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Reasoning and Argumentation Cheat Sheet

A cheat sheet in English by salthom
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Quiz 2

1. The major premise of any catego­rical syllogism is the premise that
contains the predicate of the conclusion
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
3. A term is said to be _________ when reference is made to only a portion of the class of objects
Undist­ributed
4. Two propos­itions are ________ when they can both be true, but both cannot be false
Sub-co­ntrary
5. A statement about a relati­onship of either inclusion or exclusion, partial or total, between two groups of objects or events is called
Catego­rical
6. A(n) _____ propos­ition declares that the relati­onship between two classes is one of partial inclusion
I form
7. A(n) ____ propos­ition declares that the relati­onship between two classes is one of total exclusion
E Form
8. A(n) ____ propos­ition declares that the relati­onship between two classes is one of partial exclusion
O Form
9. The propos­itions in an argument that support the conclusion are called the _____
Premises
10. Whenever a conclusion is drawn from a single premise, without reference to evidence from any other source, we call this argument
Immediate inference
11. A term is said to be a _____ when reference is about the entire class of objects
Distri­buted
12. An unreliable inference or error in reasoning is called a ____
Fallacy
Multiple Choice

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

Quiz 2 - Convert if possible

1. All envious people are difficult to work with
Can't convert (it is an A form)
2. No exams are pleasant experi­ences
No pleasant experi­ences are exams

Quiz 2 - Obvert

1. No terrorists are patriotic Americans
All terrorists are non-pa­triotic Americans
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

Quiz 2 - True, False, Unknown

Assume the following propos­ition is TRUE All patriots are voters.
1. No patriots are non-voters
True
2. All non-voters are non-pa­triots
True
3. All voters are patriots
Unknown
4. Some patriots are not voters
False
5. Only voters are patriots (No non-voters are patriots)
True
6. Only patriots are voters (No non-pa­triots are voters)
Unknown
7. Some patriots are voters
True

Quiz 2 - Restate in standard catego­rical form

1. Nearly every student must be immunized
Some students are people who must be immunized
2. Only freshmen can enroll today.
No non-fr­eshmen are students allowed to enroll today

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

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
 
2. This building was certified prior to the fire because it was inspected and all certified buildings have been inspected Answer: IB
 
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

Square of Opposition

Square of Opposition

Quiz 2

1. In the O-form propos­ition the subject is undist­ributed
True
2. No valid argument can have a false conclusion if the premises are true
True
3. Conversion is a valid operation for all four types of catego­rical propos­itions
False
4. In a valid catego­rical syllogism, the middle term must be distri­buted twice
False
5. A valid catego­rical syllogism must have exactly three terms, each used exactly twice to refer the same class
True
6. In a valid catego­rical syllogism, every term distri­buted in the premises must be distri­buted in the conclusion
False
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
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
9. If a conversion is valid, no term in the converse can be distri­buted unless it was distri­buted in the original propos­ition
True
10. All sound deductive arguments have a true conclusion
True
11. Any catego­rical propos­ition is logically equivalent to its converse
False
12. A syllogism is a deductive argument with two premises and one conclusion
True
13. It is a flaw in the argume­nt's structure or form that causes the argument to be invalid
True
14. All four forms of standard catego­rical propos­itions may be simply converted
False
15. All valid arguments must have a true conclusion
False
16. No invalid argument can have a true conclusion
False
17. If there are two exclusive premises in a syllogism, then the conclusion must be affirm­ative
False*
18. The truth of the premises guarantee the validity of the argument
False
19. If the premises are true and the argument is valid then the conclusion must be true
True
20. All four standard forms of the catego­rical propos­ition have a logical equivalent
True
21. A sound deductive argument must be both valid and have true premises
True

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