Quiz 2
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1. The major premise of any categorical syllogism is the premise that contains the predicate of the conclusion
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2. The ________ is the term occurring in a syllogism that appears in both the oremesis of a categorical syllogism but not in the conclusion Middle term
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3. A term is said to be _________ when reference is made to only a portion of the class of objects Undistributed
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4. Two propositions are ________ when they can both be true, but both cannot be false Sub-contrary
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5. A statement about a relationship of either inclusion or exclusion, partial or total, between two groups of objects or events is called Categorical
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6. A(n) _____ proposition declares that the relationship between two classes is one of partial inclusion I form
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7. A(n) ____ proposition declares that the relationship between two classes is one of total exclusion E Form
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8. A(n) ____ proposition declares that the relationship between two classes is one of partial exclusion O Form
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9. The propositions in an argument that support the conclusion are called the _____ Premises
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10. Whenever a conclusion is drawn from a single premise, without reference to evidence from any other source, we call this argument Immediate inference
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11. A term is said to be a _____ when reference is about the entire class of objects Distributed
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12. An unreliable inference or error in reasoning is called a ____ Fallacy
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Homework
1. A few lazy students do not prepare for class. Steve prepares for class. We can conclude that Steve is not a lazy student
Answer:
Some lazy students are not class preparers O
All Steve (d) are class preparer (u) A
_____________________________
Steve is not a Lazy student --> No Steve (d) are class preparer (u)
Invalid:Illicit Distribution |
A. Fallacy of four terms
B. Undistributed middle term
C. Faulty exclusion
D. Illicit distribution
E. Syllogism
Rules
Step 1: Change the claim to either its contrary if universal or subcontrary if particular |
Step 2: Leave the subject alone |
Step 3. Compliment the predicate |
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Quiz 2 - Convert if possible
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1. All envious people are difficult to work with Can't convert (it is an A form)
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2. No exams are pleasant experiences No pleasant experiences are exams
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Quiz 2 - Obvert
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1. No terrorists are patriotic Americans All terrorists are non-patriotic Americans
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2. Any term distributed in the conclusion of a categorical syllogism must be distributed in the premises No terms distributed in the conclusion of a categorical syllogism are terms that must be non-distributed in the premises
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Quiz 2 - True, False, Unknown
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Assume the following proposition is TRUE All patriots are voters. |
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1. No patriots are non-voters True
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2. All non-voters are non-patriots True
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3. All voters are patriots Unknown
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4. Some patriots are not voters False
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5. Only voters are patriots (No non-voters are patriots) True
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6. Only patriots are voters (No non-patriots are voters) Unknown
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7. Some patriots are voters True
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Quiz 2 - Restate in standard categorical form
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1. Nearly every student must be immunized Some students are people who must be immunized
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2. Only freshmen can enroll today. No non-freshmen are students allowed to enroll today
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Definitions
A |
Distributes the subject |
E |
Distributes both |
I |
Distributes neither |
O |
Distributes the predicate |
Middle Term |
occurs in the premises, distributed once, cannot be in the conclusion |
Major Premises |
the predicate of the conclusion |
Contradiction |
opposite truth value - if one's true, the other is false |
Contrary |
Both can't be true, however both can be false |
Sub-Contrary |
Both can be true at the same time, however both can't be false at the same time |
Subimplication |
The truth of the universal proposition guarantees the truth of the particular |
Superimplication |
The falsity of the particular claim guarantees the falsity of the universal |
Syllogism |
Deductive argument in which a conclusion is drawn from 2 pieces of evidence (premises) |
Arguments with missing propositions are called Enthymemes
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Quiz 2 - Consider the argument
Since all politicians are careful planners and it is also a fact that nearly all bank robbers are also careful planners. It only stands to reason that some bank robbers are politicians |
Answer: The conclusion of the argument is a - Some bank robbers are politicians |
Determine if the arguments are valid or invalid. Which reason describes the reason the syllogism is invalid. A: Fallacy of four terms B: Undistributed middle term C: Faulty exclusion D: Illicit distribution E: Syllogism satisfies all four terms |
1. Every politician provides his services and experiences freely. No criminal gives freely his experience and services. Therefore no politician is a criminal. Answer: VE |
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2. This building was certified prior to the fire because it was inspected and all certified buildings have been inspected Answer: IB |
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3. The categorical proposition Only truly dedicated men enter the priesthood. Is translated to Answer: No non-truly dedicated men are men who enter the priesthood |
Notes
(A Form): All (___) [distributed] are (___) [undistributed]: inclusive quality; universal quantity |
(I Form): Some (___) [undistributed] are (___) [undistributed]: inclusive; partical |
(E Form): No (___) [distributed] are (___) [distributed]: exclusive; universal |
(O Form): Some (___) [undistributed] are not (___) [distributed]: exclusive; partial |
Inclusive: A, I |
Exclusive: E, O |
Universal: A, E |
Partial: I, O |
Only is universal and exclusive = E Form |
A Few = I form |
Few = O form |
If there are no non's you can leave it alone |
Only use conversion on E and I forms |
A and I = Affirmative quality |
E and O = Negative quality |
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Quiz 2
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1. In the O-form proposition the subject is undistributed True
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2. No valid argument can have a false conclusion if the premises are true True
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3. Conversion is a valid operation for all four types of categorical propositions False
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4. In a valid categorical syllogism, the middle term must be distributed twice False
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5. A valid categorical syllogism must have exactly three terms, each used exactly twice to refer the same class True
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6. In a valid categorical syllogism, every term distributed in the premises must be distributed in the conclusion False
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7. When two categorical propositions differ in only their degree of generality, the truth of the more general proposition logically implies the less general True
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8. A strong inductive argument is an argument in which the premises of the argument establish a relatively high degree of probability that the conclusion is true True
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9. If a conversion is valid, no term in the converse can be distributed unless it was distributed in the original proposition True
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10. All sound deductive arguments have a true conclusion True
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11. Any categorical proposition is logically equivalent to its converse False
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12. A syllogism is a deductive argument with two premises and one conclusion True
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13. It is a flaw in the argument's structure or form that causes the argument to be invalid True
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14. All four forms of standard categorical propositions may be simply converted False
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15. All valid arguments must have a true conclusion False
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16. No invalid argument can have a true conclusion False
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17. If there are two exclusive premises in a syllogism, then the conclusion must be affirmative False*
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18. The truth of the premises guarantee the validity of the argument False
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19. If the premises are true and the argument is valid then the conclusion must be true True
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20. All four standard forms of the categorical proposition have a logical equivalent True
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21. A sound deductive argument must be both valid and have true premises True
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