Critical Thinking Tools - Rutgers...

Critical Thinking Tools

Dr. Jeff Buechner

Department of Philosophy

Rutgers University-Newark

Good reasoning: does anything go?

• “That which will demonstrate a truth to one person, possibly will never move another. Because our reason does not consist in a mathematical point: and the heart of reason, that vital and most sensible part, in which only it can be conquered fairly, is an ambulatory essence, and not fixed: it wanders up and down like a floating island, or like that which we call the life-blood …”

Jeremy Taylor, 1660, Doctor Dubitanitium or the Rule of Conscience, Bk. I, ch. 2, Rule VI; p. 485 in Vol. XI of the Works, R. Heber (ed.), London: Rivington, 1828.

When it’s good reasoning, anything doesn’t go

• Standards of good reasoning are not negotiable

• On the other hand, critical and analytical thinking skills essentially draw on the imagination—essentially involve creative thoughts

• Zen koan: How can the two co-exist without “anything goes?”

What is Critical Thinking?

• There are several different cognitive skills that are part of critical thinking—assessing how good someone’s reasons are for the claims they make, using probabilities correctly, making statistical inferences, making analogies between different subject matters, fallacies of reasoning …

Argumentation

• I will focus on one part of critical thinking—critical assessment of arguments. (Another way to put it—providing reasons for your claims about the world.)

• Argumentation is a fundamental human activity. It distinguishes us from the non-human animals.

• What is argumentation? It is the construction and evaluation of arguments.

What is an argument?

• When we make claims about how the world works, and provide reasons for those claims, we have made an argument.

• The claim we make about the world is called the conclusion of the argument.

• The reasons (or evidence, or support) we provide for that claim are called the premises of the argument.

Heated disputes and arguments

• An argument can be made by a single person. It can also be between two or more persons.

• Arguments can be very simple—stating a claim and providing a reason for it. They can be very complex—stating a claim and providing a large quantity of data to support it or complex chains of reasoning to support it.

• The verbal and psychological heat in an argument between two or more persons is not an essential feature of an argument.

• Disputes can take the form of an argument or the form of questioning whether a statement is true.

The structure of an argument

• Reasons (evidence or support) for the claim

______________________________________

A claim about how the world works

The structure of an argument

• Using the standard vocabulary, the structure of an argument is:

• Premises

____________

Conclusion

Identification of premises and conclusion

• Sometimes it is easy to identify the claim that is made and the reasons that are given for that claim.

• But sometimes it might be very difficult to make the identification. However, even if it is relatively easy to identify premises and conclusion in an argument, that does not mean the argument is good.

The next step: assessing reasons

• Identifying the premises and conclusion is not the end of the job of critically assessing an argument. It is the first step.

• The next step is the hardest step—how do you tell if the reasons are good?

• If the reasons are good (and express a truth), you are rational to believe the claim. If the reasons are bad (whether or not they express a truth), you are rational to withhold belief about the claim.

Assessing reasons

• Take a few minutes to think about how you determine whether reasons are good or bad.

• There are many false views about how to do this.

• These false views are very popular.

• Most people in the United States use these false views in assessing reasons.

• Data: 98% of all Rutgers undergraduates hold these false views. (Database: > 14,000 students, 20 years.)

The first false view about how to assess reasons

• If a reason expresses an indisputable truth, then it is a good reason. Reasons should state facts, and if the fact the reason states cannot be disputed, the reason must be good.

Why the view is false

• Premise: Jeff B. is wearing a shirt.

____________________________________

Conclusion: Jeff B will win tonight’s LOTTO game.

The premise states an indisputable truth. But is not a good reason to believe the claim (about a future state of the world)

Why the view is false

• This simple argument shows that expressing truth or expressing a fact is not enough for a reason to be good.

• A reason must express a truth. But that it does express a truth has NOTHING WHATSOEVER to do with how good a reason it is.

• That a reason expresses a truth or a fact is independent of how well it supports the claim the argument makes.

Why the false view is attractive

• Many people mistakenly think that argumentation is a simple matter of disputing “truths.” Jack says Roger Maris hit 61 home runs in 1961. Jill says that he did not. This is a dispute over whether the statement expresses a truth.

• Disputes between two or more people cover disputes over whether a statement expresses a truth, as well as whether a reason establishes a claim.

• Someone who knows more truths than another will be in a better position to verify that a statement is true. But this will not help—as you will soon see—in determining whether a reason is a good reason.

Why do we want premises to express truths?

• Consider the argument: Premise The test is positive. Conclusion You have the disease.

• Let’s not worry about the goodness of this reason. Suppose it is false. What then?

• If it is false, you do not have the information expressed by the sentence ‘The test is positive.’ Rather, you have the information expressed by the sentence ‘The test is negative.’

• Consider the argument: Premise The test is negative. Conclusion You have the disease. Is this argument the same as the first argument above? NO! They are different arguments.

• That is why you want your premises to express truths. If they do not, you do not have the argument you see in front of you. Instead, you have a different argument. If your premises truths, you do have the argument you see in front of you.


• P: The test is positive

____________________

C: You have the disease

Where your premises are false, you mistakenly think that you have the argument above.

• P: The test is negative

_____________________

C: You have the disease

In fact, this is the argument you actually have.


• Most people think that there is something wrong with a false premise—that it is not good for reasoning. But they cannot say what it is that is wrong with it.

• It is not that there is anything wrong with the false premise. It is rather that you do not have the information which it expresses. You have different information, and a different sentence than the one you are looking at.

A second false view about assessing reasons

• The problem with the previous argument is that the reason (the premise) is irrelevant to the claim. If a reason (premise) expresses an indisputable truth and is relevant to the claim the argument makes, then it is a good reason.

Why this view is false

• P: Jeff B. bought a ticket to tonight’s LOTTO game

_____________________________________

C: Jeff B. will win tonight’s LOTTO game

The premise states a truth and is relevant to the claim (you cannot win a LOTTO game without a ticket). But it is not a good reason. This shows that being true and being relevant are not enough for a reason to be a good reason.

A third false view about reason assessment

• I can see how the claim can be true given that reason. It makes sense to me. Just look at the reason. I understand what it says, and I can see how the claim can be true, given what the reason says. I can see how the reason is true and how the claim is true. That’s enough for me—the reason must be good.


• If that is your method for determining how good a reason is. You learn almost nothing about how good it is. Being able to see that the premise and conclusion can both be true only tells you that they do not contradict one another. (A contradiction is a statement, such as: I am wearing a shirt and I am not wearing a shirt.)

OBJECTION!

• Who would blindly assess arguments in this way? Only a stupid person! There is no attempt to find evidence or support!

• Sadly, neuroscience has discovered that when we understand a sentence, we tend to believe it is true.

• Where we understand the sentences in an argument, we tend to believe its conclusion is true. (The philosophy Baruch Spinoza claimed this is so. But so has modern neuroscience.)

Where to find the bad news:

• See ‘Functional Neuroimaging of Belief, Disbelief, and Uncertainty’ Sam Harris, Sameer Sheth, and Mark S. Cohen

Annals of Neurology, Vol. 65 No. 2 February, 2008, pp. 141-147

Their work builds on work done by the cognitive psychologist Daniel Gilbert.


• Imagine a scale that measures how good a reason is, and that ranges from 0 (worst) to 10 (best). If your method for determining reason goodness is to see that both reason and claim can be true, then all you learn is that the goodness of the reason is not at the zero point on the scale. But that leaves open where on the scale between 0 and 10 it is.

A true, but worthless view, about assessing reasons for claims

• A reason is good when it supports the claim, when it provides enough evidence for the claim, and when the claim follows from it.

• This is worthless. How do you tell when you have enough evidence? How do you tell when it supports the claim? How do you tell when the claim follows from it?

• If you don’t provide a method for doing these things, you have nothing.

A true, but worthless, view

• Am I being too harsh? No. Recall when you learned how to parallel park.

• Suppose the person teaching said: “Here is how to parallel park. Make sure your wheels are parallel with the curb (and about one foot from) the curb when you are finished.”

• That is worthless. You want to know how to get that to happen. What is the method that get’s that to happen? Similarly, you want to know how you get the premises to support the claim. What is the method which shows the premises support the claim?

How to correctly assess reasons

• The first thing to appreciate—it is the information expressed in a premise (reason) that you use to decide whether the claim is true. You use nothing else to do that other than that information.

• You need to determine how much information you have. How do you do that?


• Consider the argument

P: Jeff B. bought a ticket to tonight’s LOTTO game.

____________________________________________

C: Jeff B. will win tonight’s LOTTO game.

Is the reason good? Although you think it is not good, you don’t know that until you know how many possible winning numbers there are. If there is only one winning number, the reason is good.

Suppose there are 1,000,000 possible winning numbers.

Question: How much information does the premise contain, given that there are 1,000,000 possible winning numbers?


• Is there a lot of information in the premise? Or a little? Indeed, there is very, very, very little!

• How did you tell how much information was there? Since you know there are 1,000,000 possible winning numbers, and you know that I have only one of them, you know there are 999,999 possible ways for me to lose. That is, that I have only one number leaves open 999,999 possibilities. Information rules out possibilities. If you have the information that it is raining, it rules out the possibility that it is sunny. The more information you have, the more possibilities you rule out. The less information you have, the fewer possibilities you rule out.


• Suppose I bought the number 473. It is easy to imagine that number 6,791 wins. The information that I bought number 473 cannot rule out the possibility that number 6,791 wins. So I have imagined one way in which the premise is true, but the conclusion does not happen—the conclusion is false. What I have imagined gives me a reason to disbelieve the claim is true.


• Call a situation that you imagine in which you have the information expressed in the premises, but in which the conclusion does not happen, a loophole to the argument. (That is, a loophole is a situation you imagine in which the premises are true, and the conclusion is false.)

• Each loophole you imagine gives you a reason to disbelieve the conclusion

• For the previous argument, you can imagine 999,999 loopholes. So you have 999,999 different reasons to disbelieve the conclusion.


• You use your imagination to measure the size of the gap between the information expressed in the premises of the argument and the truth of the conclusion.

• The more loopholes, the greater the gap. The fewer loopholes, the smaller the gap.

• Loopholes show the information in the premises is deficient. It is deficient, because it cannot rule out the possibility the loophole describes. The more loopholes there are, the more deficient are the premises.

Loopholes

• Loopholes reveal deficiencies in the information that is expressed in the premises of an argument

How to correctly assess reasons: THE METHOD OF LOOPHOLES

• The better a reason is, the more possibilities it rules out. Thus, the fewer loopholes there are.

• The method of loopholes is the only method for determining how good a reason (premise) is.

• Notice you have to have a strong imagination to be good at reasoning.

The method of loopholes and scientific method

• Loopholes are alternative hypotheses (alternative to the hypothesis you think is true) which are compatible with the data (the premises).

• Scientific experiments are designed to acquire information which rules out alternatives compatible with the data.

• Defining probabilities over a probability space allows a scientist to make a precise claim about how well the data supports an hypothesis.

The method of loopholes and scientific method

• The point of one kind of scientific experiment is to provide information which will rule out alternative scientific hypotheses compatible with the data. That is, the experiment supplies additional data incompatible with the alternative scientific hypothesis.

• When information in a premise set is deficient, there are alternative hypotheses (LOOPHOLES) compatible with that premise set. To rule out alternative hypotheses, you must ADD additional information (i.e., premises) to your premise set.

• Determining which information (i.e. premises) need to be added is like doing a scientific experiment.

The method of loopholes and completing a story

• Finding a loophole is to find an alternative way to complete a story. Consider an argument as having the structure: a starting point (i.e., premises) and an ending (i.e., conclusion). The challenge is for you to find a different way of ending the story.

• The more ways you can end a story (while respecting the starting point), the worse the premises are for supporting the conclusion.

• The more powerful your imagination, the more alternative stories you will find.

The method of loopholes and completing a story

• Finding loopholes is like telling a different story and it is like finding alternative scientific hypotheses in science.

• So there is an analogy between story-telling and doing science.

• What makes the analogy plausible is that fundamental principles from the theory of reasoning underlies it.

A bridge between science and the humanities

• The method of loopholes is the bridge that connects, on the one hand, scientific reasoning and scientific method, and, on the other hand, narrative story telling.

• To critically assess arguments using the method of loopholes is to live in both the world of science and the world of story creation.

Too good to be true?

• No—it is simply unexpected. We have compartmentalized science from the humanities, and take both of them to be wholly other from each other.

• This compartmentalization may be important where these activities are institutionalized.

• But the compartmentalization does not reflect any intrinsic boundaries they might possess.

• Now back to basics …

OBJECTION!

• I object! You cannot imagine whatever you like. There is a fact of the matter as to which number wins. You are not free to imagine that 6,791 wins.

• Rejoinder to the objection: You ARE free to imagine 6,791 wins. Yes, there is a fact of the matter as to which number wins. But the point of the argument is to show that number 473 wins. And the only information that argument provides to establish that claim is that I bought number 473. It is compatible with that information that 6,791 wins. The arguer does not know which ticket wins. If he did know that, there would be absolutely no reason to argue!

• You do not need to argue that such-and-such is the case if you already know that such-and-such is the case.

OBJECTION!

• To repeat: the only information you have to go on to decide whether the claim is true is what is expressed by the premise. You know nothing else that what the premise says.

• What the premise says is deficient if it cannot rule out some possibility in which the claim is false. Sure, 6,791 might not win. But you do not know that. If you did, you would have added that information to the premise (to get: I bought number 473 and number 6,791 will not win).

• Since you do not know 6,791 will not win, it is possible it will win, and it is a deficiency in your premise that it does not rule out that possibility.

Some distinctions

• If an argument is loophole free, it is a valid argument. When an argument is valid, it is impossible for you to doubt the truth of the conclusion, given the premises.

• If an argument has at least one loophole, it is invalid. However, there can be invalid arguments with good reasons (and few loopholes), and invalid arguments with bad reasons (and many loopholes).

Using the method of loopholes to assess an argument

• Here is a simple argument

P: Jack jumped out of an airplane at 30,000’ altitude

without a parachute.

_______________________________________________

C: Jack died upon hitting the ground (our earth).

Is this argument valid? Can you think of a loophole to it?

A constraint on imagining loopholes

• When you imagine a loophole, it must be a situation in which the premises of the argument are true (that is, a situation in which you have the information that is expressed by the premises).

• Why? If you imagine a situation in which the premises are false, you imagine a situation in which you do not have the information expressed by the premises.

• Such a situation is irrelevant to showing a deficiency in the information that is expressed by the premises.

Using the method of loopholes to assess an argument

• Jack went to the liquor store with the intention of buying a bottle of expensive wine. Arriving at the store, he discovered he had forgotten his wallet. His guests at his dinner party tonight will be unhappy.

• What are the premises of this argument? What is the conclusion?

• Is it valid? Is it invalid? If so, describe loopholes to it.

Another argument

P1 Jack likes to chew gristle when he has supper.

P2 Chewing gristle usually clean’s one’s teeth.

_______________________________________

C Jack does not have to brush his teeth.

Another argument

P1 From a policy standpoint, building a non-governmental body for implementing biosecurity policy seems like a good investment.

P2 Initiatives for self-regulation developed by the synthetic biology community may be more effective than government regulation precisely because they are more likely to be respected and taken seriously.

___________________________________________________

C Protecting the public from the risks of synthetic biology depends on the scientific community’s will, capacity, and commitment to regulate itself.

Deficiencies of information

• Whenever you find a loophole to an argument, you have found a deficiency in the information expressed in the premises. To make a better argument, you would have to find out if the missing information (which would rule out the loophole) is some fact.

• If it is a fact, then you add it to the argument, making an argument that has stronger reasons for its claim.

Another argument

• Without natural selection, evolution would cease. But natural selection no longer operates in human beings, for it requires that a greater proportion of weak individuals than strong ones perish before reproducing. Modern medicine, however, permits the weak to survive and reproduce as readily as the strong. Human evolution has therefore come to a standstill.

A complex argument

Natural selection requires + Modern medicine permits the weak to

that a greater proportion of weak individuals survive and reproduce as readily as the

Than strong ones perish before reproducing strong

____________________________________________________________________________________

↓

Without natural selection, + Natural selection

evolution would cease no longer operates in humans

_________________↓____________________ Human evolution has come to a standstill

Analyzing the reasoning

• There are two subarguments in the complex argument. The bottom-most subargument is valid but only if one takes ‘evolution to cease’ to be synonymous with ‘evolution has come to a standstill.’ The topmost subargument is invalid—there are loopholes. For instance, evolution requires that …, but the author does not specify what in evolution it is required for. Another loophole: modern medicine permits this, but the weak die from accidents.

Reasoning and truth

• The argument also suffers from false premises. It is the responsibility of the critic of the argument to determine whether or not the premises are true. This means that the critic must learn something about evolutionary biology.

When is an argument good?

• There are two different features of a good argument: strength of reasoning and whether premises are true.

• Strength of reasoning = how good are the reasons

• How good a reason is happens to be independent of whether it is true. How good a reason is = how good is the information.

• Is the reason true = do we actually have that information

Goodness of arguments

• If reasons are false, you do not have that information. You have different information. That is, you have different premises. Thus you have a different argument. That is why good arguments need to have true premises. If the premises are false, you do not have that argument.

• If the reasoning is bad, it is not rational to believe the claim since there is not enough information to support the claim).

• If the premises are false, it is not rational to believe the claim (since you do not have the information, and thus do not have the argument—you have a different argument).

What is logic?

• Logic studies only one kind of argument—valid arguments.

• Sometimes it is hard to determine if an argument is valid—if it is loophole free.

• Logic helps you in doing that—the form of the argument determines that it is valid.

• Recognize the form, and you know that it is valid—loophole free.

What is logic?

• Any argument that has the form

P1 If A then B

P2 A

_______________

C B

is valid. (The letters ‘A’ and ‘B’ stand for any sentence whatsoever.) Knowing this saves you a lot of work. You can see instantly it is valid, without having to worry about what the words mean, and without having to search for loopholes.

Why logic is useful

• That a complex argument is valid can be difficult to determine if you cannot see the form in the argument.

• Consider the following argument: It’s not true that either the Red Sox will win or the Yankees will win. But if the Tigers win, then if the Yankees do not win, the Red Sox will win. Therefore, the Tigers will not win.

Why logic is useful

• The preceding argument is valid—loophole free. Perhaps you had a hard time with it—just hearing it can be daunting.

• But if you know logic, you can easily SEE that it is valid, because it has the form of a valid argument.

• Logic is an amazing tool for seeing that arguments are loophole free. It saves you a lot of work.

Here is why the argument is valid

• P1: ~(A v B)

• P2: C --> (~A --> B)

• 3. C --> (A v B) 2, implication

• 4. ~C 1,3, Modus tollens

where A = The Yankees will win

B = The Red Sox will win

C = The Tigers will win

Yet another argument: valid or not?

P1 If the theory of evolution is correct, then man descended from the primates.

P2 Man did indeed descend from the primates

_______________________________________

C The theory of evolution is correct

How good is the reasoning?

• It is valid only if there is only one consequence to the theory of evolution—that man descended from the apes. But if there are additional consequences, the reasoning is bad. It is a classic case of affirming the consequent—which is valid only when the consequent is uniquely contingent upon the antecedent

• If A then B, B

________________ affirming the consequent

A

FOX TV, GLENN BECK, AND BAD REASONING

• Now that you know how to correctly assess reasons, and have a bit of experience in doing that, you can see why Glenn Beck is guilty of bad reasoning. He has a false view about assessing reasons. Recall that a loophole to an argument may or may not be true. You do not know whether it is true—unless you actually determine that it is (or is not) true.

• However, Glenn Beck thinks that a loophole in a argument is ALSO a truth about the world. That is a false view, and a dangerous view. Loopholes only show that the information in an argument’s premises do not rule out possibilities that conflict with the argument’s conclusion. But that does not mean a loophole is a truth about the world. You simply do not know that. To assume you do know that is a dangerous fallacy of reasoning, and it reveals an ignorant mind.

Glenn Beck’s fallacy of reasoning

• Here is how Glenn Beck’s ignorance—his fallacious reasoning—plays itself out in assessing an argument.

• P: Jeff B. bought ticket 423 to tonight’s LOTTO game.

C: Jeff B. will win tonight’s LOTTO game.

Loophole: Ticket 1718 is the winning ticket.

Glenn Beck: Therefore, ticket 1718 IS THE WINNING TICKET!

Another false view about reason assessment

• Here is another false view about reason assessment that you can only appreciate after you know how to correctly assess reasons.

• The view is that correctly assessing a reason is making a decision about the reasons.

Intelligent literature searches

• The method of loopholes suggests a method for engaging in intelligent literature searches.

• First, conceptualize the project on which you are working as an argument: the project thesis is the claim and the evidence, reasons … are the premises.

• Find loopholes.

• Use each loophole to look for literature. Take the airplane argument above. One loophole is that Jack used a hang-glider. An intelligent literature search would be where you look in the literature for evidence that there were hang-gliders on board that airplane.

Using the method of loopholes to solve ethical dilemmas

• Ethical dilemmas—indeed, any kind of dilemma—can be solved using the method of loopholes.

• A dilemma has the form: either A or B, where A has costs and gains and B has costs and gains. Usually the costs are quite bad.

An example of solving an ethical dilemma

• An old ethical dilemma: a father’s 2 year old son will die of an acute bacterial infection unless he is given expensive antibiotics, which the father cannot afford and the druggist will not give to him on credit. He steals the drugs and saves his son’s life, but spends time in jail for the theft.

• The dilemma: steal the drug (bad) and your son lives (good) OR don’t steal the drug (good) and your son dies (bad).

• Formulate an argument whose conclusion is that the father has to steal the drug. One premise is that the father does not want his son to die. The other premises involve the situation: the son will die without the antibiotic, the druggist won’t give them to the father on credit, the father cannot afford them, the father does not want his son to die.

The technique

• Take one of the two odious horns of the dilemma as the conclusion of an argument. In our example, we take as the conclusion that Jack must steal the antibiotic.

• For the other horn of the dilemma, append to it that Jack does not want that to happen. Then negate the enriched statement, and add it to the argument as a premise. In our example, we take as a premise that Jack does not want his son to die. (This is obtained from the other horn lof the dilemma by adding ‘Jack does not want’ to ‘Jim will die,’ and negating it.)

• Take as premises all of the relevant information that describes the situation in which the dilemma arises.

The ethical dilemma recast as an argument

P1 Jim (2 years old) will die of an acute bacterial infection.

P2 An expensive antibiotic will save his life by stopping the infection.

P3 Jack, Jim’s father, cannot afford the antibiotic.

P4 The druggist will not give the antibiotic to Jack on credit.

P5 Jack does not want his son to die.

____________________________________________________

C: Jack must steal the antibiotic

Loopholes are ways out of the ethical dilemma

• Can you think of a loophole to the preceding argument? Each loophole is a way out of the dilemma. You do not do A (don’t steal the drug and let your son die) and you do not do B (steal the drug).

• Formal excursion: A dilemma has the form A or B. To escape it, find a situation in which Not-A and Not-B. Typically in a dilemma, one of the horns is especially odious (Jim will die), while the other horn is less odious (Jack will go to prison). Escaping the horns is to find a solution to the problem that does not require that Jack steals (and so he does not go to prison) and in which Jim lives.

• Here is one loophole: You ask your neighbors to hold a charity block party at which friends donate money. You use the money to purchase the antibiotic.

The subtle semantics of ‘should’

• Arguments whose conclusion has the form “S should do p,” are notoriously slippery to critically evaluate, primarily because the word ‘should’ poses interpretive obstacles.

• For example, consider the argument: P: Arsenic is poisonous. C: You should not eat it.

• One might think a loophole for this argument is that someone who wishes to commit suicide should eat. But this is not a loophole, since it does not describe a situation in which the conclusion is false. Why?

• The reason why is that ‘You should not eat it’ must be properly interpreted. What is the meaning of ‘should?’ It means that you should not eat it if you wish to continue to live. Eating it in order to commit suicide does not show that it is false that you should not eat it if you wish to continue to live. Indeed, you should eat it if you wish to die.

• There are several other ostensibly obvious loopholes that are not genuine loopholes, for the same reason. Are there any loopholes? Any such loophole must describe a situation in which you should eat it in order to live. Possibly, one loophole is eating small amounts of it in order to cure—homeopathically—an illness that will kill you if not treated.

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