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Chapter Two: The Two Steps to Evaluate Arguments
There are two ways arguments go bad. The argument may have a faulty inference or the premise(s) may be false, dubious, or unclear. In other words, every argument could be faulty because there is a problem with the facts or the reasoning/inference from the facts.
Let’s start with the latter concept since most students struggle with it. If you get confused, the exercises should clarify.
Step 1: Bad Inferences
An inference is the reasoning or movement from premise(s) to conclusion. It is the process of deriving a conclusion from premise(s) assumed or known to be true.
Many people confuse the conclusion with the inference, but the conclusion is your final destination and the inference is how you arrived there. An inference is not a statement like premises and conclusions. You cannot see an inference on paper like you can see premises and conclusions, but logic is primarily the study of inferences. Again, an inference is not a statement like a premise or conclusion, it is the reasoning process from premise(s) to conclusion. Let's examine some inferences.
When testing inferences, you should assume the premises are true and then ask whether the conclusion is well supported by those premises. Again, to test the inference, assume the premises are true even if you know they are false. Next, ask whether the conclusion is well supported by those premises. Consider the following two arguments:
Premise 1: All whales are mammals.
Premise 2: Shamu is a whale.
Conclusion: Shamu is a mammal.
Premise 1: All whales are mammals.
Premise 2: Shamu is a mammal.
Conclusion: Shamu is a whale.
Take a moment to see if you can explain why argument 1 has a good inference and argument 2 has a bad inference.
Got it? Let’s check your answer.
Argument 1 has a good inference because the premises support the conclusion. Indeed, it is a good argument (logicians call it a “valid deductive argument”) because it is impossible for the conclusion to be false if we assume the premises are true.
Argument 2 is bad/invalid because you cannot infer “Shamu is a whale” from the facts that “Shamu is a mammal” and “all whales are mammals.” This is because saying “all whales are mammals” is not equivalent to saying “all mammals are whales.”
Take a moment and think about that. “All A are B” is not the same as “all B are A.” For example, “all cats are animals” is not the same as “all animals are cats.” You cannot infer one statement from the other. The second argument about whales is invalid mainly because it indirectly tries to do just that.
Notice too that argument 2 has a true conclusion and true premises, but it is still bad because the reasoning (i.e. inference) is faulty. Many students new to logic think that if they have all the facts correct, then they have a good argument, but this is not true. Even if you have all the facts, your argument may be bad because you have a poor inference (i.e. poor reasoning) from those facts.
To better grasp this point, consider another bad argument with the same form as argument 2:
Premise 1: All cats are animals.
Premise 2: Lassie is an animal.
Conclusion: Lassie is a cat.
It is easier to see the bad inference in this argument because the conclusion is obviously false (since we know Lassie is a dog). Indeed, most students initially say it is bad because the conclusion is false, but this is mistaken and irrelevant. That is, both argument 2 and the Lassie argument are bad for the same reason . . . they have a bad inference.
In short, it does not matter if arguments with bad inferences have true or false premises. Nor does it matter if the conclusions is true or false. The problem with bad inferences is that the conclusion would not follow from the premises even if the premises were true.
Many students fail to grasp this point. They focus on whether they premises and conclusion are true instead of whether the reasoning/inference from premises to conclusion is good reasoning. I recommend reviewing this chapter and doing the exercises until you understand this point well.
Summary: To evaluate the inference of any argument, simply assume the premises are true and ask whether the conclusion is well supported by those premises. If it is, the inference is strong. If the conclusion is not well supported by the premises, the inference is weak. Yes, it is that simple.
Exercise: Underline the conclusion in each argument, and explain why each has a bad inference.
1. Hitler was a bad man, so you should not believe anything he believed.
2. I've met three redheads and they were really mean and stinky. So, all redheads are mean and stinky.
3. Everyone has DNA, so fire trucks make noises.
4. It is unreasonable to believe God exists because his nature doesn’t make sense.
5. I am not free because my cells are not free.
6. You cannot prove God does not exist, so he does.
- Even when we assume Hitler was bad, the conclusion does not follow because Hitler obviously held some true beliefs (e.g. 2+2=4, the world isn’t flat, automobiles exist).
- The conclusion (i.e. all redheads are mean and stinky) does not follow even if we assume the premise is true (i.e. I’ve met three mean and stinky redheads). In this case, I am generalizing from a sample that is too small and unrepresentative. It is the hasty generalization fallacy. See the next chapter for more on fallacies.
- The conclusion (i.e. fire trucks make noises) does not follow from the premise. There seems to be no connection between the premise and conclusion. It is a non sequitur fallacy. See the next chapter for more on fallacies.
- The conclusion (i.e. God does not exist) does not follow from the premise (i.e. the nature of God does not make sense). After all, I know light exists even though I do not understand the nature of light. This is a non sequitur because there are many paradoxical realities known to exist. The fact that this argument is weak does not mean God exists. It simply means these particular premises do not strongly support the nonexistence of God.
- The conclusion (i.e. I am not free) does not follow from the premise (my cells are not free). This is the composition fallacy. The whole does not have to have the same property as the parts, just as the whole of water may be wet though hydrogen and oxygen are usually dry.
- The conclusion (i.e. God exists) does not follow from the inability to prove he does not exist. This is the fallacy of arguing from ignorance. See the next chapter for more on fallacies.
Step 2: False or Unclear Premises
Arguments also go bad because they have false, dubious, or unclear premise(s). Most people understand this pretty well, but let’s do some exercises to ensure understanding.
Exercise 2: Underline the conclusion and identify the problematic premises.
1. All whales are stars. I am a whale. So, I am a star.
- Everyone is selfish, so you are selfish.
- Every rational person should agree with the Libertarian Party Platform, so you should too.
- If time travel were possible, I could travel to the year 1800 and be both born and not born. But it is a logical impossibility to be both born and not born. So, it is impossible to travel back in time to the year 1800.
- Since light is a wave and must travel through a medium, there must be an invisible aether through which it travels.
- The universe is complex and orderly like a watch. Just as we can infer an intelligent mind made the watch, so we can infer an intelligent mind made the universe.
Exercise 2 Answers
- The inference is good/valid, but the premises (i.e. all whales are stars, and I am a whale) are false.
- The inference is good/valid, but the first premise is dubious. Intelligent people disagree about the meaning of selfish and whether everyone is selfish. See "Batson Research" for scientific evidence against the claim that people are always selfish (i.e. against psychological egoism).
- The conclusion follows from the premise, but the premise that every rational person should agree with libertarianism is dubious.
- The conclusion is the last statement (i.e. it is impossible to travel back to the year 1800) and it seems to follow from the premises. However, the word “born” is unclear. Some philosophers argue you could be born in personal time, but not absolute time. Therefore, you could be both born personally and not born absolutely in 1800. The problem with this argument is not the inference, but the ambiguity of what it means to be born.
- The inference is good/strong, but the premise is false. Light does not have to travel through a medium like water waves do. This was a turning point in the history of science.
- This is a simple version of the teleological argument. One criticism is the first premise is false, the universe is not ordered like a watch. Even if this premise is reasonable, intelligent people disagree about what we can infer from the orderliness of Nature. So, you can question both the premise and the inference in this argument.
When evaluating arguments, take the following two steps:
Step 1: Assume the premises are true even if you know they aren’t. Now ask, “Do the assumed premises provide good reasons for believing the conclusion?”
If not, the inference is poor.
If yes, the inference is good.
Step 2: Are the premises true or reasonable?
These 2 steps are how you evaluate any and all arguments. All the vocabulary/concepts in logic follow from these two steps.
Exercise 3: Evaluate the following arguments? Is the inference good? Are the premises good?
- All libertarians are brilliant. I am a libertarian. Therefore, I am brilliant.
- All dogs are animals. Lassie is an animal. So, Lassie is a dog.
- Eating meat is moral because it is natural.
- Most people have 28 fingers, so we should make 28 fingered gloves.
Exercise 3 Answers
- The inference is good, but the two premises are dubious. So, I reject this argument.
- The inference is bad, but the premises are probably true. So, I reject this argument.
- The inference is bad (see the appeal to nature fallacy in the next chapter), and some people would also challenge the premise that it is natural. So, I reject this argument.
- The inference is strong, but the premise is false. So, I reject this argument.
Application and Value
When you evaluate arguments, it is not enough to examine the truth of the premise(s). You should also examine the inference. If you disagree with the conclusion of the argument, be specific about whether you disagree with the premise(s) or the inference to the conclusion. And, yes, you could disagree with both the inference and premises in an argument (see #6 in Exercise 2).
Again, we could have all the facts, but still draw poor inferences from those facts.
Notice then that every argument is one of these 4 types:
- Good premises and a good inference.
- Good premises and a bad inference.
- Bad premises and a good inference.
- Bad premises and a bad inference.
So, as you read the newspaper, watch television, or argue with your spouse, think about whether you disagree with their premises or the inference from the premises. Yes, you may disagree with their conclusion, but that is irrelevant. To justify your position and rationally explain your disagreement, you should clearly explain whether you disagree with the facts (premises) or the reasoning from the facts (inference). . . or both.
By the way, I do not recommend using logic too much with your spouse. For marital issues, find a book on rhetoric, patience, or love.
Final Comment on Chapter 2
If you understand this chapter well, you have the foundation needed to understand all of logic. The vocabulary of logic (e.g. deductive, inductive, valid, invalid, strong, weak, cogent, uncogent, etc.) derives from the simple concepts presented in this chapter.