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.