Fallacies are errors in reasoning that can undermine an argument and lead to false conclusions. These errors can be divided into two types:
- Formal fallacies, which are about the structure of the argument (syntax) – regardless of the specific example within that structure.
- Informal fallacies, which are about the content and context of the argument (semantics) – meaning whether the argument is fallacious or not depends on the specific details or example.
In this post, we’ll look at the difference between formal and informal fallacies, giving examples of each, and explain when and where these errors in reasoning occur.
What is a Formal Fallacy?
A formal fallacy occurs when there is a mistake in the structure of an argument.
Formal fallacies can be thought of as syntactic because they are errors in the structure or form of the argument. The term ‘syntax’ refers to the arrangement of symbols or components within a system (in this case, the logical structure of an argument).
A formal fallacy occurs when the logical form or structure of the argument is flawed, meaning that even if the premises are true, the conclusion does not necessarily follow from them. This type of error is identifiable purely by examining the form of the argument, without needing to understand the specific content or meaning of the terms involved.
Example 1: Affirming the Consequent
Affirming the consequent is an example of a formal fallacy. It takes the following form:
1. If A, then B.
2. B.
3. Therefore, A.
The invalidity of this inference can be demonstrated in the absence of any practical example via a truth table (see this post for more).
However, we can also illustrate why this argument is invalid by plugging in some practical examples that maintain exactly the same format as the argument above:
1. If it rains, the ground will be wet.
2. The ground is wet.
3. Therefore, it rained.
At first glance, this might seem a convincing argument. However, this argument is invalid – it commits a formal fallacy – because the conclusion doesn’t necessarily follow from the premises.
It’s possible for the premises to be true and the conclusion false: Just because the ground is wet, that doesn’t prove that rain was the cause. For example, it could have been months since it rained and perhaps someone used a hosepipe to water the grass. If this is the case, then 1 and 2 (the premises) would be true but 3 (the conclusion) would be false.
Again, formal fallacies are purely about the structure of the argument, so you don’t need to know anything about the content to spot the error. For instance, the same fallacy could be expressed as:
1. If I study, I will pass the test.
2. I passed the test.
3. Therefore, I studied.
In both cases, the error is in assuming that the conclusion must follow, which it doesn’t. Unlike valid argument formats – such as modus ponens and modus tollens – it’s possible for the premises of this argument structure to be true and the conclusion to be false.
Example 2: Denying the Antecedent
Denying the antecedent is another example of a formal fallacy. It follows this structure:
1. If A, then B.
2. Not A.
3. Therefore, not B.
To understand why this is also a fallacy, consider the following argument which uses the same example as before:
1. If it rains, the ground will be wet.
2. It did not rain.
3. Therefore, the ground is not wet.
Again, this argument is invalid because the conclusion does not necessarily follow from the premises – it’s possible for the premises to be true and the conclusion false.
Even if the first premise and the second premise are both true, the conclusion can still be false. Just because it didn’t rain, that doesn’t mean the ground isn’t wet. Again, someone might have watered the grass with a hose or sprinkler, which would make the ground wet despite the absence of rain.
This highlights the structural flaw in the argument: It wrongly assumes that the absence of the first condition (rain) automatically rules out the result (a wet ground). It’s possible that it didn’t rain and yet the ground is wet for some other reason.
What is an Informal Fallacy?
An informal fallacy, on the other hand, is a mistake in the content or context of an argument (check out this list for 15 examples of informal fallacies).
Unlike formal fallacies, which are purely syntactic, informal fallacies can be considered semantic because they are errors that arise from the meaning or content of the argument. The term ‘semantics’ refers to the study of meaning, so informal fallacies often involve misunderstanding or misusing terms, concepts, or language. These fallacies are dependent on the specific content of the argument and can arise from things like vague language, ambiguous terms, or improper assumptions about the meaning of concepts. Informal fallacies can’t be detected just by looking at the form – they require an understanding of the specific details of the argument, making them more subjective and context-sensitive.
Example 1: Fallacy of composition
The fallacy of composition is an example of an informal fallacy. It occurs when someone reasons from the parts of something to the whole, i.e.:
All the parts of X have property Y.
Therefore, X has property Y.
A practical example to illustrate why this is a fallacy could be the following:
Every page of the book is thin
Therefore, the book is thin.
In this example, it’s possible for the premises to be true and the conclusion false: If the book is made from 1,000,000 sheets of paper, for example, it would be a very thick book! In other words, 1 and 2 would be true, but 3 would false.
However, there are instances where this inference is not fallacious. A practical example of this could be:
Every ingredient of the salad is edible.
Therefore, the salad is edible.
Both arguments here have the same structure. But the first argument (the book) is clearly fallacious, while the second (the salad) is not.
The key difference between these two arguments is in the content, not the structure.
In the second example, the conclusion does follow because the property of being edible applies to the whole salad if it applies to all its parts. Unlike the pages of a book, which depends on how its parts combine, edibility is an inherent property of the parts that transfers directly to the whole.
Depending on the example, some features transfer from parts to whole, while others don’t. This illustrates the importance of context when identifying informal fallacies: Whether the fallacy of composition is fallacious is a matter of content, rather than structure.
Example 2: Straw man
However, some informal fallacies are always invalid. One such example is the straw man fallacy, which occurs when someone misrepresents an opponent’s argument to make it easier to refute. Instead of addressing the actual argument, they construct a distorted or exaggerated version and argue against that instead:
Person A makes claim X.
Person B misrepresents claim X as claim Y and attacks Y.
Therefore, Person B claims X is wrong.
A practical example:
Person A says we should reduce military spending and invest the money elsewhere
Person B: “Person A wants to leave the country defenceless by eliminating the military entirely, which is wrong!”
Person B could make a somewhat valid (but irrelevant) argument here, such as:
If we eliminate the military entirely, the country will be defenceless.
Being defenceless is bad.
Therefore, eliminating the military entirely is bad.
But however strong Person B’s reasoning is for this position, his overall argument commits the straw man fallacy because it attacks a position (eliminating the military entirely) that Person A never actually proposed.
Again, the problem lies in the content – the distorted interpretation of Person A’s argument – not the structure of the reasoning itself.
Summary
Both formal and informal fallacies can undermine an argument, but they require different tools to identify.
Formal fallacies (e.g. affirming the consequent) are errors that occur because of a breakdown in the logical structure of the argument – the conclusion doesn’t follow logically from the premises. As such, formal fallacies can be identified without any knowledge of the meaning of the words involved in the argument.
Informal fallacies (e.g. fallacy of composition), on the other hand, arise from issues within the argument’s content – things like assumptions, irrelevant points, emotional appeals, or misrepresentation. As such, informal fallacies can only be identified by understanding the meaning of the words involved in the argument. This dependence on content can make informal fallacies more difficult to spot – they are influenced by things like word choice, ambiguity, and contextual usage, rather than just the abstract form of the argument.
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