisesc) with a false conclusion.
An example counter-example…
1. If Lincoln was shot, then Lincoln is dead.
2. Lincoln is dead.3. Therefore, Lincoln was
shot.
The FORM IS:1. If Lincoln was shot,
then Lincoln is dead.2. Lincoln is dead.3. Therefore, Lincoln was
shot.
1. IF --P-- , THEN --Q--.
2. --Q--
3.Therefore -- P--
NEXT: We go from FORM back to ARGUMENT…
1. IF --P-- , THEN --Q--.
2. --Q--3. Therefore -- P--
1. IF Ed passes Phil 101, then Ed has perfect attendance.
2. Ed has perfect attendance.
3. Therefore, Ed Passes Phil 101
NO WAY!
Ed’s Perfect Attendance does NOT make it necessary that Ed pass PHIL 101.
SO: Even if it is true that 1. IF Ed passes Phil 101, then Ed has perfect
attendance.
2. ..AND that..Ed has perfect attendance.
IT DOES NOT FOLLOW THAT ED MUST PASS PHIL 101!
It is possible to have perfect attendance and not pass
•It is also possible to pass and have imperfect attendance
This shows that the original LINCOLN argument is INVALID.
This is ED…
Another Example?1. All fruit have seeds2. All plants have seeds3. Therefore, all fruit are plants
Form:All F are SAll P are STherefore All F are P
Another example….cont.Form:All F are SAll P are STherefore All F are P
1.All Balls (F) are round (S).
2.All Planets (P) are round (S).
3. Therefore, All Balls (F)are (P)lanets.
Formal Evaluation?
The counter-example test for validity has limits.• Counter-Examples should be obvious.• Our ability to construct an Counter-Example is
limited by our concepts and imagination.• Every invalid argument has a possible counter-
example, but no human may be able to find it.