Workshop: Science is Empirical and InductiveA. Gameshow Part 1: Is that Valid?Let’s play: Is that Valid? In teams of four, evaluate the following 12 arguments for deductivevalidity (not soundness). At the end, we’ll see which team is the winner!As a reminder, here are the steps for using Venn diagrams to examine the validity of(categorical) deductive arguments:a) Make sure each statement (premises and conclusion) is a categorical statement, andthere are exactly three terms: e.g. Queenslanders-Australians-swimmers.b) Draw three intersecting circles, and label them.c) Fill in Universal statements first (All …, No …), and particular second (Some …). Ashaded region is empty. A tick indicates at least one object in that region.d) If a “Some …” region is split, use question marks “?” instead of a tick.e) Determine the corresponding areas related to the conclusion.f) If the conclusion is contained in the premises, then the argument is valid. Otherwise,it is invalid.Apply this method (or any other method) to the following arguments to determine whetherthey are deductively valid. Alternatively, you could show that an argument is invalid with acounterexample: an argument of the same form with true premises and a false conclusion.Luke BarnesThe Method3. Fill in Universal statements first (All …, No …),particular second (Some …), as follows24A BAll A are BA BNo A are BA BSome A are B ✓A BSome A are not B ✓ Deductively valid?1.All cats are evil. All tigers are cats. So, all tigers are evil.2.Some black cats catch mice. Any cats that catch mice aregood cats. Therefore, some black cats are good cats.3.Some students are not Queenslanders. But noQueenslanders are frostbitten. Therefore, some studentsare frostbitten.4.All A are B. No B is C. Therefore, no A is C.5.No television stars are certified public accountants, butall certified public accountants are people of goodbusiness sense. It follows that no television stars havegood business sense.6.All teenagers are rebellious, and some teenagers playvideo games. Hence, some people who play video gamesare rebellious.7.No intellectuals are successful politicians, because no shyand retiring people are successful politicians, and someintellectuals are shy and retiring.8.If someone is a biologist, then they’re a scientist. Andonly scientists are clever. Therefore, all biologists areclever.9.Whenever I’m tired in the morning, I drink coffee. I’malways tired in the morning, so there is not a day when Idon’t drink my morning coffee.10.Not all students are good spellers. Only left-handedpeople are bad spellers. Therefore, it isn’t true that nostudents are left-handed.11.Olympians are fast or strong. Johannes (an Olympian) isfast. Therefore, Johannes isn’t strong.12.Good medicine makes you better. My patented MiracleCureTM is good medicine. So, my patented Miracle CureTMwill make you better. B. Gameshow Part 2: Is that an Empirical Statement?Let’s play: Is that an Empirical Statement? In teams of four, evaluate the following 25statements: are they about the natural world, and able to be investigated using theevidence of our senses? We’re not concerned here with whether they are true. At the end,we’ll see which team is the winner! Empirical?1.The colour of the sky is blue.2.The colour of the sky is blue, because of the way light scatters off atoms inthe atmosphere.3.The colour of the sky is beautiful.4.The atmosphere of Earth is heating up.6.If Earth continues heating up, rising sea levels will engulf island nations.5.If we keep burning fossil fuels, the Earth will continue heating up.7.If we keep burning fossil fuels, the Earth’s climate won’t change at all.8.We should stop burning fossil fuels.9.If we find preserved dinosaur DNA, we could clone dinosaurs.10.I’ve seen Jurassic Park – we shouldn’t clone dinosaurs.11.If this soccer ball is a sphere with radius r, then its volume is 4/3 r3.12.This soccer ball is (approximately) shaped like a sphere.13.If a planet around a star obeys Newton’s law of Gravity, the shape of its orbitis an ellipse.14.The shape of the Earth’s orbit is an ellipse.15.No mammals have gills.16.Some mammals have gills.17.All mammals nourish their young with milk.18.The chemical formula for water is CO2.19.Usain Bolt is the greatest living athlete.20.From a horoscope: “Over the next 7 weeks, a growth experience couldpresent itself.”21.New Miracle GrowTM fertilizer increases flowering by up to 15%, or more!22.Astronomy shows that the Earth is very small, compared to the universe.23.Astronomy shows that the Earth is insignificant, compared to the universe.24.Age discrimination affects mental health.25.Age discrimination is immoral. C. Reading Primary Historical SourcesIn your teams of four, you will have a choice of two readings from pre-revolution scientists.Decide amongst yourselves which one you will all read. The readings are provided in aseparate PDF. Once you have chosen, answer the questions below. Each group shouldnominate someone to lead the discussion.The first is an excerpt from “On Youth and Old Age, On Life and Death, On Breathing” byAristotle, 350BC. In it, Aristotle explains the purpose of breathing – according to his theoryof the human body, based on the four elements. The second is an excerpt from “De SphaeraMundi” (On the Sphere of the World), by Johannes de Sacrobosco, 1230 AD. This is amedieval textbook on astronomy, which was used in university courses for hundreds ofyears. We’ll look at how he demonstrates that the Earth is a sphere.Reading 1: On Youth and Old Age, On Life and Death, On Breathing – AristotleWe’re going to reconstruct Aristotle’s reasoning on the purpose of breathing. Recall the fourvital fluids (or humors), which mirror the four elements: Black bile is earth – cold and dry;phlegm is water – cold and moist; blood is air – warm and moist; yellow bile is fire – warmand dry.1. Read the first paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. The first sentence: is this an observation, or a theory?c. Why must the heart be the source of innate warmth in living things?2. Read the second paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. Why must there be “some way of cooling the heat resident in the source ofwarmth”?c. What kind of argument is this? What is Aristotle drawing on, to reachconclusions about the heart?3. Read the third paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. There are three arguments in this paragraph against the idea that breathing isfor the purpose of nutrition. See if you can identify all three.c. We now know that this conclusion is incorrect: breathing takes in oxygen,which is a vital energy source. What is wrong with the arguments above?4. Read the fourth (final) paragraph. Summarize the paragraph in two sentences.a. Share your summary. Are there any parts you didn’t understand?b. Why must the cooling effect of air travel to all parts of the body?c. How does the cooling effect of air travel throughout the body?5. Put it all together: according to Aristotle, why do we breathe?6. Aristotle is correct to say that breathing contributes to cooling, but he is wrong todismiss breathing a source of “nutrition” or energy. Prepare your case to try toconvince Aristotle that he is mistaken. What evidence would you need?Reading 2: De Sphaera Mundi (On the Sphere of the World) – Johannes de SacroboscoWe’re going to reconstruct Sacrobosco’s case for the roundness of the Earth. This case is notoriginal to Sacrobosco – De Sphaera Mundi is more like a textbook than original research.Sacrobosco’s system, like that of Ptolemy and Aristotle, assumes that the stars revolvearound the Earth, all at a fixed (large) distance – the sphere of the stars. An eclipse of themoon occurs when the moon passes into the shadow of Earth.1. Read the first paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. What is the observational evidence in this paragraph? What is needed tomake these observations?c. Why does this evidence point to a round earth? What would we expect tosee if the Earth were a flat disk inside spherical shells of stars, the sun andplanets?2. Read the second paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. Draw a diagram to illustrate this argument. Draw Earth as a sphere with anorth and south pole. Consider a person standing near the north pole, andwhich part of the sky they can and can’t see. Then move the person south.What changes?c. What would we see if the Earth were a flat disk inside a spherical sky?3. Look at the diagram. It illustrates another of Sacrobosco’s arguments for theroundness of the Earth. See if you can work out what his argument is.4. Read the third paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. Draw a diagram to illustrate this argument. Draw the sphere of the stars, anda small Earth that is off-centre. Now consider an observer on the surface ofEarth, who has negligible height compared to the Earth – what part of the skycan they see?c. Aristotle argued that the Earth is at the centre as follows: earth (thesubstance) naturally moves to the centre of the universe; thus, the Earth (theplanet) must be located there. Compare this argument to Sacrobosco’s.5. Read the fourth paragraph. Summarize the paragraph in two or three sentences.a. Share your summary. Are there any parts you didn’t understand?b. Draw a diagram to illustrate this argument. Draw the sphere of the stars.Now draw an Earth at the centre of the sphere, and about a third the size.Now consider an observer on the surface of Earth – what part of the sky canthey see?D. Informal FallaciesAs well as formal fallacies, an argument can go wrong because one of the premises is false,or because the inductive force of the argument is weak, or because the argument isincomplete. Informal fallacies come in a large number of types, of which fifteen are below.In your teams, match each informal fallacy with an example of the fallacy on the next page.• Ad hominem: attacking a person on irrelevant grounds, instead of their argument.• Argument from authority: experts can be wrong. Not necessarily fallacious – someauthorities are more reliable than others.• Argument from silence: arguing from a lack of evidence. Not always fallacious, but itcan be difficult to establish that absence of evidence shows an evidence of absence.• Biased sample: drawing a conclusion about a population from a sample that is notrepresentative of the population.• Correlation is not causation: if A and B are correlated, there are three possibilities: Acauses B, or B causes A, or some third thing C is the cause of both A and B. It isfallacious to fail to consider all these possibilities.• Equivocation: a crucial term has distinct meanings in different parts of theargument.• Fallacy of the single cause: reasoning as if there is only one cause of a particulareffect. There could be multiple causes.• False analogy: just because A is similar to B in some respects, doesn’t mean that Awill be similar to B in all respects.• False dichotomy: presenting only two options, when there are actually more.• Genetic fallacy: identifying the causes of someone’s belief doesn’t invalidate thereasons for that belief.• Hasty generalisation: drawing a general conclusion from too few examples.• Slippery slope: action X will (or could) result in consequence Y, and we don’t want Y.Not always a fallacy, for example: “X will create a legal precedent for Y.” But it canrequire speculation about the future.• Straw-man fallacy: misrepresenting an idea so that you can more easily refute it.• Subject/motive shift, or Bulverism: instead of evaluating an idea, we speculateabout the motives of adherents to the idea. You’re not a mind-reader, and whateverpeople’s motives, they may have good reasons for their beliefs as well.• Tu quoque, or “whataboutism”: the fact that someone doesn’t live up to their ownprinciples doesn’t make those principles false. Which fallacy?1.Evolution says that monkeys turn into humans. Butthere are still monkeys. So evolution is false.2.People who defend socialism are just too lazy towork, so they want to take your money. Therefore,socialism is false.3.Either an asteroid strike killed the dinosaurs, or asuper-volcano did it. We’ve ruled out the supervolcano hypothesis. Therefore, an asteroid strikekilled the dinosaurs.4.Students who eat breakfast perform better atschool. Therefore, breakfast causes students toperform better at school.5.I was sold a faulty car by someone with red hair. So,I don’t trust people with red hair.6.If they laughed at a genius like Galileo, then they’lllaugh at me. They laughed at Galileo. So it’s hardlysurprising that they laugh at me.7.Dad tells me not to smoke because I’ll get cancer.I’m not listening to him: he smokes a pack a day!8.They say that poverty causes crime. But that can’tbe right: most criminals are men, and men aren’tpoorer than women.9.Einstein believed that his theory of gravity didn’tpredict gravitational waves. Therefore, his theorydoesn’t predict gravitational waves.10.Everyone I know is voting for Labor. So there’s noway that Scott Morrison is going to win theelection.11.No man can kill the Witch-king of Angmar. Eówyn(shieldmaiden of Rohan) is a woman. Therefore,Eówyn can kill the Witch-king of Angmar.12.If we allow the government to make the vaccinemandatory, they could make any medical treatmentmandatory.13.You’re only scared of sharks because of your animalinstincts. They’re fine!14.You can’t possibly take his experimental resultseriously – he voted for Trump!15.The writings of Marco Polo never mention theGreat Wall of China. Therefore, he never went toChina.
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