Critical Reasoning Flashcards
What are the components of an argument?
premise, assumption and conclusion
what is a premise?
what is an assumption?
a proposition, statement or fact from which a conclusion is made
the implicit statement, which must be true so that the conclusion can be true
1) necessary assumption
2) what phrases ‘necessary assumption’ contain?
1) unstated facts or opinions that MUST be assumed if the reasoning is to succeed logically.
2) an assumption that the argument (reasoning) requires
an assumption on which the argument depends (relies)
sufficient assumption
unstated facts or opinions that, if assumed, allow reasoning to succeed logically
How do you negate the conditional statement to find the assumption?
Don’t negate on the conditional part “if” - only negate on the latter part
i.e: If animals doesn’t have MRS, they don’t have self-awareness
Negation: If animals doesn’t have MRS, they have self-awareness
What are some “Cause and Effect” signal words?
Therefore, Thus, So, Consequently, Hence, For this reason, As a result, It follows that
What are some “Premise” signal words?
Because, Since, For, After all
Which of the following indicates a flaw in the reasoning above?
What type of CR question is this?
Assumption-based question
What is the word claim synonym for?
Conclusion
The statements above “best support” which of the following “assertions”?
What type of CR question is this?
Inference
To reduce traffic congestion, City X’s transportation bureau plans to encourage people who work downtown to sign a form pledging to carpool or use public transportation for the next year. Everyone who signs the form will get a coupon for a free meal at any downtown restaurant.
For the transportation bureau’s plan to succeed in reducing traffic congestion, which of the following must be true?
A) Everyone who signs the pledge form will fully abide by the pledge for the next year.
B) At least some people who receive the coupon for a free meal will sometimes carpool or use public transportation during the next year.
Notice the light language is “to reduce traffic congestion” instead of “to eliminate..”:
- Even if the reduction in traffic congestion is tiny (example – say 1% reduction, i.e., 100 to 99), the plan would succeed
Therefore, we only need to assume that some of the people who sign the pledge or receive the coupon as a result will sometimes carpool or use public transportation - sufficient condition
- we don’t need (A) - “everyone” statement- must be true so that the bureau’s plan can succeed
Best strategy to use for “some, at least, none, not all”
Of all the departments at City College, the Chemistry department has the highest percentage of classes with at least 20 enrolled students. However, the Biology department at City College has the highest percentage of classes with at least 30 enrolled students.
T or F: Not all of the Chem classes have either fewer than 20 or at least 30 students
Key Lesson: Rephrase the double negative: NOT ALL A’s are B = SOME are not B
- Apply to the answer choice: Some of Chem classes have not either fewer than 20 or at least 30 students, which is our premise:
-> The Chem department has the highest percentage of classes with at least 20 enrolled students.
What is the since __ actually asking you to do?
The growing popularity of computer-based activities was widely predicted to result in a corresponding decline in television viewing. Recent studies have found that, in the United States, people who own computers watch, on average, significantly less television than people who do not own computers. In itself, however, this finding does very little to show that computer use tends to reduce television viewing time, since _______.
1) An correct answer choice must help strengthen the author argument (this finding does little to show…). In other words, it weakens the evidence of recent studies, and thereby the causation
2) In this case, Correlation/Causation + Selection Bias fallacy can do such a job: those own computers in the studies just happen to watch less TV to begin with than who don’t own computers
What are the form for sufficient condition?
1) Usual Form: If/ When/ Whenever
2) Unusual form: Every, All, Any, Each
3) Rare (tricky) form: In order to, People Who
What are the forms for necessary condition?
1) Usual Form: Then, Only/ Only If/ Unless
2) Unusual Form: Must, Required
3) Rare (tricky) form: Except, Until, Without
Translate the fallacy of this argument: Every time it rains, the baseball field get wet. The baseball field is wet. It must have rained
Key Words: Every time it rains = sufficient condition for the field get wet (A occurs, B occurs). However, the inference is the Mistaken Reversal fallacy
- B occurs then A must have occurred (F)
Premise: A & B seem to appear together
C: Change A in order to change B
What typical fallacy is this? How do we weaken this type of argument?
- Change A in order to change B implies causation
- Point out that: change A but change B won’t happen because
1) other factors cause B ->
2) third factor cause both A & B
3) Correlation between A & B
T or F: An argument by generalization is weaker when its conclusion is more precise, and stronger when its conclusion is vaguer, given the same premises.
True
When the argument relates to groups surveys, samples, or particular population, what should you be wary of?
Representativeness (types of sample bias)
Ratio/Proportion/Percentage: Variables Changes in numerator/denominator
Technique: alternative way to translate Unless X, Y
How do you draw the implication from this sentence:
Unless interest rates drop significantly, housing prices should not increase during the next six months
X is necessary for NOT Y: The drop in interest rate is necessary for the increase in housing price.
- In other words, ONLY IF IR drop significantly, housing price should increase
Translate & find sufficient (S) and necessary (N) condition in each
1) All of the State Univerisity Professors lecture on Wednesdays
2) No electrician is an architect
3) Sally will not attend the banquet unless Jan also attends the banquet
4) The children go to the park when the sun is shining
5) Only the good die young
1) If you are state univeristy professors (S), you must have lectured on wednesday (N)
2) If you are an electrician (S), you can’t be an architect (N)
3) If Sally attend the banquet (S), Jan must have attended as well (N)
4) If the sun is shining (S), the children will go to the park (N)
5) If you are the good (S), you must die young (N)
Apply Conditional Statement Inference Technique
If Country X does not intervene militarily in Country Y, then the whole region will definitely fall under enemy influence.
It most logically follows from the statement above that, if Country X does intervene militarily in Country Y, then the whole region
(A) Will definitely fall under enemy influence
(B) Will probably fall under enemy influence
(C) Will probably not fall under enemy influence
(D) Will definitely not fall under enemy influence
(E) May or may not fall under enemy influence
Analysis: Doesn’t intervene is sufficient for the fall to occur
BUT we can’t infer that if the intervene happen, the fall won’t occur (Mistake Negation)
- Therefore, any answer choices with definite “will or will not” are incorrect answers
-> We can, however, draw with an implied degree of possibility for the effect (Choice E)
What are the general steps for converting conditional statements to contrapositive form?
1) Within the context, find necessary & sufficient condition
2) Put the negation of the necessary condition (N) in the first part while delegating the negation of sufficient condition (S) to 2nd part
i.e: (1) People who are drive fast are dangerous = If you drive fast (S), you must be dangerous (N)
- Contrapositive: If you are not dangerous, then you must not be a person who drives fast - Not “N” implies Not “S”
(2) John will go to the meeting (S) only if Paul goes to the meeting (N)
- Contrapositive: If Paul doesn’t go to the meeting, then John won’t go to the meeting - Not “N” implies Not “S”
What are the correct inference/implies of conditional statements?
“S” implies “N”
“NOT N” implies “NOT S”
I will pass the exam “if and only if” I study hard
1) What is the type of conditional statement?
2) How do you rewrite into the two implies statement?
1) Biconditional statement: include both conditions for one subject
2) If I study hard (sufficient condition), then I will pass the exam. And:
- Only if I study hard (neccessary condition), i will pass the exam