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An overview of various concepts in logical reasoning, including complex propositions, types of inferences (deduction, induction, and abduction), the notions of truth, validity, soundness, and strength in arguments, as well as a detailed discussion of different logical fallacies. It covers topics such as the difference between validity and soundness, the structure of valid arguments, the characteristics of strong inductive arguments, and the identification of common fallacies like the appeal to authority, the ad hominem, the genetic fallacy, the red herring, the false dilemma, and the fallacy of begging the question. The document also explores the distinction between formal and informal fallacies, the role of premises and conclusions in arguments, and the importance of critical thinking in evaluating the strength and cogency of reasoning.
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Which sentence is a non-proposition?
Did the company really close that deal? It has had a great year. Where is the president right now? Let's go ask whether the deal was closed.
In the above paragraph, which sentence expresses a proposition?
Propositions - ✔️ Statements that can be true or false.
Non-propositions - ✔️ Sentences that are not statements about matters of fact (or fiction). They do not make a claim that can be true or false.
Which sentence expresses a complex proposition?
If the computer is not fixed, then the company either needs to buy a new one or will not be able to keep up productivity. Which of the following breaks down the complex proposition above into the simple propositions?
Simple propositions - ✔️ Simple propositions have no internal logical structure, meaning whether they are true or false does not depend on whether part of them is true or false. They are simply true or false on their own.
Complex propositions - ✔️ Complex propositions have internal logical structure, meaning they are composed of simple propositions. Whether they are true or false depends on whether their parts are true or false.
If the new employee wants to succeed, then they need to show up on time. How many times have we heard the manager complain about tardiness? Nobody likes a 7 a.m. start time, but it was in the job description. We should remind the new employee how important this is. Which is a simple proposition that is expressed in the above paragraph?
The U.S. healthcare system is difficult to navigate, and this negatively affects many of us. Many people are unsure exactly how their health insurance coverage works and are not sure where they can go to get care. What can be done to improve this? If changes are not made soon, the problem will only get worse. Which is a simple proposition that is expressed in the above paragraph?
Bad inferential structure - ✔️ Every argument with the same structure as this argument is bad (invalid or weak). The premises do not, in fact, demonstrate or maybe even support the conclusion. In other words, we can accept the premises as true without being compelled to accept the conclusion. There is something wrong with this argument's general structure.
Which pairs of sentences are arguments? Choose 2 answers.
I just heard the news about Riley's car. It was vandalized last Saturday. There is no doubt Jordan did it. I went to the bowling alley that night. I bowled a 160! Anyway, I saw Jordan there and, although it was barely noticeable, I definitely saw paint on Jordan's shirt. It is unlikely there would be paint on Jordan's shirt unless Jordan had spray-painted Riley's car. It is a shame, really, since it was such a nice shirt. It was the green one. Oh, and you know Jordan has motive. After all, Jordan has a well- known grudge against Riley. You remember when Riley borrowed Jordan's lawnmower and did not return it. And there was opportunity, because Jordan does not work on the weekend and usually stays home watching television. But the lightning storm earlier last week short-circuited Jordan's TV set. Besides, they canceled Jordan's favorite Saturday evening show. Which description best characterizes the above?
Kinds of Inferences - ✔️ Deduction Induction Inference to the best explanation or abduction
Deduction - ✔️ arguments where the premises guarantee or necessitate the conclusion — mathematical arguments, logical arguments, arguments from definition
Induction - ✔️ arguments where the premises make the conclusion probable — analogies, authority, causal inferences, scientific reasoning, extrapolations, etc.
Inference to the best explanation or abduction -
✔️ arguments where the best available explanation is chosen as the correct explanation
Truth - ✔️ A true proposition accurately represents reality.
Validity - ✔️ In a good deductive argument structure, true premises make the conclusion necessarily true. (If not, it is an invalid structure.)
Soundness - ✔️ The deductive argument is valid and all premises are true premises. (If not, it is an unsound argument.)
Sound Argument - ✔️ All True Premises + Valid Structure
Strength - ✔️ In a strong inductive argument, true premises make the conclusion probably true.
Cogency - ✔️ Strong inductive arguments with all true premises are cogent.
Consider the following argument: Smith inspected 990 jellybeans in the jar. Each of the beans Smith inspected is red. Therefore, all 1000 of the beans in the jar are red. Which kind of argument is this?
Some arguments are such that the premises of the argument entail its conclusion, which means that if the premises are true, then the conclusion must be true. What are such arguments called?
Consider the following argument: If Jones is a baseball player, then Jones is an athlete. Jones is a baseball player. Thus, Jones is an athlete. Which kind of argument is this?
Which indicator is a premise indicator?
Because flying cars will relieve traffic congestion, and since the research and development of such vehicles will be expensive, it follows that the government should encourage industry to develop flying cars and banks should help fund industry research. Which phrases contain conclusions of this argument? Choose 2 answers.
Dogs are bred for many different purposes. Poodles, for example, make good house pets, while German shepherds and other large breeds can be used for home protection. Therefore, because it is important to select the right breed for your needs, you should carefully research dog breeds to make the right choice. Which statement is the conclusion of the argument?
Everyone should vote ___________________. Which phrase would form an argument when added to this sentence?
People have fought for freedom since the beginning of time. Which descriptor best characterizes this sentence?
Jordan says, "I am the best student at our high school; I am the tallest and most athletic, and I have the best car." Taylor, Jordan's best friend, totally agrees. Which two descriptors best characterize Jordan's comments? Choose two answers.
All dogs are cute. Ginger is a dog. Therefore, Ginger is cute. Which type of reasoning is illustrated in this example?
Usually when the audience comes out of a theater laughing, that means the film was funny. The audience leaving the theater after this film is laughing. So the film probably is funny. Which type of reasoning is illustrated in this example?
All dogs can fly. Ginger is a dog. Therefore, Ginger can fly. Which types of reasoning are illustrated in this example? Choose 2 answers.
An individual drops hundreds of objects, and each time they fall to the ground. The individual therefore concludes that if someone drops a pencil, it will fall. Which terms describe the argument? Choose 2 answers.
Formal Fallacy - ✔️ The word "formal" refers to the structure of things.
Informal Fallacy - ✔️ Informal fallacies have a problem with their content.
A formal fallacy concerns _______, but an informal fallacy concerns _______. - ✔️ the structure of an argument
By definition, a formal fallacy concerns the structure of an argument and an informal fallacy concerns the information contained in the argument's structure.
A formal fallacy is a type of _______. - ✔️ Bad argument structure Formality is associated with structure.
Which questions are most appropriate for evaluating the credibility of an information source? Choose 2 answers.
Which study is most likely to be corrupted by bias?
Which questions can best help readers avoid being misled by fake news? Choose 2 answers.
Which of the following are reasons for applying the principle of charity? Choose 2 answers.
Which passage best demonstrates the principle of charity?
Smith is committed to the belief that technological advancement is always beneficial and thus never detrimental to human life. Smith reads a carefully written and sufficiently argued essay in which the author contends that the human adoption of any new technology involves both advantages and disadvantages to its adopters. Since Smith is a loyal technophile, Smith accepts the author's claims about the advantages of technology but rejects the author's claims about the disadvantages of technology. Which cognitive bias is Smith demonstrating?
Cognitive bias - ✔️ The way we naturally categorize and make sense of the world around us.
Alief - ✔️ An automatic belief-like attitude that can explain how our instinctual responses can conflict with our reasoned-out beliefs.
Heuristic -
The Bright Tooth toothpaste company runs the following advertisement: "Use Bright Tooth toothpaste. Nine out of ten dentists recommend it!" You decide to research this claim. You discover that the Bright Tooth toothpaste company surveyed only ten carefully selected dentists, nine of whom expressed support for Bright Tooth toothpaste. You also learn that, as of 2019, there were 200,419 dentists in the United States alone. Which error is committed in the advertisement?
Which is the best example of System 1 thinking?
Which is the best example of System 2 thinking?
System 1 Thinking - ✔️ This is quick, automatic thinking
System 2 Thinking - ✔️ This is deliberate thinking
When asked how likely it is for an urban cyclist to get in an accident, a survey respondent remembered that their friend got into a cycling accident last week. This makes them conclude that cycling accidents are fairly likely. Which statement is correct about the source of bias in the passage and how to avoid its impact?
Which statement about how to respond to bias is correct?
Which piece of information would be the most helpful to know in assessing the credibility of a news story?
While researching a topic on the internet, a student encounters two different websites, one of that looks more official than the other and includes tables, charts, and statistics, while the other does not. What is the line of reasoning this student should employ to determine which site is more credible?
✔️ is committed when one misrepresents another's argument then attacks the misrepresented (weaker) argument rather than the actual (stronger) argument.
red herring fallacy - ✔️ the use of irrelevant material to divert attention
appeal to authority fallacy - ✔️ error of accepting a claim merely because an authority figure endorses it
appeal to force (fallacy of relevance) - ✔️ when one uses a threat to compel agreement with one's claim
Appeal to Popularity Fallacy - ✔️ Arguing that a claim must be true because lots of people believe it.
appeal to consequences fallacy - ✔️ when one appeals to the bad (or good) consequences of accepting a claim as a reason to reject (or accept) it as true.
Fallacy of Equivocation - ✔️ when one's argument mistakenly uses the same word in two different senses.
Conner and Miller are discussing the topic of intelligent life in other solar systems. Conner asks Miller, "Do you believe that there is intelligent life in the Alpha Centauri planetary system?" Miller replies, "I don't know that there isn't intelligent life there. There's no proof that there isn't. So, I believe there is intelligent life in that planetary system." Which fallacy did Miller commit?
Suppose Jones believes that every morning that he steps out of his house with his right foot first, he will have a good day. Jones believes this because last Tuesday morning he stepped out of his house with his right foot first. Later in the day, he received a raise at work, his friends took him to lunch, and he won $500 in the lottery. Which fallacy did Jones commit?
What fallacy occurs when a person reasons that one event is likely to lead to another event due to a chain of intermediary events, even though the probability of that entire chain being realized is low?
Which of the following is the most pertinent question to ask when trying to identify the fallacy of begging the question?
Suppose a person argues that one and only one of two options is true. However, there are more than two options. In other words, the argument looks like this: Either p is true or q is true. Q is not true. Therefore, p is true. However, there is a third option, r. Which of the following fallacies is present in this argument?
Suppose that Smith asserts a claim that could be true but seems implausible. Jones recognizes this point and asks Smith to provide evidence for his claim. Smith responds: "Why don't you try to disprove my claim?" Which fallacy is found in this argument?
In which argument do premises (1) and (2) provide conjoint support for conclusion (3)?
We should buy an electric car. Granted, they are more expensive up front than gas cars, but we have the money, and we will save on gas in the long run. Additionally, electric cars are better for the environment. And they are becoming more stylish! Which is a hidden assumption of the given argument?
Which argument would require a conjoint, hidden assumption to be paired with premise (1) when mapped?
Map the given argument to help you understand its structure. Then, select which is a hidden assumption of the argument. (1) We really should be giving more foreign aid to developing nations. (2) It is desirable for the people of the world to have a more equal access to resources, and (3) our nation has more resources than developing nations do. (4) Foreign aid will help give them more equal access to resources. Additionally, (5) there will be more international trade in the future once those nations are further developed, and (6) foreign aid will help them further develop.
Map the given argument to help you understand its structure. Then, select which is a hidden assumption of the argument. (1) Over 70% of residents say that traffic congestion is a major problem in our city. (2) The research group that conducted that survey has a great track record, by the way. (3) And other nearby cities that have invested in transportation have seen significant economic benefits. (4) This all shows that it would be a good idea for our city to invest in transportation.
Professor Smith fell asleep during class today. So Professor Smith is probably a bad teacher. Which missing premise best completes the above argument?
Quinn started eating donuts for breakfast every day. Consequently, Quinn is likely to gain weight. Which missing premise best completes the above argument?
Which is the most plausible counterexample to the general moral principle that one should never lie?
A military veteran is engaged in a heated debate about national security with a reporter who has never served in the military. Which response best enables the veteran to undermine the reporter's argument?