Arguments and How They Fail

A short guide to debate and logical fallacies.

Posted Jun 22, 2019

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"I strongly object to wrong arguments on the right side," said GK Chesterton. "I think I object to them more than to the wrong arguments on the wrong side."

Arguments are attempts to persuade by providing reasons (or premises) in support of a particular claim (or conclusion). 

There are two broad kinds of argument: deductive and inductive. In a deductive argument, the conclusion follows from the premises as their logical consequence:

  • All dogs are mammals. (Premise 1)
  • Fluffy is a dog. (Premise 2)
  • Therefore, Fluffy is a mammal. (Conclusion)

In an inductive argument, the conclusion is merely supported or suggested by the premises.

  • Whenever I eat hazelnuts, my mouth tingles. (Premise 1)
  • Whenever I eat walnuts, my mouth tingles. (Premise 2)
  • I am allergic to nuts. (Conclusion)

Even when sincere, arguments are often messily made, with premises and conclusions embedded in extraneous material and presented in any order or none at all. In many cases, a premise or conclusion may be implicit, that is, taken for granted and omitted from the argument.

  • Wuthering Heights is the best book ever written in the English language. Each year for the past 10 years, it has received more votes than any other book in our survey of British readers.

If we were to reconstruct this (flawed) argument, it might run something like this:

  • British public opinion accurately reflects literary merit in the English language. (P1, an implicit, and flawed, premise)
  • Our survey accurately reflects British public opinion. (P2, another implicit premise)
  • For the past ten years, Wuthering Heights has topped our survey. (P3)
  • Therefore, Wuthering Heights is the best book ever written in the English language. (C)

Validity and soundness

Parts of arguments are either true or false—unless they are vague or ambiguous, in which case they are indeterminate. But arguments themselves, taken as a whole, are either valid or invalid. An argument is valid if its conclusion is a logical consequence of its premises, regardless of the truth or falsity of the premises, or indeed of the conclusion.

  • All organisms with wings can fly. (P1, False)
  • Penguins have wings. (P2, True)
  • Therefore, penguins can fly. (C, False)

Although the above argument is valid (it "works"), it is unsound. For an argument to be both valid and sound, all of its premises have to be true—and, of course, the conclusion has to follow logically from the premises. In such cases, the conclusion is bound to be true.

  • All mammals are warm-blooded. (P1, True)
  • Bats are mammals. (P2, True)
  • Therefore, bats are warm-blooded. (C, True)

For an inductive argument, the equivalent of soundness is cogency. An inductive argument is cogent if its premises are true and render the truth of the conclusion more or less probable.

If you’re having trouble deciding whether the form of a deductive argument is valid or invalid, it can be useful to formulate a parallel argument with exactly the same form, true premises, and an obviously false conclusion.

Argument:

  • Some farmers are landowners.
  • Some landowners are aristocrats.
  • Therefore, some farmers are aristocrats.

The argument in symbol or general form:

  • Some A are B.
  • Some B are C.
  • Therefore, some A are C.

Parallel argument:

  • Some insects are herbivores.
  • Some herbivores are mammals.
  • Therefore, some insects are mammals. 

Formal fallacies

A fallacy is some kind of defect in an argument, whether unintended or intended (with the aim to deceive). A formal fallacy is a deductive argument with an invalid form, such as the one above: The argument is invalid regardless of the truth of its premises. In contrast, an informal fallacy is a defect that can only be identified by an analysis of the content of the argument. One way to think about it, as far as deductive arguments are concerned, is that, whereas formal fallacies are invalid, informal fallacies are unsound.

Common formal fallacies include "affirming the consequent" and "denying the antecedent."

Affirming the consequent (also called converse error) is to infer the converse from the first premise. 

  • If A, then B.
  • B.
  • Therefore, A.

For example:

  • If I have the flu, then I have a fever.
  • I have a fever.
  • Therefore, I have the flu.

Denying the antecedent (also called inverse error) is to infer the inverse from the original statement.

  • If A, then B.
  • Not A.
  • Therefore, not B.

For example:

  • If it snows, Jill works from home.
  • It’s not snowing.
  • Therefore, Jill is not working from home.

You get the idea, and the idea is all you need, so let’s move on to something a little more entertaining…

Informal fallacies

Informal fallacies, popular with politicians and conmen of all stripes, are frequently found in inductive arguments and can be very hard to uncover. What follows is a selection of some of the more common or important informal fallacies, with, for each fallacy, a short definition and live example (verbatim examples are referenced at the foot of the article).

A "red herring" is a deliberate attempt to weaken or gloss over an argument by diverting attention away from it or its central tenets. 

       —Critical appraisal of the new Bordeaux vintage would be more objective and meaningful if the wines could be tasted blind. —Just Bordeaux?

Straw man is to misrepresent an argument, and then knock it down to score an easy win.

       He believes we can treat the U.S. economy like one of his casinos and default on our debts to the rest of the world, which would cause an economic catastrophe far worse than anything we experienced in 2008.

Here's another example:

       If you go with what Hillary is saying, in the ninth month, you can take the baby and rip the baby out of the womb of the mother just prior to the birth of the baby. Now, you can say that’s OK. But it’s not OK with me, because based on what she’s saying, and based on where she’s going, and where she’s been, you can take the baby and rip the baby out of the womb in the ninth month on the final day. And that’s not acceptable.

Ad hominem ("to the man") is to attack not the argument itself, but the person making it.

       Crooked Hillary Clinton is the worst (and biggest) loser of all time. She just can’t stop, which is so good for the Republican Party. Hillary, get on with your life and give it another try in three years!

Genetic fallacy is to accept or reject an argument on the basis of its proponents or origins.

       I think the people in this country have had enough of experts, people from organizations with acronyms saying that they know what is best and getting it consistently wrong.

Appeal to hypocrisy (tu quoque, "you too") is to dismiss an argument on the grounds that its proponent’s behavior is inconsistent with it.

       I don’t buy into your arguments for higher taxation. You yourself have used every trick in the book to minimize your effective tax rate—indeed, the very tricks that you propose to ban.

Note that ad hominem, genetic fallacy, and appeal to hypocrisy are all three closely related.

Appeal to popularity, also called appeal to democracy or consensus fallacy, is to conclude the truth of a proposition on the basis that most or many people believe it to be true.

       Of course he’s guilty: Even his own mother has turned her back on him.

Argument to moderation, also called the Englishman’s fallacy, is to argue that the moderate view or middle position must be the right or best one.

       Half the country favors leaving the European Union, the other half favors remaining. Let’s compromise by leaving the European Union, but remaining in the Customs Union.

Bifurcation (false dilemma, false trilemma, etc.) is the presentation of limited alternatives when there are in fact more, creating the false impression that the alternatives presented are either mutually exclusive or collectively exhaustive. Bifurcation is often an attempt to force a Hobson’s choice of "take it or leave it." 

       It’s my deal or no deal.

       It’s my deal, no deal, or no Brexit at all.

Analogical fallacy is to assume that things which are similar in one or more respects must be similar in all respects. 

       Like prisons, mental hospitals feature security officers, high walls and fences, and locked or barred windows. And, like prisons, mental hospitals are a form of punishment for deviant behavior.

Cum hoc ergo propter hoc ("with this, therefore because of this") is to assume that correlation necessarily implies causation.

       Studies have found that people who drink red wine with their meals are, on average, less likely to suffer from heart disease. Therefore, drinking red wine with meals protects against heart disease.

There could, in this case, be a third factor involved; for example, people who drink red wine with their meals may tend to eat more healthily or be less stressed.

Gambler’s fallacy is the assumption that the outcome of one or more independent events can influence the outcome of a subsequent independent event.

       June is pregnant with her fourth child. Her first three children are all boys, so this time it’s bound to be a girl.

Runaway train is an argument that is used to justify a particular course of action, but which, on its own, would also justify much more drastic action in the same direction.

       Speed kills. Reducing the speed limit from 30 to 20 mph will reduce the number of fatal road traffic accidents.

In which case, why not reduce the speed limit to 0 mph?

Argument from ignorance, also called the negative proof fallacy, upholds the truth of a proposition based on a lack of evidence against it, or the falsity of a proposition based on a lack of evidence for it. 

       Of course God exists. How else do you explain life on Earth?

Argument from ignorance is often used to shift the burden of proving or disproving something onto the other side, when normally this burden rests with the party staking the claim.

Begging the question is to argue in circles, supporting the conclusion by means of itself.

       I oppose same-sex marriage. Marriage is the union between a man and a woman. Same-sex marriage is not marriage.

This is more or less equivalent to "I’m right because I say so."

See my follow-up article, The Art of Persuasion.

References

G.K. Chesterton, The Collected Works of G.K. Chesterton Volume 32: The Illustrated London News, 1920-1922.

Hillary Clinton, National Security Speech Delivered at Balboa Park, San Diego, California, 2 June 2016.

Donald Trump, Third Presidential Debate, 20 October 2016.

Donald Trump on Twitter (@realDonaldTrump), 18 November 2017.

Michael Gove, during an interview with Faisal Islam on Sky News, June 3, 2016.

Theresa May, at various times during her prime ministership.