1. REASONING AND CRITICAL THINKING
The ability to reason is the fundamental characteristic of human beings. It has long been held that the capacity to reason is unique to human beings, but even if it is not—if it turns out, for example, that reasoning is a quality we share with dolphins or apes or even computers—the capacity to reason is nevertheless central to what we are and how we think of ourselves. Virtually every conscious human activity involves reasoning; we reason whenever we solve problems, make decisions, assess character, explain events, write poems, balance cheque books, predict elections, make discoveries, interpret works of art, or repair carburetors. We reason about everything from the meaning of life to what to have for dinner.
Of course, much of the time we are not engaged in conscious reasoning; often we simply listen to what others say, take note of things around us, experience feelings, daydream, listen to concerts, tell stories, or watch television. These activities need not involve conscious reasoning, but to the extent that we understand what is going on around or inside us we are not entirely passive. Some reasoning must be taking place, even if it is at a pre-conscious level. To understand reasoning properly, however, we need to understand how it differs from mere thinking. When we are merely thinking, our thoughts simply come to us, one after another; when we reason, we actively link thoughts together in such a way that we believe one thought provides support for another thought. This active process of reasoning is termed inference. INFERENCE involves a special relationship between different thoughts: when we infer B from A, we move from A to B because we believe that A supports or justifies or makes it reasonable to believe in the truth of B.
The difference between mere thinking and reasoning or inference is easy to understand through examples. Consider the following pairs of sentences:
Alan is broke, and he is unhappy.
Alan is broke; therefore he is unhappy.
Anne was in a car accident last week, and she deserves an extension on her essay.
Anne was in a car accident last week, so she deserves an extension on her essay.
This triangle has equal sides and equal angles.
This triangle has equal sides; hence it has equal angles.
Notice that the first sentence in each pair simply asserts two thoughts but says nothing about any relationship between them, while the second sentence asserts a relationship between two thoughts. This relationship is signalled by the words therefore, so, and hence. These are called INFERENCE INDICATORS: words that indicate that one thought is intended to support (i.e., to justify, provide a reason for, provide evidence for, or entail) another thought. Other common inference indicators include the following:
it follows that
It is important to note that sometimes the inference indicator is missing; this can occur when a speaker thinks the inference is quite obvious. For example:
It’s raining; I’d better take my umbrella.
The actual presence of an inference indicator is not important. What is important is the relationship of support between the thoughts of the speaker. This relationship is a defining condition of an inference: if two thoughts are linked by such a relationship, they constitute an inference; otherwise they do not.
When we express an inference in words, we do so by means of statements. A STATEMENT is a sentence (i.e., a set of words) that is used to make a claim that is capable of being true or false. If a sentence is not capable of being true or false, then it is not a statement. Questions (Are you awake?) and commands (Wake up!) are not capable of being true or false and, hence, are not statements. Only statements can be true or false. When an inference is expressed in statements, it is called an argument. An ARGUMENT is a set of statements that claims that one or more of those statements, called the PREMISES, support another of them, called the CONCLUSION. Thus, every argument claims that its premises support its conclusion.
1.2 THE CONCEPT OF LOGICAL STRENGTH
Since a statement makes a claim that can be true or false, any statement can be assessed by asking whether it is true or false. Is Alan really unhappy? Was Anne actually in a car accident? We can assess the truth or falsity of a statement in isolation, independent of its part in an argument (or a story or list, etc.). Every statement that is assessed without regard for its part in an argument must meet the same standard: truth. The truth or falsity of the statement Alan is unhappy does not depend upon whether it is part of an argument. To discover the truth or falsity of statements, we examine the statement itself and look for direct evidence that will show us whether it is true or false. Often, however, without further evidence it may be difficult or impossible to determine conclusively whether an isolated statement is true or false. This is why we construct arguments: they help us assess statements when the truth or falsity of a statement is not directly evident. It is also why we must learn to assess whole lines of reasoning in addition to assessing statements.
Assessing an argument is more complex than assessing an isolated statement. Since an argument always includes a claim that its premises support its conclusion, assessing an argument means assessing this claim. Do the premises really support the conclusion, and if so, how much support do they provide? In other words, how strong is the inference from the premise(s) to the conclusion? We say that an argument has LOGICAL STRENGTH when its premises, if true, actually provide support for its conclusion.
The concept of logical strength is central in critical thinking and has two important features that need to be stressed. First, the logical strength of an argument is independent of the truth or falsity of its premises: we do not need to know that the premises of an argument are true in order to assess its logical strength. When we assess the logical strength of an argument, we are really asking, If the premises are true, would we be justified in accepting the conclusion? and we can answer this question without knowing whether or not the premises actually are true. Consider the following example:
The population of Chatham is 27,000.
The population of Orillia is 26,000.
Therefore, Chatham has a larger population than Orillia.
Even if we don’t know the populations of Chatham and Orillia, we can still see that the inference in this argument is a strong one. If both premises are true, then obviously the conclusion would have to be true as well. The fact that either or both premises might be false does not affect the logical strength of the argument. For
similar reasons, an argument with premises and conclusion that are known to be true may be a very weak argument. For example:
Toronto is the capital of Ontario.
Ottawa is in Ontario.
Therefore, Ottawa is the capital of Canada.
In this example, the premises and the conclusion are all true, but the facts that Toronto is the capital of Ontario and that Ottawa is in Ontario provide no support for the statement that Ottawa is the capital of Canada. The inference is therefore a bad or weak one. Only if the information contained in the premises really provides a good reason for holding that the conclusion is true can we say the inference is a strong one.
Second, the logical strength of an argument is often a matter of degree. Some arguments are so strong that the truth of the premises guarantees the truth of the conclusion. Such arguments are called DEDUCTIVE ARGUMENTS, and they constitute strict proofs. But most arguments are not as strong as this; usually, the truth of the premises makes it reasonable to hold that the conclusion is also true, but it does not provide an absolute guarantee. Such arguments are called INDUCTIVE ARGUMENTS. For example:
Arthur has been a moderate social drinker for 20 years.
No one has ever known him to get drunk.
Therefore, he won’t get drunk at the party tonight.
This is a strong argument, since if the premises are true it is reasonable to conclude that the conclusion will also be true. Nevertheless, Arthur might get drunk tonight. Given the truth of the premises this might astonish us, but it is not impossible.
Understanding the concept of logical strength is the key to developing critical thinking skills. The fact that the logical strength of an argument is independent of the truth of its premises means that in order to assess an argument we must do more than merely determine whether its premises are true. And the fact that logical strength may be a matter of degree means that we must be sensitive to the various features of arguments that affect their degree of strength. If we lack critical thinking skills, we can easily be fooled into thinking that an argument is strong when the premises actually provide little or no support for the conclusion. Consider the following inferences:
The Liberals won a majority of seats in the last election.
So they must have received more votes than any other party.
My sister always got better grades in school than I did.
That proves that she’s smarter than I am.
Eighty per cent of those who tried Painaway said they would take it the next time they had a headache.
Therefore, Painaway is a better headache remedy.
The city council is unfair to city employees.
Jones is a city councillor.
Hence, Jones is unfair to city employees.
A majority of the union members voted in favour of the contract.
Consequently, these people must be in favour of the 1-per-cent pay reduction in the contract.
Whenever there is high unemployment, interest rates increase.
So high unemployment causes high interest rates.
These are all weak arguments: the conclusions are not adequately supported by their premises. This does not mean that the conclusions are false or even likely to be false. It only means that the evidence presented in the premises, even if true, does not entitle us to draw the conclusion. The premises do not, in other words, adequately support the conclusion.
1.3 TRUTH, LOGICAL STRENGTH, AND SOUNDNESS
In section 1.2 we drew a distinction between assessing the truth or falsity of a student and assessing the logical strength of an inference. Although these are quite different tasks, both are important if we want to arrive at the truth. Remember that a strong argument is one whose premises, if true, support its conclusion. In other words, its premises, if true, provide a justification for believing the conclusion to be true. But a logically strong argument, as we saw, may have false premises. So if we want to know whether the conclusion of an argument is likely to be true, we need to know both that the argument is a strong one and that its premises are true. What we want, in other words, are logically strong arguments with true premises. An argument that has both logical strength and true premises is called a SOUND ARGUMENT.
It is very important to be aware of the differences among these three properties. Truth
is a property of statements and never of inferences. Logical strength
is a property of inferences and never of statements. Logical strength refers to the inferential
connection between the premises and conclusion of an argument. Soundness
is a property of an argument as a whole. Always keep the question of strength separate from the question of truth when dealing with any argument. Never ask simply, Is this a good argument?
Ask two questions instead:
(1) Is this a logically strong argument? and
(2) Are its premises true?
The order in which these questions are asked is not important. What is crucial is that they be asked separately. Only when both have been answered are we in a position to know whether an argument is sound—whether we have a good reason to accept its conclusion.
Sometimes, however, it is inappropriate to ask whether the premises are true. We may, for example, want to explore the consequences of an assumption whose truth or falsity we cannot determine. For example:
No one knows for certain whether Martin Bormann died in 1945. If he did not, then he probably escaped through Switzerland and Italy to South America. That is what Adolf Eichmann and a number of other high-ranking Nazis did.
There are even times when we want to develop an argument with premises that we know or assume to be false. Such arguments are called COUNTERFACTUAL ARGUMENTS because at least one premise is a counterfactual statement. For instance, we may want to explore the logical consequences of some historical event that never happened; in this case, we posit a counterfactual claim as a supposition for the sake of argument. For example:
If Hitler had invaded Britain in 1940 he would have succeeded, because at that time the Germans had military superiority.
Or we may want to explore the consequences of the occurrence of some hypothetical situation. For example:
If the provincial sales tax were reduced to 5 per cent, there would not be a corresponding decrease in government revenues. This is because part of the decrease would be offset by an increase in sales as a result of the sales-tax reduction.
We should also note a special kind of counterfactual argument called the REDUCTIO AD ABSURDUM.
In a reductio argument, a statement is proven to be true by assuming it to be false and then deriving a contradiction from that assumption. For example:
It is preposterous to claim, as some people have, that Gorbachev engineered the August 1991 coup attempt by Communist hard-liners in order to strengthen his position and stop the secessionist movements in the republics. If he engineered the coup then we would have to conclude that he is an exceptionally stupid man, for not only did the coup weaken his personal position and strengthen the position of Yeltsin, his chief rival, but it unleashed a wave of secessionism that destroyed the Soviet Union. Gorbachev may not be the smartest man in the world, but no one could have ...