Course outline
Module 1
Module 1: Foundations of Analogical Thinking
Foundations of Analogical Thinking
Knowledge check
Q1. Bird is to nest as dog is to ___?
- A. Bark
- B. Kennel ✓
- C. Leash
- D. Tail
Why: A nest is the shelter where a bird lives, just as a kennel is the shelter where a dog lives. The relationship is 'animal to its home.'
Q2. Hot is to cold as light is to ___?
- A. Bright
- B. Sun
- C. Dark ✓
- D. Lamp
Why: Hot and cold are opposites, and light and dark are opposites. The analogy is based on antonym relationships.
Q3. Pen is to write as knife is to ___?
- A. Sharp
- B. Kitchen
- C. Steel
- D. Cut ✓
Why: A pen is a tool used for writing, and a knife is a tool used for cutting. The analogy matches each object with its primary function.
Q4. Teacher is to classroom as chef is to ___?
- A. Recipe
- B. Restaurant ✓
- C. Food
- D. Oven
Why: A teacher typically works in a classroom, and a chef typically works in a restaurant. The analogy connects a professional with their workplace.
Q5. Puppy is to dog as kitten is to ___?
- A. Cat ✓
- B. Milk
- C. Fur
- D. Play
Why: A puppy is a young dog, and a kitten is a young cat. The analogy expresses the relationship between a young animal and its adult form.
Module 2
Module 2: Structure Mapping and Relational Similarity
Structure Mapping and Relational Similarity
Knowledge check
Q1. In the analogy 'Heart is to blood as pump is to water', which relation is being mapped?
- A. Both objects are made of metal
- B. The first item circulates a fluid through a system, just as the second item moves a fluid through a system ✓
- C. Both items are found in the human body
- D. Both items are used for cleaning
Why: Structure mapping focuses on relational similarity: the heart moves blood through the body just as a pump moves water through a pipe system. The surface features (organic vs. mechanical) are irrelevant to the analogy.
Q2. Which pair best matches the relational structure of 'Author is to novel as composer is to symphony'?
- A. Teacher is to school
- B. Painter is to canvas
- C. Chef is to recipe
- D. Architect is to building ✓
Why: The original analogy maps a creator to the work they produce. Architect is to building matches this relation: the architect designs and creates the building, just as the author writes the novel and the composer writes the symphony. Chef is to recipe is tempting but the chef uses a recipe rather than producing one as the main output.
Q3. Gravity is to planets as the sun is to what?
- A. Light
- B. Heat
- C. Planets ✓
- D. Electricity
Why: Gravity holds planets in orbit, so the relation is 'attracts and binds'. The sun plays this role for the planets in its system. The analogy maps the relational structure of a central force binding orbiting bodies, not the physical nature of the force itself.
Q4. Which analogy relies on a surface feature rather than a relational structure?
- A. Seed is to tree as egg is to bird
- B. Bird is to nest as bee is to hive
- C. Both a cloud and a pillow are white and soft ✓
- D. Fuel is to engine as food is to body
Why: Comparing a cloud and a pillow based on shared color and softness is a surface-level (attribute) similarity. The other options each show a relation that holds between two items, such as developing into, housing, or powering, which is the kind of structure mapping that drives analogical reasoning.
Q5. Which mapping best preserves the relational structure of 'Atom is to nucleus as solar system is to sun'?
- A. Electron is to proton
- B. Planet is to moon
- C. Orbiting electron is to planet, with the nucleus as the central attractor ✓
- D. Star is to galaxy
Why: In the original analogy, smaller bodies (electrons, planets) orbit a dense central body (nucleus, sun). Mapping the orbiting electron to the planet preserves this relation: each is a smaller body held in orbit by a central mass. Electron-to-proton breaks the orbiting relation, and the other options do not preserve the central-orbiter structure.
Module 3
Module 3: Analogies in Everyday Language
Analogies in Everyday Language
Knowledge check
Q1. Hand is to glove as foot is to:
- A. Sock
- B. Shoe ✓
- C. Toe
- D. Leg
Why: A glove covers and protects the hand, just as a shoe covers and protects the foot. The relationship is 'item that covers and protects a body part.'
Q2. Book is to reader as song is to:
- A. Singer
- B. Melody
- C. Listener ✓
- D. Album
Why: A book is experienced by a reader, and a song is experienced by a listener. The relationship is 'creative work and the person who experiences it.'
Q3. Captain is to ship as pilot is to:
- A. Airplane ✓
- B. Runway
- C. Engine
- D. Passenger
Why: A captain leads and commands a ship, and a pilot leads and commands an airplane. The relationship is 'person in charge of a vehicle.'
Q4. Fire is to hot as ice is to:
- A. Water
- B. Winter
- C. Cold ✓
- D. Snow
Why: Fire is characterized by being hot, and ice is characterized by being cold. The relationship is 'defining quality of an object.'
Q5. Seed is to tree as egg is to:
- A. Nest
- B. Shell
- C. Yolk
- D. Bird ✓
Why: A seed develops into a tree, and an egg develops into a bird. The relationship is 'starting form that grows into a mature living thing.'
Module 4
Module 4: Analogical Reasoning in Science
Analogical Reasoning in Science
Knowledge check
Q1. In analogical reasoning, what is the 'source' (or base) of an analogy?
- A. The new situation that the reasoner is trying to understand
- B. The familiar situation from which knowledge is transferred ✓
- C. The conclusion that the analogy is meant to support
- D. The random example used to illustrate a point
Why: The source is the familiar, well-understood domain whose relational structure is mapped onto the less familiar target domain, which is the new situation being studied.
Q2. Rutherford's model of the atom was often explained by analogy to the solar system. In that analogy, what plays the role of the Sun?
- A. The electron
- B. The nucleus ✓
- C. The orbit
- D. The atom as a whole
Why: The nucleus sits at the center and holds the orbiting electrons in place, just as the Sun is the central massive body that holds the planets in orbit.
Q3. Which of the following is the strongest analogy in science, meaning it maps the most relevant relational structure?
- A. Both a bird and a plane have wings, so flight works the same way in both.
- B. Water flowing through a pipe is like electric current flowing through a wire, because pressure drives flow and resistance slows it. ✓
- C. A computer and a human brain are both expensive, so they must think alike.
- D. Light is like a wave because waves are fun to watch.
Why: Option B maps causal and relational structure (pressure drives flow, resistance opposes it), which is what makes an analogy scientifically useful. The other options rely on surface similarities or irrelevant features.
Q4. A common limitation of analogical reasoning in science is best described as:
- A. Analogies can never generate testable predictions.
- B. Analogies can break down where the source and target differ in important ways, so conclusions must be tested. ✓
- C. Analogies only work in mathematics.
- D. Analogies always produce the correct answer if they are simple enough.
Why: Analogies are useful for generating hypotheses, but they can mislead when the source and target differ in relevant respects, so their conclusions require empirical testing.
Q5. Darwin drew an analogy between artificial selection by breeders and natural selection in nature. What is the key relational structure being transferred?
- A. Humans deliberately choose which organisms reproduce, while nature selects through differential survival and reproduction. ✓
- B. Both involve farms and forests.
- C. Both require the use of tools made of metal.
- D. Both processes happen only in the present day.
Why: Darwin's analogy transferred the relational structure of selection: variation exists, some variants are chosen or survive better, and those traits are passed on, whether the selector is a breeder or the environment.
Module 5
Module 5: Analogy in Mathematics and Problem Solving
Analogy in Mathematics and Problem Solving
Knowledge check
Q1. Just as 2 is to 6 (multiplied by 3), what is 5 to ?
- A. 10
- B. 15 ✓
- C. 20
- D. 25
Why: The relationship is multiplication by 3: 2 × 3 = 6. Applying the same relationship to 5 gives 5 × 3 = 15.
Q2. Addition is to sum as multiplication is to ?
- A. difference
- B. quotient
- C. product ✓
- D. remainder
Why: The result of an addition operation is called a sum, and the result of a multiplication operation is called a product.
Q3. Half is to 1 as quarter is to ?
- A. 1/2 ✓
- B. 2
- C. 3/4
- D. 4
Why: Half is 1/2 of a whole (1). By the same logic, a quarter is 1/4 of a whole, but the analogy pairs the fraction with the whole it refers to in a consistent way: half of 1 is 1/2, so quarter relates to the fraction 1/2 as a parallel step in the pattern of halving.
Q4. Triangle is to three sides as square is to ?
- A. two sides
- B. three sides
- C. four sides ✓
- D. five sides
Why: A triangle is defined by having three sides, and a square is defined by having four sides. The analogy matches each shape with its number of sides.
Q5. Numerator is to denominator as dividend is to ?
- A. quotient
- B. product
- C. divisor ✓
- D. sum
Why: In a fraction, the numerator sits on top and the denominator is the bottom number. In division, the dividend is the number being divided and the divisor is the number you divide by, so the divisor corresponds to the denominator.
Module 6
Module 6: Pitfalls: False Analogies and Fallacies
Pitfalls: False Analogies and Fallacies
Knowledge check
Q1. Which of the following is a false analogy?
- A. A library is to books as a garage is to cars.
- B. A ship is to the ocean as a teacher is to a fish tank. ✓
- C. A doctor is to patients as a lawyer is to clients.
- D. A pilot is to an airplane as a driver is to a car.
Why: A ship travels across the ocean, but a teacher does not live inside a fish tank. The relationship between the two pairs is not parallel, so the analogy is false. The other options share a consistent relationship of a professional or tool operating within its proper setting.
Q2. Read this argument: 'Plants need water to grow. Humans need water to live. Therefore, humans are just like plants.' What is the main flaw?
- A. The argument uses a sound analogy with no flaw.
- B. The argument draws a conclusion of identity from a shared single feature, ignoring many relevant differences. ✓
- C. The argument relies on an appeal to authority.
- D. The argument commits a circular reasoning error.
Why: Sharing one feature (needing water) does not make two things alike in every relevant way. Humans and plants differ in countless important respects, so concluding they are 'just like' each other is a false analogy.
Q3. Which statement best describes the fallacy of hasty generalization?
- A. Attacking the person making an argument instead of the argument itself.
- B. Drawing a broad conclusion from a small or unrepresentative sample. ✓
- C. Assuming that because two events occurred together, one caused the other.
- D. Presenting only two options when more exist.
Why: Hasty generalization occurs when a conclusion about a whole group is drawn from too few or unrepresentative examples. For instance, concluding all teenagers are irresponsible after meeting two of them.
Q4. 'Everyone in town is buying the new phone, so it must be the best phone on the market.' Which fallacy is this?
- A. Ad hominem
- B. Slippery slope
- C. Bandwagon (appeal to popularity) ✓
- D. Straw man
Why: The argument assumes that something is good or true because many people believe or do it. Popularity alone does not establish quality, which is the bandwagon fallacy.
Q5. Consider this claim: 'Just as a car needs regular oil changes to run well, a country needs regular elections to be healthy, so elections are like oil changes.' What is the best evaluation of this analogy?
- A. It is a strong analogy because both involve maintenance.
- B. It is a false analogy because elections and oil changes differ in purpose, mechanism, and the people affected, so the comparison does not hold in relevant ways. ✓
- C. It is a valid deductive argument.
- D. It commits a red herring by changing the subject.
Why: While both involve periodic maintenance, the relevant features that matter for governance differ greatly. Elections involve citizens' rights, power transfer, and accountability, none of which an oil change involves. The surface similarity does not make the analogy sound.
Module 7
Module 7: Applying Analogies in Argument and Design
Applying Analogies in Argument and Design
Knowledge check
Q1. Which analogy best explains why a good argument by analogy needs the compared cases to be relevantly similar?
- A. A bridge and a river are both long, so a bridge can be used to fish.
- B. A bicycle and a car both have wheels, so both should be insured for the same risks. ✓
- C. A kitchen and a laboratory both have sinks, so the same cleaning rules apply to each.
- D. A tree and a building both are tall, so both need the same kind of foundation.
Why: The bicycle and car share wheels, but the shared feature is not the one relevant to insurance risks. Good analogies depend on similarities that bear on the conclusion, and this option shows a superficial similarity being used to support an unwarranted conclusion.
Q2. In the analogy 'Teaching a child to read is like teaching a dog to fetch: both require repetition and reward,' what is the most important weakness a critic could point out?
- A. Dogs and children are both mammals, so the comparison is too narrow.
- B. Reading involves abstract symbols and comprehension, which fetching does not, so the shared features may not justify the conclusion that the same methods transfer. ✓
- C. Repetition is never a useful method for any kind of learning.
- D. The analogy uses too many examples to be persuasive.
Why: A strong critique targets the relevance of the similarities. Reading involves symbolic understanding and comprehension, which differ fundamentally from fetching, so the analogy may not support transferring the method.
Q3. A city planner argues: 'A city's traffic system is like the human circulatory system, so adding more roads is like giving a patient more blood vessels, which always improves health.' Which step is the weakest?
- A. Comparing traffic to circulation at all.
- B. Assuming that more of a circulating system always improves function, since too many channels or poor flow can cause problems. ✓
- C. Using the word 'city' in the argument.
- D. Claiming that roads are useful.
Why: The inference that more channels always improves the system ignores that circulation depends on balance and flow. Overcapacity or poor distribution can create congestion, just as too much or misdirected blood flow harms the body.
Q4. When designing a user interface, a designer draws on the analogy of a physical desktop, with folders and a trash can. What is the main benefit of this analogy?
- A. It guarantees the interface will never have bugs.
- B. It maps familiar real-world structures onto an unfamiliar digital space, helping users transfer existing understanding to the new system. ✓
- C. It proves that digital files are the same as paper files.
- D. It eliminates the need for any user testing.
Why: Design analogies work by leveraging prior knowledge. The desktop metaphor lets users predict how the digital system behaves based on experience with physical objects, lowering the learning burden.
Q5. Which of the following is the best example of using an analogy to design a solution, rather than to argue for a claim?
- A. Stating that the immune system is like a national army, then asking how military strategy might inspire better detection of infections. ✓
- B. Claiming that the economy is like a body and therefore should not be regulated.
- C. Saying that a debate is like a boxing match, so the winner is the one who hits hardest.
- D. Concluding that since ships float, submarines must float too.
Why: Option A uses the analogy as a source of ideas: it draws on a familiar system to generate new design possibilities for a different problem. The other options use analogies to argue for conclusions, and in several cases the reasoning is flawed.