Essential tools to thinkwithDecember 18, 2010

" data-medium-file="" data-large-file="" class="size-medium wp-image-535 " title="Turning the Tables" alt="" src="" srcset=" 300w, 150w, 490w" sizes="(max-width: 300px) 100vw, 300px" />Despite appearances, the 2 tabletops are identical in both size and shape.

You are watching: If some men are doctors and some doctors are tall, does it follow that some men are tall?

I’m prepare a special lesson because that my high college students top top the subject of critical thinking and the scientific method. In the first half the the lesson, i aim to threaten the students’ certainty about what lock think lock know, by demonstrating the many varieties of errors and biases we space all vulnerable to. I’ll begin with optical illusions, prefer Roger Shepard’s “Turning the Tables.” closely measuring the two tabletops mirrors that castle are the same in both size and shape, even though us feel an extremely strongly the this is no the case.


Exactly one of the doors has a new car behind it. After ~ you choose door 1, the hold opens door 3 to reveal a goat. That then offers you the possibility to switch to door 2. Have to you?

We recognize we cannot constantly trust our senses, however surely our intuitions are much better in more theoretical areas? try this: if a bat and also a round together cost $1.10, and also the bat expenses $1.00 much more than the ball, how much does the sphere cost? sounds easy, and it is, but a majority of college students offer the wrong answer (hint: it’s no 10 cents). Our intuitions room especially negative when it pertains to probability. I’ll existing the famous Monty room problem, come which numerous smart world refuse to accept the correct equipment (switching doors doubles your opportunities of winning) even after it’s defined to them. I may also mention the gambler’s fallacy — if ten continually tosses of a same coin come up heads, is tails much more likely come come up next? — i beg your pardon makes many money for casinos.

Instead that jumping come conclusions based on intuition, we can attempt to construct formal logical inferences: if all Greeks space handsome, and also Socrates is a Greek, climate Socrates is handsome. Perform we ever before make mistake in our usage of logic? think about this: if some men are doctors, and some doctors are tall, can we conclude the some guys are tall? (No.) Or this: if we assume the all reptiles lay eggs, and we know that alligators place eggs, does the follow the alligators are reptiles? (Nope.)

I following turn come the fallacy that assuming the correlation means causation. If the percent of black color people among those convicted of violent crimes is substantially greater 보다 the portion of blacks in the population, have the right to we conclude that blacks room inherently more violent? No: it might be that many judges space white and also some space prejudiced, or that blacks space poorer on average and poverty reasons crime, or the blacks are treated together second-class citizens developing a self-fulfilling prophecy, etc. An additional example: let’s say surveys display that human being who usage olive oil are less likely to build heart condition than civilization who use other oils. Does that follow the olive oil helps prevent heart disease? think about that olive oil is more expensive than other oils, so human being who purchase olive oil are much more likely to belong to higher socio-economic groups — implying a more healthy diet in general, a higher chance of belonging to a gym, an ext money to spend on health and wellness care, etc. That course, this does no prove the olive oil go nothing to prevent heart disease: merely that the causal link cannot be deduced native the correlation alone.

Perhaps the many subtle causes of error are cognitive biases. I’ll talk around confirmation bias: people tend to give an ext weight to proof that support what they currently believe; they have tendency to seek data that check their hypotheses instead of attempting come disprove them; they have tendency to remember instances that assistance their theories and also forget those the don’t. One research was carried out on two teams of people: one team contained world who were in favor of resources punishment, and also the other team contained people who were against it. All subjects were presented the same set of data, which had evidence and argument for both political parties of the issue. Participants native both groups tended to report that the data had caused them to strengthen their initial beliefs! So much for objectivity. Confirmation bias is additionally what keeps plenty of superstitions alive: people an alert those times as soon as unlucky occasions happen on the 13th floor, and disregard the times as soon as they don’t, or once they take place on various other floors.

I’ll conclude the very first part that the lesson v the fallacy of appeal to authority: “Einstein was a genius, so everything he said should be so;” “If it’s created in the Bible, it should be true;” “Democracy is the best kind of government, due to the fact that that’s what they taught united state in school;” “My teacher says that appeals to authority are logical fallacies.” The truth or falsity that a case is not impacted by the government of the claimant; also Einstein do mistakes.

So far, then, we’ve seen that our senses can deceive us; ours intuitions are frequently wrong; we space prone to logical fallacies and cognitive biases; it’s daunting for united state to be objective; and even smart people can be mistaken. Is it difficult to achieve reliable information around the world?

Enter the scientific method. I’ll current the straightforward model of gathering evidence, supplying a theory to describe the observed phenomenon, do predictions based on the hypothesis, trial and error those predictions, and revising the hypothesis based on brand-new data. This method is no infallible, of course, however science makes use of numerous mechanisms because that minimizing errors and correcting them: transparency, documentation, reproducibility, peer review, etc.

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To further explore the nature of clinical theories, I’ll usage Carl Sagan’s instance of the fire-breathing dragon in mine garage: when my friend asks to watch it, ns reply the it’s invisible. She then says that we spread flour top top the floor and also look because that tracks, yet I define that this dragon floats in the air. And there’s no suggest in trying come touch it, either, due to the fact that it’s incorporeal. At this suggest my friend would certainly hopefully begin to wonder what makes me think the dragon exist at all. The dragon theory is unscientific because it’s unfalsifiable — over there is no proof that might possibly disprove it. This renders it useless: if there might never be any detectable difference in between a human being in i beg your pardon the dragon exists and also one whereby it doesn’t, why must we care?

Another advantageous heuristic because that judging scientific theories is Occam’s razor: all various other things being equal, the most basic explanation of the truth is generally the appropriate one. In various other words, we have to strive to minimize unnecessary or arbitrary assumptions. If i hear the clacking that hoofs coming from inside a race track, for instance, it might theoretically be a zebra escaped indigenous the zoo, or a recording designed to fool me, or an extraterrestrial language — but lacking any evidence for those hypotheses, it provides sense come tentatively assume the it’s steeds I’m hearing. It’s necessary to stress that all scientific knowledge is provisional: we can never attain absolute certainty, however our confidence in an hypothesis grows through the amount of supporting evidence. A clinical theory is a hypothesis of sufficient explanatory power which has endured all attempts to falsify it. But all theories are constantly open to review based on brand-new evidence.