Critical Thinking and Logic

Critical thinking is fundamentally a process of questioning information and data. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate says. You can also question a commonly held belief or a new idea. With critical thinking, anything and everything is subject to question and examination for the purpose of logically constructing reasoned perspectives.

What Is Logic, and Why Is It Important in Critical Thinking?

The word logic comes from the ancient Greek word logike, referring to the science or art of reasoning. Using logic, a person evaluates arguments and reasoning and strives to distinguish between good and bad reasoning. Using logic, you can evaluate ideas or claims people make, make good decisions, and form sound beliefs about the world.^[1]

Critical thinking involves reflective thinking, considering bias, and remaining open minded and curious. It also demands the intellectual rigor to deconstruct and evaluate claims made by others while also making sound and strong arguments, ourselves. Logic is the study and evaluation of arguments to distinguish good reasoning from bad. When using logic in critical thinking, you will consider the logical structure in order to evaluate its quality. In the next section, we will explore what logical structure is.

Logical Structure

Suppose I argue as follows: if it is raining, then the ground is wet; but since it is not raining, it follows that the ground is not wet. This is an argument whose conclusion is the statement “the ground is not wet.” The two premises of the argument are the conditional statement “if it is raining, then the ground is not wet” and the statement “it is not raining.”  We can rewrite the argument to clearly show each of the statements—the two premises and the conclusion—like this:

1. If it is raining, then the ground is wet.
2. The ground is not wet.
3. Therefore, it is not raining.

This example is a valid argument. A valid argument is an argument whose premises guarantee the truth of the conclusion. In other words, a valid argument is one such that on the assumption of the truth of the premises, it is impossible for the conclusion to be false. Think about the previous argument. Can you see that if we accept the two premises (lines 1 and 2) as true, then we must logically accept the conclusion (line 3) to be true? Valid arguments are the gold standard of reasoning in logic—it is what all arguments aspire to be. When you have constructed a valid argument, no one can argue with your reasoning (although they can still disagree with you regarding whether your premises are true). What is interesting about the concept of logical validity is that an argument can be valid (i.e., the reasoning can be good) even if the premises are obviously false or absurd. For example, consider this (slightly altered) argument from a scene in Monty Python and the Holy Grail:

1. If this woman weighs the same as a duck, then she is is made of wood.
2. Everything made of wood is a witch.
3. This woman does weigh the same as a duck.
4. Therefore, this woman is a witch.

Clearly, the first two premises of this argument (lines 1 and 2) are false. However, if we hold them (and also the premise in line 3) true, then the conclusion follows logically. That is, this argument is a valid argument. Think about the logic of this argument for a second. If we assume that lines 1 and 3 are true, then it follows that the woman is made of wood.  And if that is true then by line 2, it follows that she is a witch, which is the conclusion stated in line 4. This silly argument illustrates that logic is first and foremost about the relationship between premises and conclusion, not the actual truth of the premises. Whether or not the premises of an argument are true is often a matter that is outside logic. For example, if one of the premises of an argument were the statement “some mammals do not give live birth,” then logic alone cannot help you figure out whether that is true. For that you need another disciplines: biology.

Let’s return to the first argument for a second to illustrate what logical structure is. That argument has a certain structure that looks like this:

1. If A then B.
2. Not B.
3. Therefore, not A.

What is interesting about logic is that once we can see the form of an argument, then we can automatically know that the argument is valid without even considering or thinking about the content of the argument. Any argument that has a valid structure is a valid argument. Logic is (in part) the study of these structures. The structure that I have just identified has a name: modus tollens (which in Latin means “way of denying,” since the second premise contains a negation, “not”).  Lines 1 and 3 of the Monty Python argument above also contain a valid structure that looks like this:

1. If A then B.
2. A.
3. Therefore, B.

That argument form is called modus ponens (which in Latin means “way of affirming”).

There are many different valid argument structures; however, this is not a logic course, so we will not consider them all.  The important thing to understand is that logic concerns the strength of the relationship between the premises and the conclusion, and the goal in constructing arguments is to construct valid arguments. Again, valid arguments are such that the premises of the argument leave no possibility that the conclusion could be false. In contrast, invalid arguments are ones where the premises do leave open the possibility that the conclusion is false. In other words, the premises do not imply the truth of the conclusion. If an argument is invalid, then we should be able to give a counterexample that proves the argument is invalid. A counterexample is simply a description of a possible scenario where the premises are true and yet the conclusion is false. Let’s look at an example.

1. If the train is late, Shondra is angry.
2. Shondra is angry.
3. Therefore, the train is late.

If we assume the premises (lines 1 and 2) are true, is it possible for the conclusion to be false? If so, then this would show the argument is invalid. Here’s a hint if you can’t already see the answer: might Shondra be angry for some other reason and yet the train still be on time? Suppose Shondra is angry because she spilled coffee on her favorite pants. If so, then it could still be the case that any time the train is late, Shondra is angry but on this occasion the train is actually on time. Given this scenario, let’s check line by line the argument. In this scenario are the premises true? Yes they are—premise 1 is true since Shondra would have been angry if the train were late even though the train wasn’t late and premise 2 is true since Shondra is angry because of the coffee spill. And yet the conclusion is false since the train is not late in this scenario. Thus, we have given a counterexample: we have specified a scenario where the premises are true and yet the conclusion false. And that means the argument is invalid.

Deductive vs. Inductive Arguments

Whereas the gold standard of deductive arguments is validity (as discussed in the last section), the standard of inductive arguments is something less than validity. A strong inductive argument is typically called a cogent argument. It is important to understand the difference between deductive and inductive arguments because you need to understand what kind of argument you are trying to make or evaluate. The main difference between inductive and deductive arguments is that whereas deductive arguments seek to establish their conclusions with absolute certainty, inductive arguments only seek to establish their arguments with a high degree of probability. Here’s an example of a strong inductive argument:

1. All ravens that have ever been observed anywhere in the world have been black.
2. Therefore, all ravens are black.

Notice that this argument doesn’t quite obtain the standard of validity. It is possible that there is a non-black raven somewhere in the world that hasn’t been observed. But even if that is a possibility, it seems that the “all ravens are black” conclusion is still highly likely, given the amount of confirmation that claim possesses (i.e., the number of ravens that have been observed and that all of them have been black).

Unlike deductive arguments, there is no inductive form that is strong. Any inductive argument could be strong or weak depending on the details of the argument. In contrast, deductive arguments have valid logical structures such that any argument that possesses an inductive form is thereby a valid argument, regardless of the topic of the argument; meaning that to evaluate inductive arguments, we have to draw on our knowledge of how the world is. We can say a couple of things about strong inductive reasoning, but to further understand these concepts would require a course in logic and/or scientific reasoning. We will conclude this page with a few rules of thumb to keep in mind when it comes to inductive arguments:

• When making inductive generalizations (such as the ravens argument), make sure that the instances in your premises are not susceptible to any kind of sampling bias. For example, even if I have observed many black ravens, if I have only observed them in one part of the world, there is a good chance that my sample of ravens is not representative of all the ravens in the world.
• Many times inductive arguments depend on establishing correlations and we try to infer causation based on correlation. However, this inference must be done carefully. As the saying goes, correlation is not causation; a correlation is not sufficient to establish causation—just because A and B are strongly correlated, or tend to occur together, doesn’t mean that A caused B. To establish that causal claim would require both a plausible causal story we can tell and (ideally) further test to determine whether A really does cause B.
• Another common inductive argument is an analogical argument. Analogical arguments attempt to compare two different things (A and B) and argue that since they are similar in relevant respects, if A has a certain property (x), then B must have that property as well. The thing to be on the lookout for here is whether A and B really are similar in relevant respects; because if they aren’t, the logic of the analogical argument breaks down.

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