Formal Logic Structures
Formal Logic
"Formal logic, according to Inch and Warnick, is the distillation of arguments into standardized forms for the purpose of building, comparing and analyzing them. 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."
Example of Formal Logic
"All dogs are mammals.
All pugs are dogs.
Therefore, all pugs are mammals.
As stated, our first premise is that all dogs are mammals and we can represent this by saying, all D are M. This first premise is a general claim and we refer to is as the major premise. 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 claim 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."
Three Structures for Arguments
"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. In formal logic as suggested by Inch and Warnick, there are categorical, hypothetical, and disjunctive structures."
Categorical Logic
"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."
Hedging Language
"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."
Types of Fallacies
"There are two types of fallacies that can come up in formal logic. The first is structural fallacies and the second premise fallacies."
Structural Fallacies in Categorical Logic
"It is wrong to say that
All X are Y,
All Z are Y,
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.
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. "
Hypothetical Structure
"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.
It looks like this.
If A, then B.
A,
Therefore, B."
Structural Fallacies in Hypothetical Structure
"In terms of structural fallacies, the main issue with hypothetical structures is that people mix up the events. Take the previous example. 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.
However, there are a lot of different reasons that your clothes might be wet.
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."
Disjunctive Structure
"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"
Fallacies in Disjunctive Structure
"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."
SOURCE
https://www.coursera.org/learn/critical-thinking-skills/home/info
VOCABULARY
Claim- a statement that something is true, even though it has not been proved. General claim/
Major premise (contains a general claim)
Minor premise (contains the most specific claim)
Syllogism [ˈsɪləʤɪzm]- a statement with three parts, the first two of which prove that the third part is true.
Categorical [ˌkætɪˈgɒrɪkəl] structures. A categorical statement is a clear statement that something is definitely true or false.
Hypothetical [ˌhaɪpəʊˈθɛtɪkəl] structures
Disjunctive [dɪsˈʤʌŋktɪv] structures
Fallacy [ˈfæləsi]- a weakness in someone's argument or ideas which is caused by a mistake in their thinking.
Hedge [hɛʤ] - something that protects you against possible problems. Hedging language.
Invalid - an argument, reason etc that is invalid is not based on true facts or clear ideas, and lacks good judgment
Venn Diagram[ˈdaɪəgræm]
Pattern [ˈpætən] - the regular way in which something happens, develops, or is done.