As discussed in Chapter 2, there are seven types of critical thinking question in the TSA:
Before delving into each of these question types, it is worth considering a few points about arguments in general.
Arguments are attempts to persuade by providing reasons (or premises or propositions) in support of a particular claim (or conclusion). In a deductive or ‘truth-preserving’ argument, the conclusion follows from the premises as their logical consequence; in an inductive argument, the conclusion is merely supported or suggested by the premises.
In many cases, arguments are implicit, meaning that their rational structures and their relationships are not immediately apparent, and need to be made explicit through analysis. In some cases, one element (or several elements) of an argument may appear to be missing because it is implicitly assumed, that is, taken for granted.
Each premise and the conclusion can be either true or false. The argument itself can be either valid or invalid. An argument is valid if and only if the truth of the conclusion is a logical consequence of the premises, regardless of the truth or falsity of the premises. Thus, the following is a valid argument.
All organisms with wings can fly. (Premise 1, False)
Penguins have wings. (Premise 2, True)
Therefore, penguins can fly. (Conclusion, False)
Although the above argument is valid, it is unsound. For an argument to be both valid and sound, all of its premises have to be true. In the TSA, the emphasis is much more on validity or logic than on soundness or truth. For an inductive argument, the equivalent of soundness is cogency. An inductive argument is cogent if its premises are true and they render the truth of the conclusion probable.
When trying to decide whether the logical form of a deductive argument is valid or invalid, it can be useful to formulate a counter example, or counter argument, with exactly the same form, with premises that are true under a given interpretation but a conclusion that is false under that interpretation.
Argument:
Some farmers are landowners.
Some landowners are aristocrats.
Therefore, some farmers are aristocrats.
Counter argument:
Some insects are herbivores.
Some herbivores are mammals.
Therefore, some insects are mammals.
To formulate counter arguments, it can help to summarise the argument in symbol form. Both of the above arguments follow the same (invalid) form:
Some A are B.
Some B are C.
Therefore, some A are C.
A logical fallacy is some kind of defect in an argument, and may be unintentional or intentional (with the aim to deceive).
A formal fallacy is an invalid type of argument like the one above: it is a deductive argument with an invalid form, and is invalid irrespective of the content of the argument.
An informal fallacy is an argument that can be identified only through an analysis of the actual content of the argument. Informal fallacies often turn on the misuse of language, for example, using a key term or phrase in an ambiguous way, with one meaning in one part of the argument and another meaning in another part of the argument (fallacy of equivocation). Informal fallacies can also distract from the weakness of the argument, or appeal to the emotions rather than to reason. Informal fallacies are frequently although not exclusively found in inductive arguments, and can be hard to uncover. One way to think about it is that, whereas formal fallacies are invalid, informal fallacies are unsound.
The following non-exhaustive list of formal and informal fallacies should give you a greater insight into bad arguments. When reading through the list—which I think should be rather enjoyable—don’t worry about what the fallacies are called. Just focus on how they work—or don’t!
False conversion involves switching the subject and predicate terms of a proposition, in a proposition using ‘all’ or ‘some/not’.
All wise men are bachelors. Therefore, all bachelors are wise men.
Some books are not novels. Therefore, some novels are not books.
Exclusive premises is drawing a conclusion from two negative premises. No conclusions can ever be drawn from two negative premises.
No politicians are philosophers, and no philosophers are bankers. Therefore, no politicians are bankers.
Affirming the consequent (converse error) is to infer the converse from the original statement. The argument has the invalid form: If A, then B. B. Therefore A.
If I have the flu, then I have a fever. I have a fever. Therefore, I have the flu.
Denying the antecedent (inverse error) is to infer the inverse from the original statement. The argument has the invalid form: If A, then B. Not A. Therefore, not B.
If I were rich, I would be able to be happy. I am not rich. Therefore, I cannot be happy.
Illicit process of the major term (illicit major) is when the major term is distributed in the conclusion, but not in the major premise. (If all members of the term’s class are affected by the proposition, the class is ‘distributed’; if not, it is ‘undistributed’.) The argument takes the form: All A are B. No C are A. Therefore, no C are B.
All psychiatrists are doctors (major term). No surgeons are psychiatrists. Therefore, no surgeons are doctors.
Illicit minor is when the minor term is distributed in the conclusion, but not in the minor premise. It takes the form: All A are B. All A are C. Therefore, all C are B.
All doves are birds. All doves are animals (minor term). Therefore, all animals are birds.
Analogical fallacy is the assumption that things that are similar in some respect are similar in all respects.
Hellebores, snowdrops, and crocuses all flower in early spring. Hellebores are deadly, so snowdrops and crocuses must also be deadly.
Cum hoc ergo propter hoc (‘With this, therefore because of this’) is the assumption that because two events occur together or are otherwise correlated, one must have led to the other.
Schizophrenia is so common in cannabis users that no one can possibly doubt that smoking cannabis is an important cause of schizophrenia.
Gambler’s fallacy is the false assumption that the outcome of one or more statistically independent events can influence the outcome of another or others.
Hailstorms have damaged the vineyards of Burgundy every year for the past three years. So next year is very likely to be a good vintage.
The runaway train refers to an argument that supports a particular course of action, while also supporting much more of it.
We should increase the marginal rate of income tax from 45% to 50% because this will lead to greater income redistribution.
Begging the question is to argue in circles, supporting the conclusion by means of itself.
To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.
False precision is to talk about inexact notions in terms of exact numbers.
Picasso’s ‘Boy in Blue’ is four times more evocative than Cézanne’s ‘Mont Sainte-Victoire’.
My house is ten times cosier than yours.
Genetic fallacy is to reject an argument on the basis of its source or origins.
Eugenics is popular with fascists. I could never condone any idea that is popular with fascists.
Appeal to the popularity is to conclude the truth of a proposition on the grounds that most or many people believe it to be true.
Of course he’s guilty: even his mother has turned her back on him.
Argument to moderation is to argue that the moderate or middle view is the right or best one.
Some people are in favour of building a third runway at the existing airport, while others are in favour of building a brand new airport. The two parties ought to compromise by erecting a new terminal building at the existing airport.
Non-anticipation involves rejecting an argument on the basis that it is novel or has been rejected in the past. This is the opposite of the appeal to novelty, whereby an argument is accepted on the basis that it is novel or modern.
If congestion pricing is such a good idea, how come it hasn’t already been implemented?
Half-concealed qualification is to hide or gloss over the qualifications that limit the strength of a claim.
The B31 iceberg is six times larger than Manhattan, and large enough to warrant special attention from NASA. In November 2013, the giant iceberg broke free from the Pine Island Glacier in Antarctica. This is a fairly unusual place to observe such pieces breaking free from the frozen continent. The area has been closely monitored by researchers who *believe* that global warming *may* be leading to retreat of ice at the landmark.
Accident is to ignore exceptional cases to bolster or uphold a general rule.
I could never become a surgeon. It’s wrong to hurt people.
Bifurcation (false dilemma, false trilemma, etc.) is the presentation of limited alternatives when there are in fact more, giving the impression that the alternatives presented are either mutually exclusive or collectively exhaustive.
You can either come with me or stay at home.
Damning the alternatives is to argue in favour of something by damning its alternatives.
Tim is useless and Bob is a drunk. So I’ll marry Jimmy. He’s the right man for me.
One-sided argument is to argue for only one side of an argument, while remaining silent on the other side.
It’s not worth going on holiday. It’s expensive and tiring, and exposes you to all sorts of discomforts and dangers. Besides, by staying at home, you can enjoy your garden and all your favourite foods and entertainments.
Argument from ignorance upholds the truth or falsity of a proposition based on a lack of evidence for or against it.
Despite their best efforts, scientists have never found any evidence of current or past life on Mars. So we can be pretty sure that there has never been any life on Mars.
Ignoratio elenchi (irrelevant conclusion) is to present a valid or invalid argument that fails to address the issue in question. Aristotle asserted that, in a broad sense, all logical fallacies are a form of ignoratio elenchi.
I back military intervention in the Syrian civil war. According to one human rights organisation, at least 150,000 people have so far been killed in the three-year-old civil war, a third of them civilians. Another human rights organisation affirmed that the real toll was likely to be significantly higher at around 220,000 deaths. So you too should back military intervention.
Red herring is the use of irrelevant material to try to bolster an argument.
It would be good for the students if you attended college dinners more often. We have a new chef who trained in a Michelin-starred restaurant. The food is to die for! (OK, so maybe that’s not so irrelevant.)
Trivial objections is the use of trivial or frivolous objections which fail to undermine the central argument. Trivial objections is a special form of red herring.
Refuting the example involves demolishing the example while leaving the actual argument intact.
This type of question involves identifying the main conclusion of a passage, that is, what the author of the passage is really trying to convey. If in any doubt, summarise the argument as concisely as possible. To bring out the logical structure of the argument, try inserting a conjunctive adverb such as ‘hence’ or ‘therefore’. Do not simply assume that the main conclusion is whatever comes last: the main conclusion can be anywhere in the passage, including at the very beginning. Incorrect answer options are often a premise or assumption, an example, a minor conclusion, a partial statement of the conclusion, or an overstatement of the conclusion. Note that a minor conclusion is often recognisable in that it also serves as a premise of the main conclusion. Finally, remember that, if need be, you can test or check the conclusion by working backwards and forwards from the available answer options.
With this type of question, the conclusion or main conclusion of the passage is not explicitly stated. Your task is to infer the main conclusion from the passage and then select its closest summary from the list of answer options. To infer the main conclusion, identify and summarise the premises of the argument. Apply conjunctive adverbs like ‘so’ and ‘therefore’ to the premises to tease out the main conclusion. Your role is not to assess the truth or falsity of the premises: take them at face value, without bringing in any outside knowledge or wisdom. Get into the skin of the author. What message is he or she trying to convey? What is the point or purpose of the passage? Incorrect answer options are often premises or assumptions, counterpropositions, minor conclusions, and conclusions that are either too specific, too general, or otherwise misguided. Again, remember that you can work forwards as well as backwards from the answer options.
The following is an example of this type of question.
If Emma feels anxious about sitting her exams, choosing a career, taking out a mortgage, marrying her less-than-perfect boyfriend, or indeed anything, then this is because she only has a finite number of opportunities to ‘make good’. If she could live forever, she would have an infinite number of opportunities to get things right, and so she could fail as many times as she liked or needed. However, she is only going to live for perhaps another fifty years (some 18,000 days), and that is all the life she is going to have.
Which of the following conclusions is best supported by the above passage?
A. If people could live forever, they would feel even more anxious.
B. If people could live forever, they could fail as many times as they liked or needed.
C. The ultimate cause of all Emma’s anxiety is the prospect of her death.
D. We all wish to make a success of our life.
E. Our adult life lasts for about 18,000 days.
According to the passage, if Emma feels anxious about anything, then this is because she only has a finite number of opportunities to ‘make good’. This is because she is not going to live forever, that is, because she is going to die. If she were immortal, she would have an infinite number of opportunities to get things right, and so would have no grounds for anxiety. Therefore, the ultimate cause of all her anxiety is death (C). A contradicts the passage. B is a counterproposition offered to the reader, not a conclusion of the passage. However likely D seems, it cannot be inferred from the passage. The final sentence about our life lasting 18,000 days (E) merely serves a rhetorical function (see Chapter 6), underlining the brevity of life for the benefit of the reader. It is not a conclusion of the passage.
In this case, an assumption is not an explicit supposition or postulation (as in the normal sense of the term), but an implicit, unstated, and therefore hidden premise of the argument, without which the argument struggles or falls apart. Such an assumption is often taken for granted by the author of the passage, and can be simple or subtle, true or false. To identify the assumption, identify the conclusion of the argument and its explicit premises. Summarise the argument by splicing out distracting or cumbersome material. The assumption is the missing premise that zips up the argument. There might be more than one assumption, in which case only one will be contained in the answer options. If you cannot quickly identify the assumption or assumptions, test out each of the options. Incorrect options often contradict the assumption, or they are too general or specific, or they are peripheral to the argument. If an answer option is explicitly stated in the passage it is, by definition, not an assumption.
This type of question asks you to identify the answer option that most strengthens or weakens the argument. Once again, begin by summarising the argument, carving out extraneous material and paring it down to the bare bones. Identify any missing parts of the argument, in particular, any assumptions. Go through every answer option in turn to assess which has the greatest claim to strengthening or weakening the argument. The options often consist of facts that supply or modify an assumption of the argument. Incorrect options may be peripheral to the argument, repeat information already contained in the passage, do the opposite of strengthening or weakening the argument, or strengthen or weaken the argument less than another option.
An argument is invalid or flawed if the conclusion is unwarranted by the premises. Begin by summarising the argument. Remember that your task is to assess the validity of the argument, not its soundness. In many cases, the flaw will consist of a misguided assumption or a premise that is not a sufficient or necessary condition for the conclusion, but it could consist of any formal or informal logical fallacy. In some cases, you might need to choose the main or major among several flaws, in which case some of the other answer options will consist of minor flaws.
Matching arguments involves identifying an argument with the same (or a similar) logical structure as that in the passage. In some cases, you may be provided with a passage with a blank space in the argument, and asked to insert the word or phrase that most logically completes the argument. This is often a conjunctive adverb or phrase.
Applying principles involves identifying a statement that illustrates the same principle as that relied upon by the argument in the passage. This might, for example, consist of an ethical or legal principle.
To extract or abstract a logical form or general principle, summarise the argument (where necessary) and examine the relationship between its various components.
Be alert to the presence and function of conjunctive adverbs and phrases. For example, ‘furthermore’ introduces additional supporting information; ‘that said’ introduces qualification; ‘similarly’ introduces comparison; and ‘yet’ and ‘at the same time’ introduce contrast.
It might be helpful to sketch out the structure of the argument in symbol form, like so:
If undetermined events such as quantum leaps occur by chance, and if free actions are undetermined events, then free actions also occur by chance.
If all A are B, and all C are A, then all C are B.
In this case, notice that the major and minor premises are universal affirmatives, as is the conclusion. An answer option that does not reflect this structure is going to be incorrect. While the above argument is valid, some of the questions may involve an invalid or fallacious argument.
In many cases, the answer options are quite lengthy, and sifting through them can be quite confusing and time consuming. For applying principles questions, incorrect options may consist of the converse principle, similar but different principles, or mere statements of fact.
As ever, practice is key.