Ethical Realism

September 9, 2012

10 Myths About Logic

Logic is greatly misunderstood. Not only do very few people understand logic properly, but even critical thinking educators believe false things about logic. I will discuss ten myths (false beliefs) I believe many people have about logic.

  1. Logic has nothing to do with everyday life.
  2. Logic is subjective.
  3. Logic can’t help improve our thinking.
  4. I am a critical thinker, but other people should learn about it.
  5. Arguments are hostile disputes.
  6. Some arguments are true, and some are false.
  7. All good arguments are logically valid.
  8. All good arguments have true premises.
  9. If a premise is false, then the conclusion is false.
  10. We know about good argumentation from observation.

Once more—each of these assertions are false.

1. Logic has nothing to do with everyday life.

Logic is a philosophical domain concerned with argumentation, reasoning, errors in reasoning, and proper argument form. Many people think logic is too abstract to have any relation to their life. However, logic has a lot to do with everyone’s life.

First, logic as it was developed by Aristotle, the Stoic philosophers, and other philosophers is now being used by computers (and everything else that uses computers, such as cell phones).

Second, understanding logic helps us become more reasonable. In particular, it helps us better understand good argumentation, and what we should believe. One popular argumentative tactic is to insult those who disagree with us in order to take what they say less seriously. We all know why that’s not a good argument. However, there are more subtle ways that arguments can fail us. For example, we should not form beliefs based on logically invalid deductive arguments. Such an invalid deductive argument is the following:

  1. If dogs are mammals, then dogs are animals.
  2. Dogs are animals.
  3. Therefore, dogs are mammals.

The problem is that the first two statements (the premises) are insufficient to support the conclusion. This argument has an invalid argument form—“If A, then B. B. Therefore A.” A counterexample to this argument form is “If dogs are reptiles, then dogs are animals. Dogs are animals. Therefore, dogs are reptiles.”

2. Logic is subjective.

Some people conceive of logic as what makes things “sound good.” Whatever you believe “sounds good” to you, but other beliefs “sounds good” to other people. However, this is a complete misunderstanding about what logic is about. It’s not about what “sounds good.” There is rational criteria involved that determines when an argument is rational, when a conclusion is likely true, and when we should believe something is true.

3. Logic can’t help improve our thinking.

It’s hard to say why anyone would think logic can’t help improve our thinking, but many people do seem to think that. Perhaps they only think that because they think logic is subjective. However, there is data that indicates that logic can improve our critical thinking skills.

First, a study provides evidence that an applied logic class significantly helped improve the critical thinking skills of high school students.1

Second, a meta-analysis by Claudia María Álvarez Ortiz compares how well several different classes improve the critical thinking of students, and various classes were found to be effective:

  1. Critical thinking classes are effective, which generally focus on “informal logic.”
  2. Critical thinking classes involving lots of argument mapping practice were the most effective.
  3. Other logic classes (that focus more on “formal logic”) were also found to be effective.

(See Does Philosophy Improve Critical Thinking Skills? [2007, PDF] for more information.)

Third, a study by Richard Arum has found that certain college classes were better at improving critical thinking than others. “Students who majored in the traditional liberal arts—including the social sciences, humanities, natural sciences and mathematics—showed significantly greater gains over time than other students in critical thinking, complex reasoning and writing skills.”2

4. I am a critical thinker, but other people should learn about it.

Many people think that logic is important, but they don’t think they need to take a class on logic (or spend much time educating themselves about logic). However, the fact is that even a college education does not guarantee that you know very much about logic or critical thinking. It is important to study these subjects to understand them as well as possible.

First, Richard Arum’s study found that “[f]orty-five percent of students made no significant improvement in their critical thinking, reasoning or writing skills during the first two years of college… After four years, 36 percent showed no significant gains in these so-called “higher order” thinking skills.”3

Second, most teachers know very little about critical thinking, even though they say that they think it’s important. “Though the overwhelming majority (89%) claimed critical thinking to be a primary objective of their instruction, only a small minority (19%) could give a clear explanation of what critical thinking is. Furthermore, according to their answers, only 9% of the respondents were clearly teaching for critical thinking on a typical day in class.”4

5. Arguments are hostile disputes.

Perhaps one of the largest barriers to an interest in logic is the view of arguments as hostile disputes. Sometimes we talk about “arguments” when we are talking about shouting matches or some other disrespectful exchange of words. That is not what logical arguments are. Logical arguments are reasons given to believe something involving premises and a conclusion. The premises are supposed to be a reason to believe the conclusion is true. Some arguments are very good reasons to believe the conclusions to be true, and it can be perfectly respectful to tell someone what you think is true and why by using an argument.

The word “debate” is similarly equated with “hostile dispute” when in reality a debate involving logical arguments can be highly educational and perhaps even indispensable to improving ourselves in certain ways. In particular, debates have been shown to help us find out when our reasoning process involves mistakes.

6. Some arguments are true, and some are false.

Arguments can be good, valid, sound, strong, or cogent. But they can’t be true or false. Consider the following good argument:

  1. All men are mortal.
  2. Socrates is a man.
  3. Therefore, Socrates is mortal.

In this case the premises and the conclusion are all true. It is unclear why anyone would think the argument itself could be true or false.

7. All good arguments are logically valid.

Logically valid arguments have conclusions that must be true if we assume the premises are true. For example:

  1. All lizards are mammals.
  2. If all lizards are mammals, then all lizards are animals.
  3. Therefore, all lizards are animals.

The premises are false and the conclusion is true, but that’s not the point. We can imagine that the premises are true and that scenario would force us to imagine that the conclusion is also true. The premises are meant to be a reason to believe the conclusion precisely because true premises would be a good reason to think the conclusion is also true.

Invalid deductive arguments don’t give us a reason to believe the conclusion is true. For example:

  1. All men are mortal.
  2. Socrates is a mortal.
  3. Therefore, Socrates is a man.

If we knew the premises are true, that would not mean that we know the conclusion is true. We know all dogs are mortal and Socrates is a mortal, but that doesn’t mean Socrates is a dog.

All good deductive arguments are valid, but not all good inductive arguments are valid. Deductive arguments are supposed to be valid by definition—that’s how we define deductive arguments. However, inductive arguments are not supposed to be valid. That’s how we define them. An example of a good inductive argument is the following:

  1. The Sun has risen every day of human history.
  2. Therefore, the Sun will probably rise tomorrow.

This argument is technically logically invalid, but it’s not supposed to be logically valid. Inductive arguments make predictions and generalizations based on limited information, and the predictions and generalizations can be wrong. They provide us with hypotheses and theories that can be falsified. Even so, good inductive arguments still give us a good reason to believe the conclusions to be true.

8. All good arguments have true premises.

We should try to have true premises for our arguments, but there is rarely a way to guarantee that any of our premises are true. The best we can hope for is to use premises that are highly justified—premises that are probably true based on our limited information. For example, consider the example of an inductive argument above. We have a very good reason to believe the premise is true, but maybe it’s not. For example, the whole universe might have been created an hour ago and we might all have false memories. In that case the Sun did not rise every day of human history after all.

9. If a premise is false, then the conclusion is false.

Many people refute the argument given by someone else by proving a premise to be false, and seem to assume that the conclusion must also be false as a result. However, an argument can have a false premise and a true conclusion. Consider the following argument:

  1. If more than two people exist, then “1+1=3.”
  2. 1+1=3
  3. Therefore, more than two people exist.

This is a horrible argument. Both premises are false. Even so, the conclusion is true.

10. We know about good argumentation from observation.

Many people think that natural science is the only way to justify our beliefs—they think that we know everything we know because of natural science. However, natural science has never discovered that “1+1=2,” or that contradictions are impossible, or that a good argument must have justified premises. In fact, natural science has never discovered anything about logic. We know a lot about logic, and we know a lot more about logic now than we did two thousand years ago. Even so, we didn’t learn about logic through natural science.

Evidence that Critical Thinking Educators Don’t Understand Logic

Critical thinking traditionally focuses on “informal logic,” so the fact that many critical thinking educators don’t understand logic as well as they should is a problem. I applaud many critical thinking educators who share valuable materials online to give everyone a chance to learn about it, but their false assertions are apparent to experts in the field. The following webpages are created by critical thinking educators that believe in at least one of the myths that were discussed above:

  • Good Arguments (Joe Lau & Jonathan Chan falsely state that good arguments must have true premises, and that good deductive arguments must be logically sound. A sound argument must be valid and have true premises. However, good arguments don’t need true premises. They both have PhD’s in philosophy, so this error is more disappointing than usual.)
  • Field Guide to Critical Thinking (James Lett falsely asserts that arguments must be logically sound. Arguments need not have true premises and they need not be valid.)
  • Purdue University: Using Logic (Ryan Weber & Allen Brizee falsely assert that a syllogism is false. A syllogism is a type of argument, and arguments can’t be false. See Example D.)


Some related blog posts I’ve written:

Free introductions to logic:


1 Dan Bouhnik and Yahel Giat. “Teaching High School Students Applied Logical Reasoning” (PDF) (2009.)

2 Rimer, Sara. Study: Many College Students Not Learning To Think Critically. (2011. The findings were published in the book, Academically Adrift.)

3 Ibid.

4 Dr. Richard Paul, Dr. Linda Elder, and Dr. Ted Bartell. Research Findings. (1997.)


  1. “8. All good arguments have true premises.”

    This is also false for another reason: a common form of argument is the reductio ad absurdem, which often begins by assuming the proposition which is to be proved false. Why is this a good argument? Because it takes the denier of some proposition P from premises she herself accepts to the conclusion that P is true – in short, because it is rationally coercive.

    “The best we can hope for is to use premises that are highly justified—premises that are probably true based on our limited information.”

    Well, if what I said above is correct, then it seems that the premises in a good argument need not all be justified, and it may be that some are even likely to be false – what matters is that the target audience for the argument will grant its truth on the way to the conclusion the argument is intended to convince them of. For instance, (and here you’ll see where I’m coming from), an argument against the existence of God may use any number of propositions which the theist would endorse, but which are controversial, or even denied by most philosophers – e.g. propositions asserting divine simplicity, divine command theory, libertarian free will, the existence of intrinsic value, and so on. To assert any of these in the argument is fine, again, because such an argument can be rationally coercive to those who believe that God exists.

    Comment by TaiChi — September 9, 2012 @ 8:37 am | Reply

    • TaiChi,

      Thank you for the comment. I agree with what you are saying. I want to keep my answer simple and I will change it if I figure out a way to improve it while keeping it simple.

      Comment by JW Gray — September 9, 2012 @ 7:40 pm | Reply

      • Sure, that seems reasonable to me.

        Comment by TaiChi — September 10, 2012 @ 5:23 am

  2. Reblogged this on kimmeasmile and commented:
    I found this blog quite thought-provoking… It’s one of those I will have to revisit more than a few times to really absorb its contents. I find philosophy, critical thinking, and logic subject matters that really wet my whistle and fuel to my fire if you know what I mean.

    Comment by kimmeasmile — March 9, 2015 @ 1:50 pm | Reply

    • I’m glad you like it, and like to hear encouraging words. I hope to continue to make updates as soon as I can find the time.

      Comment by JW Gray — March 18, 2015 @ 6:18 am | Reply

  3. Perhaps I’m a bit late, but I think this is worth pointing out. The example argument that you gave in “9. If a premise is false, then the conclusion is false” is not a sound argument. Symbolically, if you let P be the statement that more than two people exist and Q be the statement that 1+1=3, then the example argument goes: If P implies Q and Q is true, then P is true. This is not necessarily true.

    Comment by Kevin Hsu — October 27, 2015 @ 9:35 am | Reply

    • The example argument isn’t supposed to be sound. I think you missed the point I was making. It is an example of an argument with a false premise and a true conclusion.

      Comment by JW Gray — October 27, 2015 @ 3:58 pm | Reply

      • Oh I see, thanks for the clarification!

        Comment by Kevin Hsu — October 28, 2015 @ 1:56 am

  4. What’s disconcerting to me is the more I talk or debate with people, the more I become convinced that many people don’t understand logic, which is inimical to humanity, isn’t it? If people don’t know how they can be certain a conclusion is logical, they are more likely to make illogical choices, right? Even worse is that people use the word “illogical” when what they really mean is ” I don’t like your idea” or “your idea sounds ridiculous to me.” To top it all off, no one is talking about this. I had to learn symbolic logic in college as an elective, and everything I have learned after that has been through my own studies. Shouldn’t logic be more important to the functioning of a society, especially in a democracy (if you’re in America) where everyone must decide who has logical arguments and who does not?

    Comment by William Quayd Escobedo — May 23, 2016 @ 3:45 pm | Reply

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