Problem 8

Question 1

Syllogism

Answer 1

Refers to a deductive argument consisting of 2 premises + one conclusion

–> can be translated into standard form

Question 2

Categorical syllogism

Answer 2

Consists of 3 categorial propositions + 3 different terms each of which appear twice in distinct propositions

a) Major term
b) Minor term
c) middle term

ex. : All soldiers are patriots.
- -> Majore premise

No traitors are patriots.
–> Minor premise

Therefore, no traitors are soldiers.
–> conclusion

Question 3

Major term

Answer 3

Refers to the predicate of the conclusion

ex.: soldiers

Question 4

Minor term

Answer 4

Refers to the subject of the conclusion

ex.: traitors

Question 5

Middle term

Answer 5

Provides the middle ground between the 2 premises

–> occurs in each premise, but not in conclusion

ex.: patriots

Question 6

Major premise

Answer 6

Contains the major term

Question 7

Minor premise

Answer 7

Contains the minor term

Question 8

Standard-form categorical syllogism meets 4 conditions.

Name them.

Answer 8

1. All 3 statements are standard form categorical propositions
2. The 2 occurrences of each term are identical
3. Each term is used in the same sense throughout the argument
4. The major premise is listed first, minor second, conclusion last

Question 9

Categorical syllogism

Answer 9

Refers to a deductive argument consisting of 3 categorical propositions that can be translated into standard form

–> after that validity may be determined through inspection of the form

Question 10

Mood

Answer 10

Consists of the letter names of the propositions that make it up

ex.: Major premise =A, Conclusion = E, minor = O

–> AOE

Question 11

Figure

Answer 11

Is determined by the location of the 2 occurrences of the middle term in the premises

–> 4 arrangements are possible

Question 12

When do we use the aristotelian standpoint in syllogism ?

Answer 12

If the syllogism doesn’t appear in the list of unconditionally valid forms

–> then see if it appears as a conditionally valid form

Question 13

Which 6 Factors does one ought to be cautious about when constructing a Venn diagram for syllogisms, adopting the Boolean standpoint ?

Answer 13

1. Marks are only made for premises
2. UPs are entered first
3. Should concentrate on the circles corresponding to the 2 terms in the statement
4. Shade all of the area in question !
5. If one part has already been shaded the X goes in the other unshaded part
6. If no part has been shaded the X goes on the line separating the 2 parts
7. An X can never be placed on the intersection of 2 lines

Question 14

If a syllogism according to the Boolean standpoint is invalid, one proceeds to test it by adopting the Aristotelian standpoint.

How do we test whether a syllogism is valid with the aid of a Venn diagram, when adopting the Aristotelian standpoint ?

Answer 14

Look to see if there is a Venn circle that is completely shaded except for one area

–> if there is enter a circled X in that area + retest the form, if not invalid

THUS: Syllogism is valid if the X represents sth that exists

Question 15

How are the different statement types (A,E,I,O) distributed ?

Answer 15

A = Subject

E = Subject + Predicate

I = none

O = Predicate

Question 16

Name the 5 rules, which when violated result in the invalidity of the syllogism.

Answer 16

1. Middle term must be distributed at least once
2. If a term is distributed in the conclusion, it must be distributed in a premise
3. 2 negative premises are not allowed
4. Negative premise requires a negative conclusion + vice versa
5. If both premises are universal, the conclusion can’t be particular

BUT: if only #5 is violated it can still be valid if the subject actually exists

Question 17

All photographers are non-writers.
Some editors are writers.
Therefore, some non-photographers are not non-editors.

This example appears to be having six terms.
Can it still be tested on validity ?

Answer 17

Yes,

Seen as some of them are just complements of the opposite terms.

–> one just has to rewrite, thus reduce the sentences to bring them back into standard form

ex.:
Some W are not non-E.
All W are non-P.
Some non-P are not non-E.

Question 18

Name the 2 crucial rules on when we are not to use conversion or contraposition ?

Answer 18

1. Conversion must never be used on A + O statements

2. Contraposition must never be used on E + I statements

Question 19

Many arguments are initially not in standard-form categorical syllogisms.

What can be done, so the argument can be tested by means of a Venn diagram or the rule for syllogisms ?

Answer 19

1. Inserting quantifiers
2. Modifying S+P
3. Introducing copulas

Question 20

Enthymeme

Answer 20

Refers to an argument that is expressible as a categorical syllogism

BUT: missing a premise or conclusion

ex.: The corporate income tax should be abolished; it encourages waste + high prices

–> misses premise: whatever encourages waste + high prices should be abolished

Question 21

Sorite

Answer 21

Refers to a chain of categorial syllogisms in which the intermediate conclusions have been left out

ex.: All bloodhounds are dogs.
All dogs are mammals.
No fish are mammals.
Therefore, no fish are bloodhounds.

–> missing: All bloodhounds are mammals

Question 22

How do you test the validity of sorites ?

Answer 22

1. Find premise that contains the P of the conclusion, then placing it first
2. Find the premise with the other term of the first premise, then place it second
   - -> continue like this
3. Draw intermediate conclusion, w/ the help of Venn diagrams

Question 23

You can test the validity of Sorites by rearranging them, then using a Venn diagram.

There is also a second, more easy way of testing it.

How so ?

Answer 23

Applying 5 rules

1. Each middle term must be distributed at least once
2. Terms distributed in conclusion must be distributed in premise
3. No 2 negative premises allowed
4. Negative conclusion requires negative premise and vice versa
5. If all premises are universal, conclusion can’t be particular

Question 24

How do you draw Venn diagrams of sorites ?

Answer 24

Find the intermediate conclusions, then draw Venn diagrams of these intermediate conclusions

–> intermediate conclusions are drawn from first 2 premises, then IC + 3. premise, then IC + 4. .. etc.