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The math topics covered in the last few postings were a subset of a broader category of fallacies, errors in reasoning that come up so frequently that they have been organized, categorized and assigned cool names in both English and Latin (which gives you a sense of how long people have been breaking logical rules).

We can start by making a distinction between formal and informal fallacies. Like formal logic, formal fallacies are only concerned with the structure of an argument – in this case mistakes in that structure – rather than the content of statements in the argument.

For example, in his 1975 comedy Love and Death, Woody Allen made this fallacious version of an argument that’s been used to teach students logic since at least the Middle Ages:

Premise 1: All men are mortal.

Premise 2: Socrates is a man.

Conclusion: Therefore, all men are Socrates.

The conclusion to the correct version of this argument is “Socrates is mortal,” but in Allen’s version, he mixed up which terms to include in the conclusion, a structural error that makes this a formal fallacy.

While this example was meant to jump out at you for comic effect, other formal fallacies are harder to spot. For example, if someone claims that if the country continues to open up the economy the stock market will go up, and the stock market is indeed going up, claiming that economic opening is the cause of the rise in stock prices would be fallacious. Why? Because there are any number of reasons why the stock market goes up (and down) that have nothing to do with the status of economic opening.

You can see this more clearly in an example structured exactly the same way as our stock market argument:

Premise 1: If Torrance gambled away all his money, he would be broke.

Premise 2: Torrance is broke.

Conclusion: Therefore, Torrance gambled away all his money.

As with our argument over economic opening, there are many ways Torrance might have gone broke that do not involve him gambling.

Unlike formal fallacies, informal fallacies are concerned with the content of the statements in an argument. For example, the widespread practice of condemning people for the behavior of their Twitter followers (whether or not that condemnation is accompanied by trying to get them de-platformed or fired from their jobs) is an example of an association fallacy, more commonly referred to as guilt by association.

Similarly, Donald Trump’s advocacy for various unproven remedies for COVID based on their support from doctors and scientists represents a fallacy called argumentation from authority.

But aren’t those doctors and scientists actual experts in their fields? Well, yes, but some of those fields are not ones associated with the creation of anti-viral cures. And even if some of his preferred experts do have experience in the right branches of medicine, because their opinions are outside the mainstream of medical consensus, Trump is committing a fallacy by not pointing that out.

This doesn’t mean that treatments proposed by such mavericks are necessarily quack cures (many scientific breakthroughs came from bold thinkers ready to break from consensus, after all). But if you want to avoid committing authority-related fallacies, you need to make clear the nature of the authorities you turn to.

If you take the time to pore over this list of fallacies, you’ll notice that there are far more informal fallacies than formal fallacies, highlighting the fact that a lot more can go wrong with the substance of an argument than with its structure.

Given how easy it is to spot fallacies in the news of the day, let’s see next time how many of them we can find in campaign commercials that have been released since election 2020 kicked off post-convention.


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