How to win an argument (Part 1)

Can you win an argument without any evidence, or without even being right? By the end of these articles, you should be able to.

Think about how many times we have come across someone who is clearly wrong, but seems to have all the answers, all the arguments and absolutely no weak points? They may be suffering from argumentum verbosium, which is when someone

tries to persuade by overwhelming those considering an argument with such a volume of material that the argument sounds plausible, superficially appears to be well-researched, and it is so laborious to untangle and check supporting facts that the argument might be allowed to slide by unchallenged. Wikipedia

So how do we defeat these ‘masters of argument’?

Identifying the problems, mistakes, assumptions and fallacies in an argument can be tricky. This is especially because the symbols usually used to explain them can be very confusing.

Take this for example:

∃x[sky(x) & blue(x) & ∀y(sky(y) → x=y)]

Which means “The sky is blue.”1 Great.

I’m going to put together a list of fallacies (misconceptions as a result of incorrect reasoning) while trying not to use the brain-blending symbolism above. I will use symbols, but they will likely be of breasts or bananas, or other things beginning with ‘b’.

There are two broad categories of fallacy: problems with reasoning and problems with words. The latter is usually to do with the fact that words can mean more than one thing. The former is mainly to do with the fact that our natural reasoning is not as rigorous as true, proper, mathematical, godlike logical reasoning. Well, not necessarily godlike. Or true. But that’s another discussion entirely.

Problematic reasoning stems from generalisations, assumed implications, distractions, circularity or just plain old laziness. Today I will talk about generalisations and assumed implications, because I’m just lazy.

-- Surgeons

Generalisations are the most common mistake people make. We are very good at generalising, it’s hard wired into our brains to look for patterns and generalisations to make our lives easier. The problem comes when we start to construct arguments around them.

We are all guilty of generalising from too little evidence. For a long time people said that all swans were white. Until they found a black one. Then they felt silly. This is known as destroying the exception, because in claiming that all swans are white, you destroy the possibility of there being any black ones (or fuschia ones for that matter).

Another problem with generalisations is disregarding the exception. Cutting people up with knives is a crime. That clearly doesn’t apply to surgeons. So to argue that because surgeons cut people up with knives, they must all be criminals, is silly. And probably wrong.

Which brings me to an aside. The argument about surgeons being criminals is invalid. This doesn’t mean, however, that its conclusion is wrong. All surgeons might be criminals - but they wouldn’t be criminals because they cut people up with knives. Finding fallacies in an argument does not automatically make the conclusion come out false - it just means that your opponent has to find another argument to support their position.

-- Clouds

Another natural mistake in our everyday reasoning is assuming implication. If it is true that one thing implies another, we implicitly allow for the possibility that the implication works the other way round. It is true that rain implies clouds, but not that clouds imply rain. But we do get the feeling that clouds imply rain. We’re wrong, clouds imply rain maybe occurred or maybe is occurring or maybe is going to occur. Rain implies clouds. Straight, bang, just like that - no wishy-washy maybes.

In symbolic logic, an arrow is used to describe this relationship. The arrow goes from rain to clouds, but not from clouds to rain. It is unfortunately called confirming the consequent when we assume that the arrow goes the other way. Like this:

(1) “If it is raining, then there are clouds.”

- Setting up the arrow from rain to clouds.

(2) “There are clouds.”

- Confirming the consequent (the bit after ‘then’).

(3) “Therefore, it is raining.”

- Mistaking the direction of the arrow.

It might not be raining. In fact, I just looked out of the window and there are clouds and no rain. Ha. Mistaking the direction of the arrow.

You can also mistake the meaning of the arrow. To be more specific, the arrow means that the existence of rain implies the existence of clouds. It does not mean, as is assumed in the next example, that the non-existence of rain implies the non-existence of clouds.

(1) “If it is raining, then there are clouds.”

- Setting up the arrow from rain to clouds.

(2) “It is not raining.”

- Denying the antecedent (the bit before ‘then’).

(3) “Therefore, there are no clouds.”

- Mistaking the meaning of the arrow.

As we saw in the previous example, we can have clouds without rain.

So far we have seen four fallacies: two from not being careful with generalisations and two from not being careful with implications (or conditional relations).

1. Destroying the exception - all swans are white, until you find a black one.
2. Disregarding the exception - all surgeons are criminals cos they cut people up.
3. Mistaking the direction of the arrow (confirming the consequent) - clouds mean it must be raining.
4. Mistaking the meaning of the arrow (denying the antecedent) - no rain means there must be no clouds.

Next time...

Distractions, circularity and plain old laziness.

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Footnotes:
(1) Take a deep breath... “There exists a thing, such that the thing is a sky AND the thing is blue AND for all the stuff that might not be the thing, if it’s a sky, then it’s the thing.”