Introduction to Logic

Once you have something to say, the next step is to say it. Naturally, you want your thoughts to be clear and understood, and you also want what you say to be convincing. Most of all, you want to be correct. Logic is the study of correct reasoning. And the way we express correct reasoning is through argument.

Statements - The Building Blocks of Arguments

An argument is formed by making complimentary statements, and structuring them in an ordered way. A statement is any sentence about which we can ask, "Is it true or false?"

For example, the following sentences are statements:

I have a pet dog.
The capital of the USA is Albuquerque.
My favourite food is pizza.
Pizza is the best food in the world.
Animals have natural rights.

They may be true or false, but they are statements none the less.

The following sentences are not statements:

Can you help me?
Please let me borrow your pen.
May I go to the washroom?
Give me a break!
Don't tell him about the surprise party.
Do you like chocolate ice cream?
Do your homework!

They are not statements, because it does not make sense to ask if they are true or false. They are questions, requests, and commands. They do not fit into the framework of logical argumentation. They can only distract or mislead us from our quest for truth.

How Arguments are Built

An argument is built by organizing statements into premises and conclusions. A premise is a statement that supports a conclusion. They are the reasons why we should accept the conclusion.

For example:

If something grows from the ground and contains seeds, then it is a fruit.
Tomatoes grow from the ground and contain seeds.
Therefore, tomatoes are fruits.

In this example, premises 1 and 2 support the conclusion (3).

Most arguments are not written quite so neatly as in the example above. An argument might be written like this: "Snowy White has lovely fur, and since anything that has fur is a mammal, it follows that Snowy White is a mammal." You will have to pay attention to key words and phrasing to discern the elements of an argument. The argument contained within that sentence could be written out plainly like this:

Anything that has fur is a mammal.
Snowy White has fur.
So, Snowy White is a mammal.

Note that some details in the way an argument is communicated may be irrelevant to the argument itself. In the example above, it does not matter whether the fur is lovely or not. The fact that Snowy White has fur at all is sufficient.

Recognizing an Argument

As important as it is to be able to recognize arguments, it is perhaps more important to learn to recognize when something is not an argument. Many times, in casual and official communication alike, non-arguments are being used to persuade us. People tend to present non-arguments as if they were true arguments quite naturally, so it is imporatant to build a robust defense against their influence, and learn to recognize them immediately.

An argument has two central features:

An argument is trying to convinceus of something. It is trying to prove something. The thing that is being proved is called the conclusion.
It provides evidence to support that conclusion.

Often, when people speak their mind about a subject, they are not providing an argument. They are listing facts, or stating their opinion without arguing their case. Even when people argue (read: fight) for a position they feel strongly about, they are not actually arguing (even if they think they are). Consider these examples:

Snowy White's fur is really soft. She has really cute ears, too. She must be a bunny.
There's no way tomatoes are a fruit. Fruits are sweet, and they don't belong on pizza!
Don't pretend to know anything about history. You don't even know the basics of political geography.
You should really study more. If you worked harder, you could really be something.

Although the claims above appear to be made with some conviction, they are not, in fact, arguments. Even if the speaker believes they are being quite convincing, they are not actually convincing us of anything! (At least, I hope not.) Perhaps it is more clear to say that they do nothing to prove their claims. Let's see what would have to be done to convert the claims into arguments:

1. Snowy White's fur is really soft.
2. Snowy White's ears are really cute.
3. Anything that has really soft fur and really cute ears must be a bunny.
4. Therefore, Snowy White must be a bunny.
Here we can see the true argument which the speaker relies upon to prove their claim. But does it seem quite so convincing now? I can think of many things that have soft fur and cute ears, but that belong to different species of animal. Does the speaker really mean that only bunnies have soft fur and cute ears? More likely, they meant:
1. If something looks like a bunny, then it's a bunny.
2. Snowy White looks like a bunny.
3. So, Snowy White is a bunny.
This works as an argument, and may be what the speaker actually intended to say. Through careful analysis of logic, and correct argumentation, we can achieve greater clarity in our everyday lives!
1. Sweet things don't belong on pizza.
2. Fruit is sweet.
3. Tomatoes belong on pizza (and so they cannot be sweet).
4. Therefore, tomatoes cannot be fruit (since they are not sweet).
This one is a bit more confused, but you can see the argument they seem to be implying more clearly now.

1. In order to know anything about history, one must know the basics of political geography.
2. You don't know the basics of political geography.
3. So, you don't know anything about history.
Still insulting, but at least they're making an argument now. It has clear premises which can be debated, and the exchange is less likely to devolve into a shouting match.

1. You have the latent potential to really be something.
2. In order for latent potential to be realized, it is required that they work hard.
3. If one has the latent potential to really be something, then it should be realized.
This common saying feels weightier when turned into a proper argument. It becomes a question of ethics, or what ought we to do in a given situation.

When clearly expressed as arguments, the claims above become much easier to understand and interact with. Their supporting premises may be strengthened, or contested, opening the way to clear and concise communication.

Of course, we cannot expect people to speak this way in their daily lives. It is also common for people to assert claims with no intention of providing reasons at all! In order to identify an argument, and the premises which may support it, we must pay careful attention to the context in which a claim is said.

When trying to figure out whether something is an argument or not, explanations can be confusing. Let's make this perfectly clear: explanations are not arguments.

However they can help us understand the key difference between arguments and other forms of persuasive rhetoric, because they tell us that such is the case. They do not prove anything. See? I just told you that because of x, y is the case. I did nothing to prove that this is so. I merely told you.

Conditional statements are also commonly mistaken for arguments. They use an IF x, THEN y framework which sounds very much like an argument, but conditional statements are not arguments.

A conditional statement sounds like a premise which leads to a conclusion - but this is not enough to form an argument. An argument must consist of at least two premises, and a conditional statement is only able to serve as a single premise.

See:

If it's raining, then you should take an umbrella with you.

is not an argument.

It is telling us that we should remember to take an umbrella along if it's raining. It does not prove anything as it is.

Now consider:

If it's raining, then you should take an umbrella with you.
It is raining.
So, you should take an umbrella with you.

This is an argument. It proves its conclusion, such that if [1.] and [2.] are true, it utterly convinces us that we should take an umbrella with us. If we are an umbrella-hater, but we recognize that [1.] and [2.] are correct, we are utterly defeated through its argument.

But what if we don't admit defeat so easily? If we don't agree that premise [1.] or [2.] is true, then we don't need to accept the conclusion, [3.] - but what if we agree with the premises, and yet don't believe that the conclusion necessarily follows from them? You may not own an umbrella, and taking an umbrella would be wrong to do (or annoy someone bigger and stronger than you). Your umbrella may be broken.

If we consider these potential objections, we can strengthen the argument:

If it's raining, and you own an accessible, functional umbrella, then you should take it with you.
It is raining, and you own an accessible, functional umbrella.
So, you should take your umbrella with you.

There are many ways to strengthen arguments like this in writing. In a paragraph, it might be written as follows:

It is important not to get wet unnecessarily, so if it's raining, and we have access to a functional umbrella, then we should remember to take it with us. We can clearly see that it is raining, and we have access to an umbrella. So, taking it with us is the right thing to do.

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