CR notes Flashcards
Common argument types - what is the following an example of?
In October, a local news station completed a redesign of its website. In November, the number of articles read on the website increased by 50%. Thus, the redesigned website clearly attracted more users or encouraged users to read more articles per visit.
> Anticipate WHAT IFS
> How would you strengthen this argument? Weaken this argument?
> What are examples of flawed reasoning?
Causation
Conclusion: Last sentence –> The redesigned website is the CAUSE for the 50% increase in readership.
Premises:
- Oct - redesign complete
- Nov - readership increase
Anticipate WHAT IF Q’s (do you believe the author’s conclusion?)
- what if there are OTHER CAUSES for the increase?
Test by:
> removing cause and observing whether the effect is the same
> or observing effects in similar situations
Strengthen by:
> Providing more evidence in support of causation (when cause occurs, the effect occurs; when cause does not occur, the effect also does not occur)
> Providing evidence that REVERSE CAUSATION is not true
> Eliminating any alternate causes for the effect
> Showing that the data used are accurate
Weaken by:
> Providing evidence of OTHER CAUSES (what ifs) or REVERSE causation or CHANCE/CORRELATION
> Showing that even when the cause occurs, the effect does NOT occur (counterexample)
> Show that even when the effect occurs, the cause did not occur (counterexample)
Flawed Reasoning:
> One event occurs before another => incorrectly assume that the first event causes the second event
> Simultaneous occurrence of two events => incorrect assume one event caused the other (ignores chance, correlation, and third event)
> Incorrectly assume only one cause and ignores other possibilities
Common argument types - what is the following an example of?
Metropolis has experienced an increase in the amount of trash in its city parks. In order to reduce the amount of litter in the parks, Metropolis plans to double the number of trash cans in each city park.
> What is the conclusion?
Anticipate WHAT IFS
Plan
Conclusion: “In order to reduce the amount of litter in the parks” –> GOAL of a plan
(Amount of litter in the park will reduce).
Background: Statement of Fact
- Increase in the amount of trash in city parks
Premise: (Why there will be a reduction in the amount of litter in the parks?)
- Double the number of trash cans in each city park.
Anticipate WHAT IF Q’s (do you believe the author’s conclusion?)
- What if the plan doesn’t work (e.g., missed steps, unexpected hindrances?)
Common argument types - what is the following an example of?
Rainfall totals were higher this year than they were last year in Eastown. Since wheat farmers rely on rain to irrigate their fields, yields of wheat per acre in Eastown will be higher than last year’s yields.
> What is the conclusion?
Anticipate WHAT IFS
Prediction (future tense conclusion)
Conclusion: Yields of wheat per acre will be higher than last year’s yields in Eastown.
Premise:
- Rainfall totals were higher this year than they were last year in Eastown
- Wheat farmers rely on rain to irrigate their fields
Anticipate WHAT IF Q’s (do you believe the author’s conclusion?)
- What if the author missed other factors/circumstances that might work against the prediction? (e.g., temperature)
What type of question is the following:
“Which of the following indicates a vulnerability of the argument above?”
What is the strategy for solving these types of questions?
Find the flaw **(02/23 unclear)
- “indicates a vulnerability” IN the argument (aka a flaw in logical organization)
- Question stem does not contain “if true” (vs weaken questions)
- Answer choices are more abstract (e.g., author “failed to establish, does not specify or identify)
Strategy for solving:
> Goal is to find the ERROR of REASONING in the argument
e.g., what ASSUMPTION is the author making that is FLAWED THINKING
> Think about the STRUCTURE of the argument and where the error lies
> See list of common errors of reasoning
Common trap answers:
- No tie to conclusion
- Reverse logic (strengthens argument)
- Irrelevant distinction
- Not quite right (half wrong = all wrong)
- Opposite Answer
What type of question is the following:
“Which of the following, if true, most strongly suggests that the plan will fail to achieve its desired outcome?”
What is the strategy for solving these types of questions?
Weaken the argument (make the conclusion less likely to be true)
> Most common way to weaken: Premises could still be true, however, the conclusion does not necessarily follow the premises! (b/c of author’s failure to account for some element or possibility)
OR could attack premise
Correct answers DO NOT have to destroy the argument
Strategy for solving:
> Which of the following answer choices make the CONCLUSION LESS LIKELY to be true
Look for answer choices that:
> Prove ALTERNATE causation (for cause and effect arguments)
> Prove reverse causation (for cause and effect arguments)
> Provide evidence of ANOTHER reason (for conclusions stating something “must” be the only way)
> Introduce new circumstances NOT CONSIDERED by the author (author incorrectly assumes other elements do not exist)
> if you remove the action, the effect is not observed
> Attack questionable ASSUMPTIONS made by the author
> Identify DISSIMILARITY between an analogy
Things to keep in mind:
- Question stem could contain “flaw”
- Answer choice represent NEW PIECES of info
WRONG answer traps:
> Out of Scope (irrelevant)
> Opposite Answer
> Not Quite Right
What type of question is the following:
“Which of the following conclusions is most strongly supported by the statements given above?”
What is the strategy for solving these types of questions?
Inference
Strategy for solving:
> What answer MUST BE TRUE based on the premises (eliminate likely or NOT NECESSARILY true - “maybes” - or NEVER TRUE answers)
Things to keep in mind:
- Inference arguments lack conclusions
- Therefore, conclusions are IN the answer choices (can’t be Strengthen the Argument - support the conclusion)
Look for answer choices:
> either a PARAPHRASE of premise or
> a COMBO of 2 or more premises (logical consequence)
** NO INFO outside the sphere of the stimulus is allowed in the correct answer choice (unlike strengthen/weaken/evaluate)
What type of question is the following:
“Which of the following, if true, would provide the strongest justification for the mayor’s conclusion?”
What is the strategy for solving these types of questions?
Strengthen the Argument
Strategy for solving:
> Which answer presents the strongest support/rationale for the CONCLUSION => strengthen the conclusion = make the conclusion more likely to be true
Strengthen by:
> More evidence in support of the argument (e.g., additional benefits, suggests that the PLAN is practical)
> Eliminate a WEAKENERS (e.g., capacity constraints, additional costs, OBJECTIONS to the plan) / closes logical gaps **
> Strengthens the analogy or survey / establishes their soundness
> Strengthens causation
Things to keep in mind:
> the correct answer could either strengthen the argument just a little or a lot
Incorrect Answer Traps:
- Opposite Answer
- No Quite Right
- OOS
What type of question is the following:
“Which of the following is an assumption on which the school board’s argument depends?”
“Which of the following is REQUIRED for the mayor’s plan to succeed?”
What is the strategy for solving these types of questions?
Find the Assumption (FA)
*assumptions are UNSTATED PREMISES
> Strategy 1: Find something that author must believe TO BE TRUE for the CONCLUSION to make sense.
– Mentally map out logic jump from premises to conclusion
– Assumptions can play a Supporter role (link gaps, especially when there is new info) or a Defender role (eliminate weakeners)
FIGURE out the CORRECT CONCLUSION
> Strategy 2 (FOR HARDER QUESTIONS): Negation Technique - If a VALID assumption is untrue (logical opposite), then the argument BREAKS DOWN > weakens the conclusion)!
– Cover with your hand parts of the answer to help with negation technique (must be the LOGICAL OPPOSITE)
Things to keep in mind:
> Incorrect answers contain extraneous info
> Assumptions are unlikely to be very extreme cases (“only”, “no”, ‘all’. ‘primary’, ‘best’)
Examples of logical opposites (plus vice versa, a dichotomy)
> “All” or “Any” (100%) <=> “not all” (0% to 99%)
> “some” (1+) = “none” (0)
> “Sometimes” = “Never”
> “Everywhere” = “Not everywhere”
> “Always” = “Not always”
> “Necessarily” = “Not necessarily”
> “Will” = “Might not”
> “most” (>50%) = “not most” (<50%)
What type of question is the following:
“Which of the following would be most useful to research in order to assess the likelihood that the teacher’s claim is correct?”
What is the strategy for solving these types of questions?
Evaluate the Argument **(02/23 unclear)
“useful to know”
“in order to evaluate/assess/determine”
- “research” something to assess whether the teacher’s claim is correct/valid
- What ADDITIONAL info is helpful to determine whether the assumption/argument is VALID or INVALID (aka, is the argument GOOD or BAD)
–> info would EITHER strengthen or weaken that argument
Strategy for solving:
> Pre-think what would WEAKEN and STRENGTHEN the argument/conclusion
> Correct answer will allow for two possible “paths” –> one way would strengthen the argument, the other way would weaken the argument
> incorrect answers won’t affect the conclusion!
> Variance Test –> look at the EXTREMES of each answer choice and its impact on the conclusion.
e.g., “whether revenues would be impacted by the plan” –> yes, revenues would be impacted by the plan, or no, revenues would not be impacted by the plan. –> does the conclusion change?
e.g., 0% vs 100%
*only apply Variance Test to contenders to save time
What type of question is the following:
“Which of the following, if true, most helps to explain the surprising finding?”
Explain the Discrepancy (something that is a surprise, a paradox, or unusual finding –> two statements seemingly contradict with each other)
- “explain”
- “paradoxical”
Explain the discrepancy arguments lack conclusions
Strategy for solving:
> Find the statement that best EXPLAINS why the discrepancy exists (including analogies or examples of similar phenomenon) —-> What would ALLOW BOTH STATEMENTS to be true? (coexist)
What type of question is the following:
“The boldfaced portion plays which of the following roles?”
What is the strategy for solving these types of questions?
Describe the Role (R)
e.g., premises, conclusions/claims, background, counterpremises, counterconclusions, intermediate conclusions
Strategy for solving:
> first Identify the CONCLUSION
> Then, figure out HOW the Boldface statements RELATE to the CONCLUSION
> think about whether the sentences are on the SAME side or OPPOSITE sides.
Ex markers for the SAME side:
- “something is based on another”
- “X supports a generalization. Y is that generalization”.
- restatement
Recall:
> Premises: evidence
> Conclusions: claims
What type of question is the following:
“In the passage above, the biologist responds to the journalist’s claim by doing which of the following?”
What is the strategy for solving these types of questions?
Describe the argument (DA) - method of reasoning **02/23 unclear
- typically presented in a “two people speaking” format
- e.g., “A responds to B by” or “A challenges B’s argument by”
- Other: “A develops the argument by doing which of the following”
Strategy for solving:
- Figure out which PIECE of the argument that the response addresses
- Then, choose the answer that also attacks the SAME PART of the argument and matches what the PERSON DID.
What are common assumptions for Causation arguments
a) assumptions about the ORDER of causation
e.g., A –> B, therefore A –> C requires B –> C
b) Assumptions that EXCLUDE reverse causation or other causes / alternatives
c) Sometimes even assumptions ABOUT the RELATIVE size of OPPOSING forces (e.g., costs versus benefits)
> costs / damage is equivalent
> benefits outweigh costs
List of possible ERRORS in invalid arguments
A) Errors in the Use of Evidence:
> Overgeneralization of an exceptional case
> Irrelevant data
> Self-Contradiction (internal contradiction - occurs when the author makes conflicting statements)
> Errors in assessing the Force of Evidence:
– Author cites the lack of evidence in favour of a position as a reason why that the position is false
– Author cites the lack of evidence against a position as a reason why that position is true (evidence could be discovered later)
– Weaken claim might be confused with falsehood of the conclusion
– Strengthen claim might be confused with truth
B) Errors in Conditional Reasoning (any logical relationship composed of sufficient and necessary conditions):
> takes the absence of an occurrence (sufficient condition) as evidence that the necessary condition also did not take place
> mistakes sufficient condition for necessary condition
C) Errors in Cause-effect reasoning:
> Assumes a causal relationship based on a sequence of events (e.g., just because A > B > C does not mean that A causes B which causes C)
> Mistaking correlation for causation
> Failure to consider alternate causes
> Failure to consider reverse causation
D) Errors of Composition and Division (judgements made about groups or parts of a group)
> Attributes a characteristic of a part of the group to the entire group (generalization) - e.g., Every party I attend is fun and exciting. Therefore, my life is fun and exciting.
> Attributes a characteristic of the whole to a part of the group - e.g., the US is the wealthiest nation in the world. Therefore, everyone in the US is wealthy.
e.g., oil industry is profiting, so a single gas station must also be profiting
E) Source Argument (ad hominem) Error by Attacking the Person Making the argument rather than on the argument itself
F) Circular reasoning: premise = conclusion
G) Straw Man - author attacks an opponent’s argument by IGNORING the ACTUAL statements made and DISTORTS/REFASHIONS the argument, making it weaker in the process
> often accompanied by the phrase “What you’re saying is” or “if I understand you correctly”
H) Appeal to Authority/Popular Opinion or Numbers/Emotion Fallacy
I) Survey errors
> Biased sample (e.g., self-selection, demographic bias)
> Leading survey questions
J) Uncertain use of a term (that can be interpreted as ambiguous)
K) False analogy (analogy is used that is too dissimilar to the original situation to be applicable)
L) Numbers and Percentages Errors
> Equates a percentage with a definite quantity
> Uses quantity information to make a judgement about the percentage
Conditional reasoning:
What is a sufficient condition? What is a necessary condition?
If (sufficient condition exists) —> then (necessary condition must have occurred)
Sufficient condition - an event whose occurrence indicates that a necessary condition must also occur
> if sufficient condition occurs, you AUTOMATICALLY know that the necessary condition also occurs
> if a necessary condition does NOT occur, then there is no way for the sufficient condition to happen.
Necessary condition - an event whose occurrence is REQUIRED in order for a sufficient condition to occur
> if a necessary condition occurs, you DO NOT know automatically that the sufficient condition will occur
> if the sufficient condition does NOT occur, we don’t know if the necessary condition also occurs.
e.g., In order for A to go to the party, B must go. So if A is at the party, B must also be at the party. However, if B is at the party, A might not be at the party. Also if B is not at the party, then A is also not at the party.
SO in conclusion we know two things:
1) If the sufficient condition occurs, the necessary condition must also have occurred (either before, at the same time, or after the sufficient condition)
> e.g., A is there, B is there.
2) if the necessary condition does not occur, then the sufficient condition must also not have occurred.
> e.g., B is not there, A is not there
(Negate both conditions and swap order)
WRONG ANSWERS: Typically found in Find the Flaw questions
- Mistaken Reversal (switches the necessary and sufficient)
e.g., If B is at the party, then A is also at the party.
(Swap order without negation)
- Mistaken Negation (negates both conditions, creating a statement that does not have to be true)
e.g., If A is not at the party, then B is also not at the party.
(negate both conditions, BUT order is not swapped)
Things to keep in mind when solving CR questions involving numbers and percentages
1) An increase in % does NOT necessarily lead to increasing numbers
> b/c the size of the pie could be decreasing, resulting in a larger percentage of a smaller pie.
> b/c the size of the pie could be increasing, resulting in a smaller percentage of a larger pie
e.g., just because the # of bike-related accidents rose this month, it does not mean that bike-related accidents make up a “greater percentage” of all road accidents this month (b/c the whole could be getting bigger too)
> b/c the size of the pie could be decreasing too
e.g., Porsche sold 18,000 cars in the US in 2003, but the figure represented only 1% of total US car sales in 2003.
CONCLUSION:
> Percentages do not tell you anything concrete about the size of the whole and direction of the numbers (increase/decrease)
> Numbers/quantities do not tell you anything concrete about the percentages relative to a whole and the direction of numbers
Key words in CR
“Some”
“prefer” or “preference”
“difficult to do”
“Some” - just because “some” people behave differently doesn’t mean that the conclusion is wrong, as long as the IMPORTANT factors are present.
> often not the right answer in weaken questions
> “some” just means “more than 1”
“Prefer” or “preference”
> not necessarily an assumption!
“difficult to do”
> not necessarily an assumption!
If two groups of people have the same possible acceptance rates, but the aggregate acceptance rate of one group is larger than the other, what does this imply?
Weighted average
> The group with the larger aggregate acceptance rate has more people in the HIGHER acceptance rate bucket than does the group with the lower aggregate acceptance rate
Conclusions relating to REDUCTIONS (i.e. in profit, pollution etc.)
Relative changes DO NOT MATTER
> it doesn’t matter that the decrease won’t be very large –> as long as there IS A REDUCTION, the conclusion is true.
e.g., Irrelevant to know that city A has less plastic than city B. When new regulations are imposed, city A will likely experience a REDUCTION in pollution.
Conclusions relating to weakening an increase or decrease?
Find evidence that the effect either STAYS THE SAME or is the opposite
e.g., weaken conclusion that pollution will decrease
> evidence that pollution will REMAIN the SAME or that pollution will INCREASE
What type of question is the following?
Which of the following is most like the argument above in its logical structure?
Parallel reasoning
EXCEPT question types and LEAST question types
Weaken Except - the correct answer DOES NOT weaken the conclusion (e.g., strengthens or does nothing)
Strengthen Except - the correct answer DOES NOT strengthen the conclusion (e.g., weakens or does nothing)
Explain the discrepancy Except - the correct answer DOES NOT resolve the discrepancy
“Least” functions the same as “Except”
e.g., Which of the following, if true, helps LEAST to resolve the apparent discrepancy described above?
> 4 incorrect answer choices: resolve the apparent discrepancy
> 1 correct answer choice: does NOT resolve the discrepancy
Steps to solving CR questions
1) Read question stem
2) Think about logical chain and structure (premises, conclusions)
> know PRECISELY what the author said (do not generalize) —> modifier and indicator words (such as “some”, “only”, “all”, “none”, “very low”)
> IDENTIFY THE CONCLUSION
3) Pre-think the answer
4) Process of elimination
> read ALL the choices, and sort answer choices into contenders and losers
**just decide whether it is a contender or loser, not necessarily proving it is the RIGHT answer or absolutely WRONG answer
> return to the choices that strike you as most likely to be correct and choose your answer
> eliminate broad answers that indicate some irrelevant distinction or relationship
IF YOU ELIMINATE ALL five answer choices –> re-evaluate the argument
> the info ALWAYS resides in the stimulus (either implicitly or explicitly)
Other notes:
> Be ware of YOUR OWN UNSTATED ASSUMPTIONS
–> can make you blind to the correct answer
e.g., criminals often drive when committing serious crimes > not the same as saying that criminals OFTEN VIOLATE TRAFFIC RULES TOO
