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Last lesson we looked at the basics of arguments in formal logic,

premises and conclusions.

In this lesson, we'll look more closely at formal logic.

An understanding of formal logic is like understanding the building blocks

of argument and can immeasurably improve your critical thinking, and argumentation.

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That means that in formal logic, we break arguments down into their most basic form.

We do this to look at the structure of the argument.

Looking at the structure of the argument means that we need to represent it in

the most basic form that we can.

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Our second premise is that all pugs are dogs and

we can represent this by saying, all P are D.

The second premise is the most specific crime and

we refer to it as the minor premise.

Lastly, our conclusion is that all pugs

are mammals which we can represent by saying, all P are M.

In formal logic, we will represent a whole argument by saying,

all D are M, all P are D.

And therefore, all P are M.

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This is the general pattern for formal logic and

is often represented simply using A, B and C and

works by making a very specific claim for a more general claim.

In this format provided that what is given in the premises is valid,

the conclusion must also be valid.

It is essentially mathematical.

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Formal logic can be broken down into three broad structures for arguments.

These are often called syllogisms, but we'll continue to call them structures for

simplicity.

For each of these structures, we will also consider some of the formal,

logical fallacies that can occur.

In formal logic as suggested by Inch and

Warnick, there are categorical, hypothetical and disjunctive structures.

Categorical logic is when you use classification of things in order to make

your argument.

Let's take the example from earlier.

All dogs are mammals.

All pugs are dogs.

Therefore, all pugs are mammals.

In this argument,

you're claiming that pugs are part of a larger group of things called mammals.

Your evidence for this is that pugs are also part of a smaller group of things

called dogs and that dogs belong to this larger mammals group.

One way to represent this is to use a Venn Diagram, like so.

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What's important in all argument structures is that an argument is

only as strong as its weakest point.

Regardless of how true or correct your conclusion is,

if your premises are not true or correct, then it's a bad argument.

For example, if there's an argument of a dog that's not also a mammal,

then the conclusion is no longer valid.

Similarly, if there's an example of a pug that's not also a dog,

then the argument becomes invalid again.

As a side note, this is where hedging language becomes quite important.

Hedging language is language that's used to soften or hedge a premise, or

conclusion to make the argument more defensible.

If I said, all dogs are friendly and I want a friendly pet,

so I should get a dog, you could make my argument invalid by finding evidence of

one dog that's not friendly.

However, if I said most dogs are friendly and then you went and found a dog that

wasn't friendly, my premise and therefore, my argument would still be strong.

When we hedge, we use words like might, may, apparently, often or rarely.

However, this does change the type of argument.

We'll come back to this later in the course when we discuss inductive and

deductive reasoning.

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Let's move on now, and look at the kinds of fallacies or

mistakes that can happen in formal logic.

There are two types of fallacies that can come up in formal logic.

The first is structural fallacies and the second premise fallacies.

The incorrect argument in the question you saw is an example of a premise fallacy and

we'll consider them more in the lesson tomorrow and later in the course, but

let's have a look at some structural fallacies now.

Why is it wrong to say that all X are Y, all Z are Y.

And therefore, all Z are X.

Consider our argument from before.

Dogs are mammals.

Pugs are mammals.

Therefore, pugs are dogs.

Even though each of the statements is correct, the reasoning is incorrect,.

Just because dogs and pugs are both mammals does not mean that pugs are dogs.

Take this example.

If I changed the terms around, so that X is dogs, Y is mammals and

Z is cats, we get these premises.

Dogs are mammals and cats are mammals.

Both of these premises are true.

However, using the previous structure, our conclusion would be,

therefore, cats are dogs.

Of course, this is incorrect.

Remember, for this kind of categorical logic to work,

it needs to follow the right pattern.

If formal logic is used correctly, it's impossible for

the premises to be valid and the conclusion invalid.

In this case, the wrong formula has been applied.

Therefore, remember that all A are B.

All C are A.

Therefore, all C are B.

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The second type of formal logic structure is the hypothetical structure,

which looks like this.

If A, then B.

A, therefore, B.

This type of structure implies a conditional meaning that an event will

occur, if another event occurs.

For example, if I jump into the pool wearing my clothes,

my clothes will be wet.

I jumped into the pool wearing my clothes.

Therefore, my clothes are wet.

Again, in order for the conclusion to be valid, all the premises need to be valid.

In terms of structural fallacies, the main issue with hypothetical structures is

that people mix up the events.

Take the previous example.

However, let's change the events around and say,

if I jump into the pool wearing my clothes, my clothes will be wet.

My clothes are wet.

Therefore, I jumped into the pool wearing my clothes.

Is this logically sound?

Unfortunately, neither example was logically sound.

In the second example,

there are a lot of different reasons that you might not be able to drive your car.

You might have an issue with the engine or a problem with the ignition.

In both of these examples, the structure has been changed to if A, then B.

B, therefore, A.

In this case, it is possible for the premises to be valid, but the conclusion

invalid which means there is a problem with the structure of the argument.

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The last formal of logic structure that we'll

look at is the disjunctive structure which follows this form, either A or B.

Not A, therefore, B.

Take the following example.

It's either day or night.

It's not day.

Therefore, it's night.

Interestingly, changing the premises around still results in a logical argument

for this structure.

Thus, either A or B not B.

Therefore, A is still a logical argument.

For example, it's either day or night.

It's not night.

Therefore, it's day.

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The main logical fallacies that this particular structure has are related to

the premises.

Arguments are rarely ever black and white.

And when we're considering an either or argument, we can forget about answers or

solutions that are both or neither.

Take this example, we can either have vegetarian food for dinner or

Chinese food.

John doesn't want vegetarian food.

Therefore, we'll have Chinese food.

What's the issue with this argument?

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Of course, most arguments are not as neat and

tidy as the examples that we've given you.

A lot of the time, premises and sometimes even conclusions are implicit.

Moreover, we rarely have just two premises for a conclusion.

In fact, most of the time,

we'll have a number of premises that will lead to a probable conclusion and

this probable conclusion will be used as a premise for another argument.

In the next lesson, we'll look at some common fallacies related to premises

that occur in academic study.

And over the rest of the course, we'll look at how to evaluate and

construct arguments using evidence.

Good luck.

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