0:12

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

Â premises and conclusions.

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

Â An understanding of formal logic is like understanding the building blocks

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

Â 0:43

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

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

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

Â the most basic form that we can.

Â 1:22

Our second premise is that all pugs are dogs and

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

Â The second premise is the most specific crime and

Â we refer to it as the minor premise.

Â Lastly, our conclusion is that all pugs

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

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

Â all D are M, all P are D.

Â And therefore, all P are M.

Â 1:54

This is the general pattern for formal logic and

Â is often represented simply using A, B and C and

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

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

Â the conclusion must also be valid.

Â It is essentially mathematical.

Â 2:17

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

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

Â simplicity.

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

Â logical fallacies that can occur.

Â In formal logic as suggested by Inch and

Â Warnick, there are categorical, hypothetical and disjunctive structures.

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

Â your argument.

Â Let's take the example from earlier.

Â All dogs are mammals.

Â All pugs are dogs.

Â Therefore, all pugs are mammals.

Â In this argument,

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

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

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

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

Â 3:12

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

Â only as strong as its weakest point.

Â Regardless of how true or correct your conclusion is,

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

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

Â then the conclusion is no longer valid.

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

Â then the argument becomes invalid again.

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

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

Â conclusion to make the argument more defensible.

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

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

Â one dog that's not friendly.

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

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

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

Â However, this does change the type of argument.

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

Â deductive reasoning.

Â 4:23

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

Â mistakes that can happen in formal logic.

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

Â The first is structural fallacies and the second premise fallacies.

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

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

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

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

Â And therefore, all Z are X.

Â Consider our argument from before.

Â Dogs are mammals.

Â Pugs are mammals.

Â Therefore, pugs are dogs.

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

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

Â Take this example.

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

Â Z is cats, we get these premises.

Â Dogs are mammals and cats are mammals.

Â Both of these premises are true.

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

Â therefore, cats are dogs.

Â Of course, this is incorrect.

Â Remember, for this kind of categorical logic to work,

Â it needs to follow the right pattern.

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

Â the premises to be valid and the conclusion invalid.

Â In this case, the wrong formula has been applied.

Â Therefore, remember that all A are B.

Â All C are A.

Â Therefore, all C are B.

Â 5:56

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

Â which looks like this.

Â If A, then B.

Â A, therefore, B.

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

Â occur, if another event occurs.

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

Â my clothes will be wet.

Â I jumped into the pool wearing my clothes.

Â Therefore, my clothes are wet.

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

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

Â that people mix up the events.

Â Take the previous example.

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

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

Â My clothes are wet.

Â Therefore, I jumped into the pool wearing my clothes.

Â Is this logically sound?

Â Unfortunately, neither example was logically sound.

Â In the second example,

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

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

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

Â B, therefore, A.

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

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

Â 7:20

The last formal of logic structure that we'll

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

Â Not A, therefore, B.

Â Take the following example.

Â It's either day or night.

Â It's not day.

Â Therefore, it's night.

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

Â for this structure.

Â Thus, either A or B not B.

Â Therefore, A is still a logical argument.

Â For example, it's either day or night.

Â It's not night.

Â Therefore, it's day.

Â 7:55

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

Â the premises.

Â Arguments are rarely ever black and white.

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

Â solutions that are both or neither.

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

Â Chinese food.

Â John doesn't want vegetarian food.

Â Therefore, we'll have Chinese food.

Â What's the issue with this argument?

Â 8:25

Of course, most arguments are not as neat and

Â tidy as the examples that we've given you.

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

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

Â In fact, most of the time,

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

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

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

Â that occur in academic study.

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

Â construct arguments using evidence.

Â Good luck.

Â [MUSIC]

Â