From the Star Trek TOS episode “I, Mudd”

As anyone who frequents this blog knows, I spend a lot of time talking about logical fallacies. I frequently criticize peoples’ arguments for having them, and I present them as a reason for rejecting particular lines of thought. Nevertheless, many people fail to realize just how important they are, and showing someone that they have committed a fallacy rarely makes them reject their argument. Indeed, I once had someone say, “just because my argument technically contains a fallacy doesn’t mean that the underlying logic is wrong.” In reality, however, that is exactly what it means. Logical fallacies are, by definition, flawed lines of reasoning, and anytime that an argument contains a fallacy, that argument must be rejected. Therefore, understanding logical fallacies is critical for analyzing arguments and holding rational views, and in this post, I want to try to explain why fallacies are so important, how to detect them, and why their presence destroys an argument.

The structure of an argument

All arguments can be broken down into premises and conclusions. The premises are the facts that you are presenting, the conclusion is the thing that you are arguing for, and the goal is to set up the argument such that the conclusion must follow necessarily from the premises. In other words, for an argument to be a good argument, it must be set up such that if the premises are true, then the conclusion must also be true (this is what we call a “valid argument”). Additionally, the premises must, of course, actually be true (when both conditions are met, the argument is said to be “sound”). For now, I want to focus on the requirement that the conclusion must follow necessarily from the premises, but we will come back to the true premise requirement later.

 Note: I am talking specifically about deductive arguments here and throughout this post. There are other types (such as inductive and probabilistic) in which the premises show that the conclusion is most likely true, rather than that it must be true.

 To illustrate how this works, let me use the following example (this is set up in what is known as a syllogism).

• Premise 1: Bill is larger than Bob
• Premise 2: Bob is larger than Tom
• Conclusion: Therefore, Bill is larger than Tom

This is a logically valid argument. In other words, as long as those premises are true, then the conclusion must also be true. There are no other options. If Bill is larger than Bob, and Bob is larger than Tom, then it must be true that Bill is larger than Tom (this example is also an illustration of something known as the law of transitive properties). Importantly, you should note that the underlying logical structure is what matters here. As long as that structure works (which it does), we can replace those premises with any other true premises, and the resulting conclusion will be true (as long as we haven’t changed the underlying structure). In other words, we can reduce this argument to the following logical structure:

• Premise 1: A is larger than B
• Premise 2: B is larger than C
• Conclusion: Therefore, A is larger than C

Now, we can replace A, B, and C with any true facts, and the argument will work. For example,

• Premise 1: Jupiter is larger than earth
• Premise 2: The earth is larger than the moon
• Conclusion: Therefore, Jupiter is larger than the moon

Or

• Premise 1: A train is larger than an ant
• Premise 2: An ant is larger than a bacterium
• Conclusion: Therefore, a train is larger than a bacterium

I could keep going, but hopefully you get the point. It doesn’t matter what premises I use, or how disparate the items in them are. As long as the premises are true and I retain the same logical structure, then the conclusion must be true. Further, if you can find a single example in which this structure and true premises results in a demonstrably false conclusion, then you have shown that the argument’s structure must be flawed. In other words, for a deductive argument, the logical structure must work 100% of the time, or else the logical structure is flawed.

It may seem like I am off topic here, but understanding this is really important, because, as I will explain below, many logical fallacies operate by breaking an argument’s logical structure. In other words, they change the argument so that the conclusion does not follow necessarily from the premises.

Non-sequitur fallacies

Now that you understand the importance of a logical structure, let’s look at a large family of fallacies collectively known as non-sequitur fallacies. These occur anytime that an argument’s structure is such that the conclusion does not follow necessarily from the premises, but there are many specific subcategories and types of fallacies within that overarching umbrella term.

To begin, let’s look at what is probably the most common example in all of philosophy. Consider the following deductive argument:

• Premise 1: All men are mortals
• Premise 2: Socrates is a man
• Conclusion: Therefore, Socrates is a mortal

We can reduce this argument to the following structure:

• Premise 1: All X are Y
• Premise 2: Z is X
• Conclusion: Therefore, Z is Y

That may seem confusing, but if you think about it for a second, you should be able to convince yourself that it will work 100% of the time. If all X are Y, and Z is X, then Z must also be Y.

Now, consider the following extremely similar argument:

• Premise 1: All men are mortals
• Premise 2: Socrates is a mortal
• Conclusion: Therefore, Socrates is a man

An example of an affirming the consequent fallacy

Now we have a problem. This argument does not work. The conclusion does not follow necessarily from the premises, and the reason for that is a logical fallacy known as affirming the consequent. This fallacy alters the logical structure in a way that prevents the premises from leading necessarily to the conclusion. We can write it as follows:

• Premise 1: All X are Y
• Premise 2: Z is Y
• Conclusion: Therefore, Z is X

Again, if you think about that for a minute, you should see the problem. The fact that all X are Y does not mean that all Y are X. Thus, it is possible for Z to be Y, but not X. We can easily illustrate this with an example.

• Premise 1: All men are mortals
• Premise 2: My pet iguana is a mortal
• Conclusion: Therefore, my pet iguana is a man

Obviously, that doesn’t work. It is clearly a bad argument. It has an invalid logical structure in which the conclusion does not follow necessarily from the premises, and, as a result, it produces an incorrect conclusion. Remember, if a deductive logical structure is valid, then it must produce true conclusions 100% of the time (when supplied with true premises). Therefore, the fact that my example has an incorrect conclusion proves that this structure is invalid.

Now, what does this have to do with affirming the consequent fallacies? Well that name, “affirming the consequent” is simply the term that we use to describe this logical structure. In other words, by demonstrating that this logical structure is invalid, I have shown that an argument that contains this structure (i.e., that contains an affirming the consequent fallacy) is invalid. This is why it is so important to understand logical fallacies and take them seriously when they are pointed out to you: they result in arguments with invalid logical structures. In other words, they create arguments in which the truth of the premises does not guarantee the truth of the conclusion.

To further illustrate this, let’s move on from affirming the consequent fallacies and talk about a different fallacy: post hoc ergo propter hoc (or just “post hoc” for short). This is one of the most common fallacies that I encounter in debates about scientific topics, and it takes the following logical structure.

• Premise 1: Q happened before U
• Conclusion: Therefore, Q caused U

The problem with that should be pretty obvious: the fact that one thing happened before another doesn’t mean that one caused the other. In other words, the conclusion does not follow necessarily from the premise. We can easily illustrate this with simple examples.

• Premise 1: I performed a sacrifice, then it rained
• Conclusion: Therefore, my sacrifice caused the rain

Or

• Premise 1: I read a book, then had a heart attack
• Conclusion: Therefore, reading the book caused the heart attack

Do you see how that works (or, rather, doesn’t work)? The fact that one thing happened before another does not lead to the conclusion that there is a causal relationship. The logical structure is invalid, and any arguments containing this structure (i.e. containing a post hoc fallacy) must be rejected. On a side note, this is a fundamental reason why anecdotes are worthless as evidence of causation. The fact the you got better after taking something doesn’t mean that it worked, and the fact that you had an adverse event after taking something doesn’t mean that the treatment caused the event. Both of those arguments contain this structure (i.e., they are post hoc fallacies), and, as such, they are not valid, and the conclusion does not follow necessarily from the premise.

There are lots of other examples of this overarching type of fallacy, such as denying the antecedent, correlation fallacies, guilt by association, arguments from ignorance, etc., but they all have the same problem. Namely, they are invalid because they set up a logical structure in which the conclusion does not follow necessarily from the premises.

The fallacies of untrue premises

Another major “group” of fallacies work by either implicitly or explicitly making an untrue premise. The problem here should be obvious: if an argument relies on an untrue claim, then the argument must be rejected (i.e., it is not sound). As before, an easy way to test for this problem is to see if you can find any examples in which the argument doesn’t work.

Note: these groupings of fallacies are not officially recognized. They are just groupings that I personally find to be useful when thinking about fallacies and how/why they work (or don’t work, as the case may be).

Let me explain what I mean by using one of the most common variants of these fallacies: the appeal to nature fallacy. This fallacy occurs whenever someone asserts that something is good/useful/healthy because it is natural or that something is bad/useless/unhealthy because it is unnatural. When can set this argument up the following way.

• Premise 1: X is natural
• Conclusion: Therefore, X is good

That obviously doesn’t work, however, because there are plenty of true things that we can substitute for premise 1 that clearly result in false conclusions. For example:

• Premise 1: The plague is natural
• Conclusions: Therefore, the plague is good

Now, you could stop right there, and call this another variant of the non-sequitur fallacy, and you wouldn’t be wrong. This structure, as I have presented it, clearly is invalid because the conclusion does not follow from the premise. However, I think that there is a more useful way to think about this fallacy and others like it. Namely, this fallacy has an assumed premise that is false. It assumes that everything natural is good. Thus, there is really an implicit second premise.

• Premise 1: X is natural
• Premise 2: Everything natural is good
• Conclusion: Therefore, X is good

That second premise is, however, clearly false, and as a result, the argument fails (i.e., it’s not sound). Importantly, that premise (or some variant thereof, including the inverse “everything unnatural is bad”) is present in all appeal to nature fallacies. Thus, anytime that this fallacy is present, the argument must be rejected, because it inherently assumes an untrue premise.

There are many other, “appeal to” fallacies, and they all have the same basic structure and problem. For example, appeal to authority fallacies occur when you say that something is true because of the person who says that it is true. When you do that, however, you are inherently invoking the premise that the person in question is infallible, which is clearly false. Other examples include appeals to popularity (which assume that everything popular is good/right), appeals to antiquity (which assume that anything old is good/right), appeals to tradition (which assume that anything traditional is good/right), etc. (note: the one exception to this structure is the appeal to emotion fallacy, which simply makes an argument based on emotions, rather than facts or logic).

Note: You could also apply my “implicit untrue premise” explanation to some of the non-sequitur fallacies that I described earlier. For example, you could say that post hoc ergo propter hoc fallacies include the assumed premise that if Q happens before U, then Q caused U. There is nothing wrong with that way of conceptualizing those fallacies, and you are welcome to use it, I just personally find that explanation to be more complicated when the premise isn’t as simple as “everything natural is good.” You can, however, think of these fallacies either way. You can think of them as having an implicit and untrue premise or as having an invalid structure. I don’t care which you use, just so that you understand the concepts.

Another common fallacy is much less subtle and directly states untrue premises. I am, of course, referring to the straw man fallacy. This occurs whenever you attack a weakened or misrepresented version of your opponent’s argument, then claim to have defeated their actual view.  In other words, you say, “My opponent believes X, and X is wrong for reasons Y” when, in reality, X is a distortion or misrepresentation of what your opponent believes. Thus, your first premise is false (there are also subsets of this fallacy such as reductio ad absurdum).

Fallacies of the false dilemma are yet another example of fallacies that operate via untrue premises. These take the form of “Either X or Y is true, X is false, therefore Y is true.” This sounds great, until you realize that premise one is false, and there was actually a third option (Z) that wasn’t stated.

Detecting logical fallacies

Finally, I want to briefly talk about some tools for detecting whether a logical fallacy has been committed. Obviously, your best bet is to study the different types of fallacies and learn how each of them works. I have compiled a list of common fallacies to help with that, as have many other sites (e.g. Internet Encyclopedia of Philosophy [this is probably the most comprehensive one], Skeptical Raptor, Your Logical Fallacy Is, and many others) . Let’s assume, however, that you don’t have time for that, you can’t be bothered, or maybe you have studied them, but still struggle with particular arguments (don’t worry, that happens to all of us). Fortunately, there are some simple things that you can do.

First, I strongly recommend that you practice breaking an argument down into a syllogism like I have done throughout this post (start with the actual facts in the argument). Often, when you do that the problems will jump right out at you. If nothing immediately jumps out at you however, then try replacing the facts with letters (again, like I have done throughout). Then, look carefully at that structure and see if it is valid. See if the conclusion has to follow from those premises, and see if there are any implicit premises that need to be added. If, at that point, it is clear that either the conclusion does not follow necessarily from the premises or that there is an implicit and untrue premise, then you are done. The argument is flawed and you should reject it. If neither of those are obvious, then move onto the next tool.

The second tool is simply to try to find examples where the logical structure of the argument fails. Use the syllogism that you constructed before, but this time, make actual premises that are true but unrelated to the topic of debate (like I did by using a sacrifice to show that post hoc fallacies were invalid). If you can find any examples (hypothetical or actual) where the premises are true, but the conclusion is clearly false, then you have just demonstrated that the logical structure is invalid (assuming that you were careful and did not alter the structure, otherwise you’ve committed a straw man fallacy). This is a very useful tactic that you should get in the habit of using (I explained it in more detail here).

Although those two tools are useful, unfortunately, they aren’t all-encompassing. There are many other types of fallacies that I have not covered here because they are more specialized and difficult to generalize. Many of these are actually errors in debate tactics more than errors in reasoning. For example, a red herring fallacy occurs when, in a debate, you ignore your opponent’s argument/question and go off on an irrelevant side tangent in order to dodge a problem that they pointed out (politicians are masters of this). This type of fallacy is much harder to detect via a simple key like what I have presented, because there is no way to really construct a syllogism. It’s not a proper argument. Rather, it is a means of avoiding an argument. Similarly, for both straw man fallacies and false dilemma fallacies, you need to have enough knowledge on the topic at hand to tell that a false premise has been presented. That is the only way to detect them. So, although the tools that I have presented are useful and work in many situations, there really is no substitute for actually studying fallacies and becoming familiar with them.

Conclusion

Obviously, this post has been far from exhaustive, and there are many other fallacies (and even types of fallacies) that I didn’t address. However, this should give you a basic understanding of why fallacies are a problem, as well as some tools for detecting them. Anytime that a fallacy is present, the argument must be rejected, because you cannot be confident that the conclusion is actually supported by that argument. Thus, you should be mindful of logical fallacies and strive to avoid them in your arguments and views. Further, if someone points out that you have committed a fallacy, take that accusation seriously and look closely at their claim to see if it is correct. No one is immune to these flaws in reasoning, but there is no excuse for ignoring them once they have been pointed out to you.

 Note: It is worth emphasizing that when an argument contains a logical fallacy you must reject the argument not the conclusion (rejecting the conclusion rather than the argument is actually a fallacy known as the fallacy fallacy [that’s not a typo]). It is entirely possible to have an invalid argument, but a true conclusion. In other words, your conclusion may be true, but you cannot use that particular argument to support it, and it must be supported by other lines of evidence/reasoning.

Related posts

• Don’t attack the straw men: Straw man fallacies and reductio ad absurdum fallacies
• Dying the way that nature intended: Appeal to nature fallacies
• Stop accusing me of ad hominem fallacies you stupid idiots
• The genetic fallacy: When is it okay to criticize a source?
• The nirvana fallacy: An imperfect solution is often better than no solution
• The Rules of Logic Part 1: Why Logic Always Works
• The Rules of Logic Part 2: Good vs. Bad Arguments
• The Rules of Logic Part 3: Logical Fallacies
• The Rules of Logic Part 6: Appealing to Authority vs. Deferring to Experts
• The Rules of Logic Part 7: Using Consistent Reasoning to Compare Apples and Oranges