Class 6: Reasoning and problem solving Flashcards
True/False? A straw man argument is when an individual misrepresents someone’s argument in a way that makes it weaker, and then attacks that misrepresentation instead of the actual argument.
True.
filll in the blank: The goal of exposing these fallacies and coaxing people into renouncing them is called ______.
critical thinking.
True or false, Deductive reasoning: The process of drawing a logical conclusion from a set of premises, such that the conclusion must be true if the premises are true.
TRUE
In your own words describe what the argument from authority is
The argument from authority is when someone believes that a person can reference a smarter person or power that knows all and cannot be wrong and therefore their own statement cannot be wrong.
What are informal fallacies?
Informal fallacies are errors in reasoning that occur when people do not follow the rules of logic at all.
What is the relationship between critical thinking and rationality?
Critical thinking is a key component of rationality, as it involves using reason and evidence to evaluate arguments and make informed judgments. Without critical thinking, our decision-making is more likely to be influenced by biases, emotions, and faulty reasoning.
Propositional logic can be used to evaluate the validity of an argument by constructing a truth table to determine whether the premises support the conclusion. (True or False).
True!
What is the difference between a valid and sound argument?
A valid argument correctly applies rules of inference, only telling us that the conclusion must be true if the premises are true. Whereas, a sound argument is where rules are a to a true premise and then must, therefore, yield a true conclusion.
Bloodletting was a popular form of treatment for centuries. What type of fallacy is this an example of?
The bandwagon fallacy. Physicians continued to use bloodletting simply because it was a widely accepted and established practice, rather than because it had been shown to be effective.
True or False: Denying the antecedent is one type of logical fallacy which occurs when someone assumes the antecedent to be false, and therefore assume the consequent that follows must also be false.
TRUE
An arguer makes a controversial statement which is refuted by an opponent. (For example: Climate change is a hoax. It’s just a way for scientists to get funding.). But then changes the goalposts to a more moderate argument e.g. “Okay, I didn’t mean it’s a complete hoax. I just think some of the data is exaggerated, and we need to approach the issue with caution.”. This is an example of the [blank] fallacy.
Motte and Bailey
What is the difference between deductive and inductive reasoning?
Deductive reasoning starts with general principles and applies them to specific cases, while inductive reasoning starts with specific cases and uses them to infer general principles.
Is deontic logic a real branch of logic?
Yes, it is concerned with permission, obligation, and duty and studies concepts such as ‘ought’, ‘should’, and ‘must’, for example.
What is the difference between deductive and inductive reasoning?
Deductive reasoning starts with a set of premises and reaches a specific conclusion, while inductive reasoning starts with observations and generalizes to a broader conclusion.
Which fallacy is best described by a person trying to refute an opponent’s argument not by reason, but by insulting his/ her character?
Ad hominem
What are Informal Fallacies?
They are errors in reasoning due to the content of an argument rather than logical structure. It is difficult to detect because they rely on emotional or psychological appeals rather than formal logic.
True or False: According to Pinker, the concept of “common sense” is a reliable guide to making good decisions.
False. Pinker argues that “common sense” can often be misleading, and that relying solely on intuition can lead to poor decision-making.
True or False Rationality is implemented in the mind as a list of propositions and a chain of logical rules
False The mind forms rationale using a family of cognitive models such as pattern associators
What are Formal Fallacies?
They are errors in the structure of an argument which can be explained by incorrect logic form or propositional calculus.
How is family resemblance described in the article?
Family resemblance is where there are no necessary and sufficient features to identify or define a category, but rather a variety of features that run through different subsets of the category. This allows people to identify whether something belongs to that category. For example, physical features of members of a family are not always identical for everyone, but most of the members will have at least some of them, and thus it is easier to identify them as part of the same family.
What is the difference between validity and soundness? a. Validity refers to the logical relationship between the premises and the conclusion, while soundness refers to the truth of the conclusion. b. Validity refers to the truth of the conclusion, while soundness refers to the truth of the premises. c. Validity refers to the strength of the argument, while soundness refers to the relevance of the argument. d. Validity refers to the relevance of the argument, while soundness refers to the strength of the argument.
The correct answer is a. Validity refers to to the logical relationship between the premises and the conclusion, while soundness refers to the truth of the conclusion. A valid argument correctly applies rules of inference to the premises. It only tells us that if the premises are true, then the conclusion must be true. It makes no commitment as to whether the premises are true, and thus says nothing about the truth of the conclusion. This may be contrasted with a sound argument, one that applies the rules correctly to true premises and thus yields a true conclusion.
Fill in the blank: L________ L______ U_____ is a theoretical world where background knowledge is disregarded and all relevant facts are laid out as premises, which allows for deduction of new knowledge without existing information affecting it.
Leibniz’s Logical Utopia
define tautologies
statements that are inherently true due to logical structure, they don’t provide new information. For example: it is what it is – restates the same idea, it is useful in clarifying points or emphasising ideas, overuse leads to lack of clarity and precision
Define syllogism.
Syllogism is a three-part logical argument. The first two propositions are two premises combined to arrive at the third proposition which is the conclusion.
They are the foundation upon which an argument is built and are considered to be true or accepted as true.
Premises
When do the laws of logic apply?
The laws of logic are general-purpose. They apply when the content is topical, obscure, or even non-sensical.
What is a rational argumentation?
A common ground is established on premises that are accepted as truth, in conjunction with conditional statements that ensure that it is agreed that one proposition follows on from another, and thus, using inference yields the logical implications
Which formal logical fallacy is best represented in the following statement? “You know, Joe Rogan is the ultimate human - I mean, the man is so disciplined that he takes ice baths every morning, fasts for 16 hours a day, and even communicates with machine elves on a regular basis. I guess that’s just what it takes to achieve peak performance these days.”
This example contains several tendentious presuppositions. Firstly, it presupposes that Joe Rogan is the ultimate human, which is a subjective and biased opinion. Secondly, it presupposes that taking ice baths and practicing intermittent fasting are essential to achieving peak performance, which may not necessarily be true for everyone. Finally, the reference to machine elves is a humorous exaggeration that reinforces the presupposition that Joe Rogan is some sort of superhuman, even though communicating with machine elves is not a proven or scientifically recognized practice.
How do we counter informal fallacies?
By using Critical Thinking.
Why is critical thinking and logic important?
Its an pretty essential skill when navigating the world and for making informed decisions that helps us to avoid errors in reasoning and judgment.
The example in pinker ’s logic which identified the mnemonic symbols we use for connectors in formal logic are not synonymous with the ways they are used in conversation is_________________.
The difference between“if” in everyday English and iF in logic is an example.
What is the purpose of Bayesian reasoning? A) To analyze and evaluate information in order to make well-reasoned judgments and decisions B) To compare two things as if they are equal when they are not, leading to a false or misleading conclusion C) To draw a conclusion from two premises using deductive reasoning D) To update prior beliefs or probabilities based on new evidence or data E) To conclude that something is true simply because it has not been proven false, or vice versa
D) To update prior beliefs or probabilities based on new evidence or data.
Give a brief explanation about a type of logical fallacy of “Denying the Antecedent”
“Denying the antecedent” is a type of logical fallacy that occurs when someone assumes the antecedent to be false, then the consequent that follows must also be false (e.g., “it didn’t rain, therefore the streets are not wet”). However, this type of fallacy is a common mistake which can lead to flawed conclusions as there may be other factors that may lead to the same outcome.
Which formal logical fallacy does the following statement contain? If I study hard, I will get good grades. I didn’t study hard. Therefore, I didn’t get good grades.
Denying the antecedent. This refers to the fallacy that occurs when an individual assumes in an “if-then” statement that if the antecedent is false, then the consequent must also be false. However, in this example there may be other ways apart from study that lead on to get good grades.
Fill in the blanks: A _ is a logical argument in which a conclusion is drawn from two premises. The classic example is “All men are mortal. Socrates is a man. Therefore, Socrates is mortal.”
Syllogism.
According to Pinker 2021, Systems of logic are formalized as what?
Rules that allow one to deduce new statements from old statements by replacing some strings of symbols with others.
Judging truth or false: critical thinking is the basis of logic.
False. Critical thinking is using logic and reasoning to evaluate arguments and evidence. Logic provides the framework and rules for making valid inferences and deductions, while critical thinking applies these principles to analyse and evaluate arguments and evidence. In other words, critical thinking requires logical thinking to identify flaws in reasoning and develop well-supported arguments. Logic is, therefore, the foundation on which critical thinking is built.
What is an example of an ad hominem fallacy, and how does it differ from a legitimate criticism of the person making the argument?
A legitimate criticism of the person making the argument would be relevant to the argument’s merits, such as questioning their expertise in the relevant field.
Define family resemblance categories.
Categories that are not easily stipulated in logic and often have stereotypes.
What is the difference between a valid argument and a sound argument?
A valid argument needs only to apply rules of inference to premises and does not make a comment on the truthfulness of premises. A sound argument however, applies rules to true premises resulting in truthful conclusions.
True or False: Many technology critics fear that as Al systems are entrusted with decisions about the fates of people, they could perpetuate biases that no one can identify and uproot.
TRUE
What is deductive reasoning?
Deductive reasoning is when we use general principles to draw specific conclusions.
What are some examples of how logical fallacies can lead to erroneous thinking, according to Pinker? a) Stereotyping, confirmation bias, and overgeneralization b) Slippery slope, appeal to authority, and false dichotomy c) Hasty generalization, ad hominem, and strawman argument d) All of the above
b) Slippery slope, appeal to authority, and false dichotomy
According to Steven Pinker, what is rationality and why is it important for human progress?
Rationality, according to Steven Pinker, is the ability to think critically, weigh evidence, and make decisions based on probabilities. It involves updating beliefs based on new information and avoiding cognitive biases and emotional influences. Pinker argues that rationality is important for human progress because it allows us to solve complex problems, make informed decisions, and build institutions that promote collective well-being.
Jenny says Oliver went to prep school stating “You look stupid and rich”. Oliver protests “Actually, I’m smart and poor”. What else could Oliver have said to contradict Jenny?
He also could have stated “I’m stupid and poor”, or “I’m smart and rich”, because he only had to contradict one part of her statement because she used the word AND not the word OR
The following is an example of what type of logical fallacy? First, we allow people to carry guns in public. Then, we’ll have to allow them to carry guns in schools. After that, we’ll have to allow them to carry guns in churches. And before we know it, we’ll have a society where everyone is carrying guns everywhere they go.
The slippery slope fallacy
The statement “95% if people agree with my opinion, so you should too!” is an example of which fallacy?
The bandwagon fallacy
If someone is allergic to peanuts, they will experience hives. If Julie experienced hives, therefore she must be allergic to peanuts. This is an example of which fallacy? A) Denying the Antecedent B) Affirming the Antecedent C) Denying the Consequent D) Affirming the Consequent
D) This is an example of Affirming the Consequent as the fact that Julie experienced hives does not necessarily mean that she is allergic to peanuts. There are many other possible reasons for why Julie could experience hives.
What is the difference between logic and critical thinking according to Pinker’s analysis in “Rationality: What it is, why it seems scarce, why it matters”?
Pinker distinguishes between logic and critical thinking by explaining that logic is the formal system of rules used to determine the validity of arguments, while critical thinking involves the ability to evaluate evidence and arguments in a systematic and unbiased way, taking into account factors like reliability, relevance, and consistency
What kind of argument correctly applies rules of inference to the premises, but only tells us that if the premises are true then the conclusion must be true? It makes no guarantee as to whether the premises are true, and therefore says nothing about the truth of the conclusion.
A valid argument
____ consists in laying out a common ground of premises that everyone accepts as true, together with conditional statements that everyone agrees make one proposition follow from another, and then cranking through valid rules of inference that yield the logical, and only the logical, implications of the premises.
Rational argumentation
How might our understanding of rationality change in the future, given advances in technology, neuroscience, and other fields? Will we need to redefine what it means to be rational, or will the core principles remain the same?
Our understanding of rationality may change in the future as new technologies and scientific discoveries emerge. For example, advances in neuroscience may shed new light on the nature of human reasoning and decision-making, and may lead to new tools for improving rational thinking. Similarly, the rise of artificial intelligence and machine learning may require us to rethink what it means to be rational in the context of intelligent machines.
What is false dichotomy?
A false dichotomy is a fallacy that presents only two options as if they are the only ones available, when in fact there may be other options. It is a false choice because it ignores the possibility of other alternatives.
Why should an individual use deductive compared to inductive reasoning?
Deductive reasoning is useful when you want to prove something with absolute certainty, while inductive reasoning is useful when you want to make predictions based on observations.
“If it’s a holiday, then the store will be closed. The store is closed. Therefore, it must be a holiday.” This argument is not valid because the store could be closed for other reasons, such as renovations or a power outage. This is an example of: A. denying the antecedent B. Denying the consequent C. Affirming the antecedent D. Affirming the consequent
D. Affirming the consequent. This is a common invalid inference/formal fallacy where sequences of statements are made in which the conclusions may seem to follow from the premises but in fact do not. i.e. “If P then Q. Q. Therefore, P.”
What is the ability to think and make decisions based on logic called?
Rationality
What is the difference between deductive and inductive reasoning?
Deductive reasoning is a logical process that involves drawing a conclusion based on previously accepted premises, while inductive reasoning involves using specific observations or examples to arrive at a general conclusion.
What is the difference between a necessary and a sufficient condition? a. A necessary condition is one that is required for an event to occur, while a sufficient condition is one that guarantees an event will occur. b. A necessary condition is one that guarantees an event will occur, while a sufficient condition is one that is required for an event to occur. c. A necessary condition is one that is required for an event to occur, while a sufficient condition is one that is not required for an event to occur. d. A necessary condition is one that is not required for an event to occur, while a sufficient condition is one that is required for an event to occur.
The correct answer is a. A necessary condition is one that is required for an event to occur, while a sufficient condition is one that guarantees an event will occur. A necessary condition is a condition that must be present for an event to occur, while a sufficient condition is a condition that, if present, guarantees that the event will occur.
The following is an example of what type of logical fallacy? Alice and Bob are running for mayor of their town. Alice has a plan to improve public transportation and reduce traffic congestion. Bob does not like Alice’s plan and wants to persuade voters not to support her. He finds out that Alice’s cousin is a notorious criminal who has been arrested several times for fraud and theft. He decides to use this information against Alice in his campaign ads.
Guilt by association which is a form of an ad hominem argument.
What is the goal of critical thinking
The goal of critical thinking is to identify and eliminate these fallacies to arrive at sound conclusions. However, logic is not always suitable for all kinds of knowledge and goals.
Define ‘Formal Fallacies’
The errors in deductive reasoning that arise from a flaw in the logical structure of an argument
According to Steven Pinker’s chapter on “Logic and critical thinking” in “Rationality why is critical thinking important?
Critical thinking is important because it helps us evaluate arguments and evidence, avoid fallacies and errors in thinking, and make well-reasoned decisions.
Denying the Antecedent is a type of logical fallacy that occurs when someone assumes that if the antecedent of an if-then statement is false, then the consequent must also be “true or false”?
FALSE
Explain what an empirical truth is and why it cannot be proven with only logic.
An empirical truth is a truth obtained via experimentation or observation. Logic, while important in thinking of possible explanations for these truths, needs observation to formulate it.
If determining whether something belongs to a certain category, such as prime numbers, is simply true or false, what type of category does it belong to?
Classical category. A number is either prime or it is not
True or False: Steven Pinker argues that critical thinking is an innate human ability that requires no training or practice.
False. Pinker acknowledges that critical thinking skills require training and practice, and that they don’t come naturally to everyone.
What is Deductive Logic?
It is a potent tool that enables an individual to draw out conclusions that are already contained in a premise.
What is rational argumentation?
It consists of laying out a common ground of premises that everyone accepts as true, together with conditional statements that everyone agrees make one proposition follow from another, and then cranking through valid rules of inference that yield the logical implications of the premises.
A type of fallacy where you attack the character or attributes of the person with the argument opposing yours.
Ad hominem fallacy
Is the statement, “If Canada had invaded Washington DC in 2010, they would have captured the president” sound, valid, both or neither?
Neither. The statement is not valid or sound because the scenario did not occur, and the president being captured after invading DC does not necessarily follow logically.
Why does Pinker believe that logical thinking and critical thinking are essential?
Pinker believes these can help an individual understand the world and make decisions based on these skills
Why are almost all arguments in practice considered enthymemes?
No mortal has the time or attention span to lay out every last premise and implication in an argument.
What are some achievements of human rationality enabled by propositional reasoning? A. Science, morality, and law. B. Superstition, prejudice, and ignorance. C. Violence, chaos, and anarchy. D. None of the above.
A
What is a logical fallacy?
A logical fallacy is an error in reasoning that can lead to incorrect conclusions
define genetic fallacy
evaluating an idea not by its truth but by its origins
A woman is mortal, Tia is a woman, therefore Tia is mortal. What is this an example of relating to the P and Q statements?
If P then Q “affirming the antecedent”
What`s the “Straw man fallacy”?
A type of argument that misrepresents an opponent’s position. It then attacks that misrepresentation instead of their actual argument. This fallacy is often used as a way to undermine an opponent’s argument without engaging with their actual claims.
define the term Syllogism
Definition: A form of deductive reasoning in which a conclusion is drawn from two premises, using a major premise, a minor premise, and a conclusion.
Fill in the blanks: _ _ involves drawing general conclusions based on specific observations or examples. This type of _ is used in many scientific and social scientific fields to develop hypotheses and theories.
Inductive reasoning ; reasoning.
What is critical thinking?
Critical thinking involves the ability to evaluate arguments and evidence in a rational way.
“I really shouldn’t eat this slice of pizza because if I do I’ll probably lose all control and go off my diet, and then I’ll keep gaining weight and eventually get diabetes” is an example of what fallacy
Slippery slope fallacy
Describe in short what logic is?
Logic is the study of arguments and reasoning, that provides a framework for evaluating the strength of the argument.
Discuss the reasons why people often appear to be irrational, according to Pinker. What are some cognitive biases and emotional influences that can lead to irrational decision-making and how can we overcome these challenges?
According to Pinker, people often appear to be irrational due to cognitive biases such as confirmation bias, availability bias, and the sunk cost fallacy. These biases can distort our perception of reality and lead us to make decisions that are not in our best interest. Emotional influences, such as fear, anger, or desire, can also cloud our judgment and lead us to make impulsive or irrational choices. To overcome these challenges, Pinker suggests that we need to cultivate self-awareness, critical thinking skills, and a willingness to update our beliefs in response to new evidence.
Which of the following is an example of a deductive reasoning process? A) Bayesian Reasoning B) Critical Thinking C) Inductive Reasoning D) Confirmation Bias E) Argument from Ignorance
C) Inductive Reasoning.
“Everyone in Australia likes to surf. I am in Australia. Therefore, I like to surf.” What kind of logic is this?
Deductive logic
How do Pinker’s chapter on logic and critical thinking relate to the broader themes of his book, Rationality: What it is, why it seems scarce, why it matters?
Pinker’s chapter on logic and critical thinking is a key component of his broader exploration of rationality in his book. By discussing the importance of logical reasoning and critical thinking, he highlights the role that these skills play in promoting rational decision-making and in avoiding fallacious reasoning. Through his exploration of rationality, Pinker aims to provide insights into why people sometimes fail to make rational decisions and to suggest ways that individuals and societies can promote rationality more effectively.
Fallacious argument
Deductively invalid, inductively very weak, contains an unjustified premise, or ignores relevant evidence that is available and should be known by the arguer
True or False: Categorical reasoning is a mode of thinking that deals with the contents of statements, not their forms.
False. Categorical reasoning is a mode of thinking that deals with the forms of statements, not their contents.
What is the difference between a cognitive bias and a logical fallacy?
A cognitive bias is a systematic error in thinking or decision-making that arises from the way our brains process information, while a logical fallacy is a mistake in reasoning that occurs when someone makes an argument that is not logically valid. Both can lead to errors in judgment or decision-making, but require different strategies to address.
“Most people I know think astrology is scientific, so there must be something to it” is an example of what kind of fallacy?
Bandwagon fallacy
True or false: Formal logic takes into account the content of the proposition, context, and background knowledge in order to come to a rational decision/outcome.
False - formal logic in the strict sense means forgetting everything you know that might be mixed into the deliberation - content of the proposition, context, background information - and just dealing with what lies in front of you.
True or False: Pinker believes that formal logic and mathematics are the only tools necessary for effective critical thinking.
False. Pinker acknowledges that while formal logic and mathematics can be useful, critical thinking also requires an understanding of informal fallacies, cognitive biases, and statistical reasoning.
What is the purpose of ‘deductive logic’?
Deductive logic is a potent tool used for drawing out conclusions that are already contained in the premises.
True or false: For an argument to be valid, it also needs to be sound.
False. An argument can be valid without being sound.
Which of the following is NOT a characteristic of deductive reasoning? a) It involves drawing a conclusion based on general principles or premises b) It is based on valid logical inference c) It always leads to a true conclusion d) It is used to test the validity of arguments
c) It always leads to a true conclusion
What is the main difference between Logical & Empirical truths?
Logical truths are true by definition/laws of logics while empirical truths are based on observations made and evidence.
What is an ad hominem attack?
A fallacious type of argument that is directed at a particular person and not the stance they maintain.
What is the fallacy of affirming the consequent?
The fallacy of affirming the consequent occurs when someone assumes that if a particular outcome occurred, then a particular condition must have been met, when in fact there may be other explanations for the outcome.
What is special pleading?
An informal fallacy that arguers engage in where they replace their proposition with one that is easily defensible and move the goalposts in the conversation to supplement their arguments.
Why are conditional statements an important tool?
It is an essential part of logical thinking as it allows us to reason about cause-and-effect relationships and make predictions about what will happen under certain events/conditions.
True or False. Jennifer does not agree with an idea proposed by her professor, so she badmouthed the professor and said that he does not know what he is talking about. The argument made by Jennifer is an example of an ad hominem argument.
True. An ad hominem argument is when one attempted to rebut an idea by attacking or insulting the person, not the idea itself.
True or false? Modus ponens, a valid rule of inference, refers to “denying the consequent”.
False. Modus ponens refers to “affirming the antecedent”, whereas modus tollens, another valid rule of inference, refers to “denying the consequent”.
What is deductive logic and what is inductive logic?
Deductive logic is using premises given to us and making a conclusion only from these premises, while inductive logic requires us to look at a number of evidence and making a generalised conclusion from them.
