Critical Thinking Toolkit: Non Sequiturs

Whenever we are presenting reasons for a position we believe or are involved in dialogue with a person we disagree with, one of the most important things for us to do is to to clearly lay out our reasons for what we believe. Built into this important criteria of conversation is the idea that our reasons actually do support what we say they support. This is where the idea of non-sequiturs come in.

Before we can discuss the nature of a non-sequitur, we first need to do a brief review of formal logic.

What is Formal Logic?

I’ve discussed some formal logic in my discussion of mathematics, as mathematics heavily relies on formal logic. But for this article, we need not go through every single detail. The overarching idea is much more important. In philosophy, the notion of formal logic is the notion of “irrefutable lines of reasoning.” Something would be considered “irrefutable” if denying it basically requires you to completely give up your mental integrity. I’ll give two examples of formal arguments:

Argument 1

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

Argument 2

  1. Either A is true or B is true.
  2. A is not true.
  3. Therefore, B is true.

Take a moment to think about those. Pick either one of the arguments. Suppose you already agree with (1) and (2) in that argument. Can you see that you then are forced to believe (3) as well? A person who agrees with (1) and (2) but disagrees with (3) is in denial. Perhaps rejecting either (1) or (2) is understandable, but you just can’t say that both (1) and (2) are true and that (3) is false. You just… can’t. It probably feels like I’m rambling on about nothing. In a sense, that is right. This is extremely basic. And that is the point I want to make. Formal logic is just the realm of things that are this basic.


We can now get to the main theme of the article. A non sequitur happens when somebody claims to be using formal logic but really is not. The name non sequitur comes from Latin, where it translates into English as “it does not follow.” For this reason, non sequiturs are also called formal fallacies, because it is a mistake in formal logic.

Examples of Non Sequiturs

There are many, many examples of non sequiturs. I am going to restrict myself to those that are, in a sense, most basic. When I say “most basic,” I mean those that use such simple language that, if you don’t pause to think about it, you migth actually think are valid. Here are some examples of non sequiturs:

Affirming the Consequent

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

Denying the Antecedent

  1. If A is true, then B is true.
  2. A is not true.
  3. Therefore, B is not true.

Affirming a Disjunct

  1. Either A is true or B is true.
  2. A is true.
  3. Therefore, B is not true.

Denying a Conjunct

  1. At least one of A and B is false.
  2. A is false.
  3. Therefore, B is true.

These may look weird. That’s ok. Statements of formal logic, whether they are correct or not, look weird sometimes. I encourage my readers to find some ways to fill in A and B in these four examples where you agree with (1) and (2) but might disagree with (3). I’ll give you an example for “affirming the consequent.”

  1. If it is raining, the ground is wet.
  2. The ground is wet.
  3. Therefore, it is raining.

Although is is quite possible that all of (1), (2), and (3) are true, it is pretty easy to think of a situation where (1) and (2) are true and (3) is not true. Maybe it just stopped raining 5 minutes ago. Then the ground would still be wet, so (2) is right, and it is still quite reasonable to say that the ground is always wet when it is raining, so (1) is right as well. But it is not now raining, so (3) would be wrong. This is what it looks like for a series of statement to be a non sequitur – by claiming that (1) and (2) are true, it does not follow that (3) is true. (3) may or may not be true.

Things that are Not Non Sequiturs

There are such things as informal arguments, and these are not non sequiturs. For example, pretty much all of science relies on informal arguments called inductive arguments. Inductive arguments involve collecting lots of data and inferring that, were you to go collect more data, that data would agree with whatever patterns you find in the data you already have. If you try to make this into a formal argument, then it is a non sequitur. There is no undeniable, infallible rule of logic that dictates this way of thinking. But scientists do not claim to be using formal logic, and so they are not guilty of a non sequitur. This is important.

It is also important if you are going to understand non sequiturs to understand what the rules of logic actually are. To see those basic rules, see my post here, which is an overview of the rules of logic.

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