logic chapter categorical Syllogism

1. Categorical Syllogism
Refrence: Chapter# 6
(Copi, Cohen, Introduction to Logic, 14 th Edition)

2. 1 Standard-Form Categorical Syllogisms
2 The Formal Nature of Syllogistic Argument
3 Venn Diagram Technique for Testing
Syllogisms
4 Syllogistic Rules and Syllogistic Fallacies
5 Exposition of the Fifteen Valid Forms of the
Categorical Syllogism

3. •Syllogism:
Any deductive argument in which a conclusion is inferred from two
premises.
•Categorical Syllogism:
A deductive argument consisting of three categorical propositions that
together contain exactly three terms, each of which occurs in exactly
two of the constituent propositions.

4. Standard Form
It will be convenient to have an example to use as we discuss the parts and
features of the syllogism. Here is a valid standard-form categorical syllogism
that we shall use as an illustration:
• No heroes are cowards.
• Some soldiers are cowards.
• Therefore some soldiers are not heroes.
To analyze such an argument accurately, it needs to be in standard form. A
categoric syllogism is said to be in standard form (as the above example is)
when two things are true of it:
(1) its premises and its conclusion are all standard-formcategorical
propositions (A, E, I, or O);
(2) those propositions are arranged in a specified standard order.

12. Venn Diagrams
• Label the 3 circles of a Venn Diagram with the syllogism’s 3 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

13. Rules and Fallacies
• Rule 1 . Avoid using 4 terms (even unintentionally)
• Power tends to corrupt
• Knowledge is power
• Knowledge tends to corrupt
• Although this seems to have 3 terms, it actually has 4 since the word power is
being used in 2 different ways. In the first sense it means control over things
or people; in the second it means the ability to control things.

14. Rules and Fallacies
• Rule 2. Distribute the middle term in at least one premise.
• If the middle term is not distributed into 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
• Therefore, all sharks are salmon
• The middle term is what connects the major and minor terms. If the middle term is
not distributed, then the major and minor terms might be related to different parts
of the M class, thus giving no common ground between the S and P.

15. Rules and Fallacies
• 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 the
term than the premise did.
• Fallacy of illicit process
• All tigers are mammals
• All mammals are animals
• Therefore, all animals are tigers

16. Rules and Fallacies
• Rule 4. Avoid two negative premises.
• 2 premises asserting exclusion cannot provide the linkage that the
conclusion asserts.
• Fallacy of the 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 P and S is
denied. The conclusion cannot, therefore, say anything in a positive manner.
That information goes beyond what is contained in the premises.

17. Rules and Fallacies
• 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

18. Rules and Fallacies
• 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

19. Rules and Fallacies
Rule Fallacy Avoided
Rule 1. Avoid four terms. the fallacy of four terms
Rule 2. Distribute the middle in at least
one premise.
the fallacy of the undistributed middle
Rule 3. Any term distributed in the
conclusion must be distributed in the
premises
the fallacy of illicit process
illicit process of the major term (illicit
major)
illicit process of the minor term (illicit
minor)
Rule 4. Avoid two negative premises. the fallacy of exclusive premisses
Rule 5. If either premise is negative, the
conclusion must be negative.
the fallacy of drawing an affiermative
conclusion from a negative premiss
Rule 6. From two universal premises no
particular conclusion may be drawn.
the existential fallacy

20. 15 Valid Forms
• There are 64 possible moods
• There are 4 possible figures
• There are 64x4 = 256 possible logical forms
• Only 15 are valid
• It is possible, through a process of elimination, to prove that only
these 15 forms can avoid violating all six basic rules.

21. The 15 Valid Forms
First Figure Second Figure Third Figure Fourth Figure
M-P
S-M
P-M
S-M
M-P
M-S
P-M
M-S
1. AAA-1
Barbara
5. AEE-2
Camestres
9. AII – 3
Datisi
13. AEE-4
Camenes
2. EAE -1
Celarent
6. EAE -2
Cesare
10. IAI – 3
Dismasis
14. IAI-4
Dimaris
3. AII-1
Darii
7. AOO – 2
Baroko
11. EIO-3
Ferison
15. EIO – 4
Fresison
4. EIO -1
Ferio
8. EIO -2
Festino
12. OAO -3
Bokardo

22. Questions for Discussion
• 1. “All good stereos are made in Japan, but no good stereos are inexpensive;
therefore, no Japanese stereos are inexpensive.” Rewrite this syllogism in
standard form, and name its mood and figure.
• 2. Come up with a random list of four possible moods; then, pick one of the four
figures and use it to produce four different syllogisms. Are any of the syllogisms
valid?
• 3. What is the method of logical analogies? Apply it to this argument to see if it is
valid: “No logic professors are successful politicians, because no conceited people
are successful politicians, and some logic professors are conceited people.”
• 4. Write out AOO-3 using S and P as the subject and predicate terms and M as the
middle term. (You may need to refer to the chart of the four syllogistic figures.)
• 5. Using the syllogistic form in question #4 (or any other form, if you like)
construct a Venn diagram to test it for validity.