Problem 8 Flashcards
Syllogism
Refers to a deductive argument consisting of 2 premises + one conclusion
–> can be translated into standard form
Categorical syllogism
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
Major term
Refers to the predicate of the conclusion
ex.: soldiers
Minor term
Refers to the subject of the conclusion
ex.: traitors
Middle term
Provides the middle ground between the 2 premises
–> occurs in each premise, but not in conclusion
ex.: patriots
Major premise
Contains the major term
Minor premise
Contains the minor term
Standard-form categorical syllogism meets 4 conditions.
Name them.
- All 3 statements are standard form categorical propositions
- The 2 occurrences of each term are identical
- Each term is used in the same sense throughout the argument
- The major premise is listed first, minor second, conclusion last
Categorical syllogism
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
Mood
Consists of the letter names of the propositions that make it up
ex.: Major premise =A, Conclusion = E, minor = O
–> AOE
Figure
Is determined by the location of the 2 occurrences of the middle term in the premises
–> 4 arrangements are possible
When do we use the aristotelian standpoint in syllogism ?
If the syllogism doesn’t appear in the list of unconditionally valid forms
–> then see if it appears as a conditionally valid form
Which 6 Factors does one ought to be cautious about when constructing a Venn diagram for syllogisms, adopting the Boolean standpoint ?
- Marks are only made for premises
- UPs are entered first
- Should concentrate on the circles corresponding to the 2 terms in the statement
- Shade all of the area in question !
- If one part has already been shaded the X goes in the other unshaded part
- If no part has been shaded the X goes on the line separating the 2 parts
- An X can never be placed on the intersection of 2 lines
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 ?
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
How are the different statement types (A,E,I,O) distributed ?
A = Subject
E = Subject + Predicate
I = none
O = Predicate
Name the 5 rules, which when violated result in the invalidity of the syllogism.
- Middle term must be distributed at least once
- If a term is distributed in the conclusion, it must be distributed in a premise
- 2 negative premises are not allowed
- Negative premise requires a negative conclusion + vice versa
- 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
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 ?
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.
Name the 2 crucial rules on when we are not to use conversion or contraposition ?
- Conversion must never be used on A + O statements
2. Contraposition must never be used on E + I statements
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 ?
- Inserting quantifiers
- Modifying S+P
- Introducing copulas
Enthymeme
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
Sorite
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
How do you test the validity of sorites ?
- Find premise that contains the P of the conclusion, then placing it first
- Find the premise with the other term of the first premise, then place it second
- -> continue like this - Draw intermediate conclusion, w/ the help of Venn diagrams
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 ?
Applying 5 rules
- Each middle term must be distributed at least once
- Terms distributed in conclusion must be distributed in premise
- No 2 negative premises allowed
- Negative conclusion requires negative premise and vice versa
- If all premises are universal, conclusion can’t be particular
How do you draw Venn diagrams of sorites ?
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.
