Transcript Philosophy 103 Linguistics 103 Introductory Logic

Philosophy 103
Linguistics 103
Yet, still, even further more,
expanded,
Introductory Logic:
Critical Thinking
Dr. Robert Barnard
Last Time:
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Definitions
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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
American
Peter is from Ohio
--- Therefore Peter is an American.
Modus Tollens Example
If P then Q
Q 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 Q
P 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 Q
If 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 P
b) 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 Reductio
1. 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 Q
Q 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 Q
P is false
Therefore Q is false
1. If Tom is not hungry then Tom ate lunch
2. Tom is Hungry
3. 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 Q
P is true
Therefore not-Q
John is Tim’s father or Sally is Tim’s
mother
John is Tim’s Father
Therefore Sally is not Tim’s mother
Illicit Hypothetical Syllogism
If P then not-Q
If Q then not-R
Therefore If P then not-R
1. If I like fish then I won’t eat beef
2. If I eat beef then I won’t eat cheese
3. 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 argument
2) Determine its form
(Important to do correctly – best to isolate
conclusion first)
3) Formulate another argument:
a) With the same form
b) with true premises
c) 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 seeds
2. All plants have seeds
3. Therefore, all fruit are plants
Form:
All F are S
All P are S
Therefore All F are P
Another example….cont.
Form:
All F are S
All P are S
Therefore 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 counterexample, but no human may be able to find it.