# Hum 200 w7 ch6 syllog

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## Hum 200 w7 ch6 syllogPresentation Transcript

• Logic
HUM 200
Categorical Syllogisms
1
• Objectives
2
When you complete this lesson, you will be able to:
Describe a standard-form categorical syllogism
Recognize the terms of the syllogism
Identify the mood and figure of a syllogism
Use the Venn diagram technique for testing syllogisms
List and describe the syllogistic rules and syllogistic fallacies
List the fifteen valid forms of the categorical syllogism
• Standard-Form Categorical Syllogisms
3
Syllogism
Any deductive argument in which a conclusion is inferred from two premises
Categorical syllogism
Deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions
• Standard-Form Categorical Syllogisms, continued
4
Example
No heroes are cowards.
Some soldiers are cowards.
Therefore some soldiers are not heroes.
Standard-form categorical syllogism
Premises and conclusion are all standard-form categorical propositions
Propositions are arranged in a specific standard order
• Terms of the Syllogism
5
To identify the terms by name, look at the conclusion
“Some soldiers are not heroes.”
Major term
Term that occurs as the predicate (heroes)
Minor term
Term that occurs as the subject (soldiers)
Middle term
Never appears in the conclusion (cowards)
• Terms of the Syllogism, continued
6
Major premise
Contains the major term (heroes)
“No heroes are cowards”
Minor premise
Contains the minor term (soldiers)
“Some soldiers are cowards”
Order of standard form
The major premise is stated first
The minor premise is stated second
The conclusion is stated last
• Mood of the Syllogism
7
Determined by the types of categorical propositions contained in the argument
No heroes are cowards (E proposition)
Some soldiers are cowards (I proposition)
Some soldiers are not heroes (O proposition)
Mood is EIO
64 possible moods
• The Figure of the Syllogism
8
Determined by the position of the middle term
Types
First figure
Middle term is the subject term of the major premise and the predicate term of the minor premise
Second figure
Middle term is the predicate term of both premises
Third figure
Middle term is the subject of both premises
Fourth figure
Middle term is the predicate term of the major premise and the subject of the minor premise
• The Figure of the Syllogism, continued
9
M – P
S – M
∴ S – P
P – M
S – M
∴ S – P
M – P
M – S
∴ S – P
P – M
M – S
∴ S – P
First Figure
Second Figure
Third Figure
Fourth Figure
• The Figure of the Syllogism, continued
10
Example
No heroes are cowards.
Some soldiers are cowards.
Therefore some soldiers are not heroes.
Middle term (cowards) appears as predicate in both premises (second figure)
The syllogism is EIO-2
• The Formal Nature of Syllogistic Argument
11
A valid syllogism is valid by virtue of its form alone
AAA-1 syllogisms are always valid
All M is P.
All S is M.
Therefore all S is P.
Valid regardless of subject matter
All Greeks are humans.
All Athenians are Greeks.
Therefore all Athenians are humans.
• Exercises
12
No nuclear-powered submarines are commercial vessels, so no warships are commercial
vessels, since all nuclear-powered submarines are warships.
Solution
Step 1. The conclusion is “No warships are commercial vessels”.
Step 2. “Commercial vessels” is the predicate term of this conclusion, and is therefore the
major terms of the syllogism.
Step 3. The major premise, the premise that contains this term, is “No nuclear-powered
submarines are commercial vessels”.
Step 4. The remaining premise, “All nuclear-powered submarines are warships”, is indeed
the major premise, since it does contain the subject term of the conclusion, “warships”.
Step 5. In standard form this syllogism is written thus:
No nuclear-powered submarines are commercial vessels.
All nuclear-powered submarines are warships.
Therefore no warships are commercial vessels.
Step 6. The three propositions in this syllogism are, in order, E, A and E. The middle term
“nuclear-powered submarines,” is the subject term of both premises, so the syllogism
is in the third figure. The mood and figure of the syllogism therefore are
EAE-3.
13
Some objects of worship are fir trees.
All fir trees are evergreens.
Therefore some evergreens are objects of worship. IAI-4.
14
Some artificial satellites are not American inventions.
All artificial satellites are important scientific achievements.
Therefore some important scientific achievements are not American inventions.
OAO-3.
15
#4
All certified public accounts are people of good business sense.
No television stars are certified public accountants.
Therefore no television stars are people of good business sense.
AEE-1.
16
#6
No delicate mechanisms are suitable toys for children.
All CD players are delicate mechanisms.
Therefore no CD players are suitable toys for children.
EAE-1.
17
#7
Some juvenile delinquents are products of broken homes.
All juvenile delinquents are maladjusted individuals.
Therefore some maladjusted individuals are products of broken homes.
IAI-3.
• 18
P
S
SPM
SPM
SPM
SPM
SPM
SPM
SPM
SPM
M
Venn Diagram Technique for Testing Syllogisms
If S stands for Swede, P for peasant, and M for musician, then
SPM represents all Swedes who are not peasants or musicians
SPM represents all Swedish peasants who are not musicians, etc.
• 19
P
S
M
P
S
M
Venn Diagram Technique for Testing Syllogisms, continued
“All M is P”
Conclusion“All S is P” confirmed
• Venn Diagram Technique for Testing Syllogisms, continued
20
Invalid argument
All dogs are mammals.
All cats are mammals.
Therefore all cats are dogs.
Dogs
Cats
Cats that are not dogs
Dogs that are not cats
Mammals
• Exercises pg. 232-233
21
#1
All business executives are active opponents of increased corporation taxes, for all active opponents of increased corporation taxes are members of the chamber of commerce, and all members of the chamber of commerce are business executives.
One possible refuting analogy is this:
All bipeds are astronauts,
All astronauts are humans
Therefore all humans are bipeds.
• Group Exercises pg. 232-233
22
Do numbers 3, 4, 5 and 7
• 23
Diagram the universal premise first if the other premise is particular
All artists are egotists.
Some artists are paupers.
Therefore some paupers are egotists.
Egotists
Paupers
x
Artists
Venn Diagram Technique for Testing Syllogisms, continued
• Venn Diagram Technique for Testing Syllogisms, continued
24
Example
All great scientists are college graduates.
Some professional athletes are college graduates.
Therefore some professional athletes are great scientists.
Greatscientists
Professionalathletes
x
• Venn Diagram Technique for Testing Syllogisms, continued
25
Label the circles of a three-circle Venn diagram with the syllogism’s three terms
Diagram both premises, starting with the universal premise
Inspect the diagram to see whether the diagram of the premises contains a diagram of the conclusion
• Group Exercises
26
Do 2,3,4 and 6
• Group Exercises #2
27
• Group Exercises #3
28
• Group Exercises #4
29
• Group Exercises #6
30
• Syllogistic Rules and Syllogistic Fallacies
31
Rule 1. Avoid four terms
Syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument
Fallacy of four terms
Power tends to corrupt
Knowledge is power
Knowledge tends to corrupt
Justification: This syllogism appears to have only three terms, but there are really four since one of them, the middle term “power” is used in different senses in the two premises. To reveal the argument’s invalidity we need only note that the word “power” in the first premise means “ the possession of control or command over people,” whereas the word “power” in the second premise means “the ability to control things.
• Syllogistic Rules and Syllogistic Fallacies, continued
32
Rule 2. Distribute the middle term in at least one premise
If the middle term is not distributed in at least one premise, the connection required by the conclusion cannot be made
Fallacy of the undistributed middle
All sharks are fish
All salmon are fish
All salmon are sharks
Justification: The middle term is what connects the major and the minor term. If the middle term is never distributed, then the major and minor terms might be related to different parts of the M class, thus giving no common ground to relate S and P.
• Syllogistic Rules and Syllogistic Fallacies, continued
33
Rule 3. Any term distributed in the conclusion must be distributed in the premises
When the conclusion distributes a term that was undistributed in the premises, it says more about that term than the premises did
Fallacy of illicit process
All tigers are mammals
All mammals are animals
All animals are tigers
Worth Diagramming
• Syllogistic Rules and Syllogistic Fallacies, continued
34
Rule 4. Avoid two negative premises
Two premises asserting exclusion cannot provide the linkage that the conclusion asserts
Fallacy of exclusive premises
No fish are mammals
Some dogs are not fish
Some dogs are not mammals
If the premises are both negative, then the relationship between S and P is denied. The conclusion cannot, therefore, say anything in a positive fashion. That information goes beyond what is contained in the premises.
• Syllogistic Rules and Syllogistic Fallacies, continued
35
Rule 5. If either premise is negative, the conclusion must be negative
Class inclusion can only be stated by affirmative propositions
Fallacy of drawing an affirmative conclusion from a negative premise
All crows are birds
Some wolves are not crows
Some wolves are birds
• Syllogistic Rules and Syllogistic Fallacies, continued
36
Rule 6. From two universal premises no particular conclusion may be drawn
Universal propositions have no existential import
Particular propositions have existential import
Cannot draw a conclusion with existential import from premises that do not have existential import
Existential fallacy
All mammals are animals
All tigers are mammals
Some tigers are animals
• Exposition of the 15 Valid Forms of the Categorical Syllogism
37
Mood (64 possible)
Figure (4 possible)
Logical form ( 64 x 4 = 256)
Out of 256 forms, only 15 are valid
Valid forms have names that contain the vowels of the mood
EAE-1 is Celarent
EAE-2 is Cesare
• The 15 Valid Forms of the Categorical Syllogism
38
Valid form in the First Figure
AAA-1Barbara
EAE-1Celarent
AII-1Darii
EIO-1Ferio
• The 15 Valid Forms of the Categorical Syllogism, continued
39
Valid forms in the Second Figure
AEE-2Camestres
EAE-2Cesare
AOO-2Baroko
EIO-2Festino
• The 15 Valid Forms of the Categorical Syllogism, continued
40
Valid forms in the Third Figure
AII-3Datisi
IAI-3Disamis
EIO-3Ferison
OAO-3Bokardo
• The 15 Valid Forms of the Categorical Syllogism, continued
41
Valid forms in the Fourth Figure
AEE-4Camenes
IAI-4Dimaris
EIO-4Fresison
• Exercises pg 253
42
• Exercises pg 253
43
• Summary
44
Standard-form categorical syllogism
Syllogism terms
Mood and figure
Venn diagram technique for testing syllogisms
Syllogistic rules and syllogistic fallacies
Valid forms of the categorical syllogism