1. Critical Thinking Lecture 3 Formalizing an argument
By David Kelsey

2. Formalizing
Formalizing is the process of breaking down an argument into its most simplified parts.
When you formalize you list and number the necessary parts of the argument…
You will begin the process with a passage.
You must from the passage pull out the premises and conclusion of the argument.

3. Formalizing the argument in a passage
Formalizing the argument in the passage:
To find the argument’s premises and conclusion you simply pull out the claims from the passage that look to be important or required.
To help you find the sentences in a passage that are required for the argument look for premise or conclusion indicator words.

4. Listing the premises and conclusion
When listing the sentences that seem to be required for the author’s argument you will need to number those claims.
You will also need to simplify them.

5. Formalizing by the structure rule
An argument’s structure is its pattern of reasoning.
In formalizing follow the structure rule:
Number any inferred claim after what it is inferred from.
Following the structure rule, the conclusion of the argument will always be listed when?

6. Finding the argument’s structure
Begin with a listed and numbered set of sentences pulled from the passage.
Once we find the structure of the argument we can then renumber our list to reflect the arguments structure.
To find an arguments structure we will use a set of symbols.

7. Symbols When one proposition Q is inferred from another P we write:
P → Q

8. Symbolizing Dependent Premises
Dependent Premises: When you have two or more propositions, P and Q, that dependently support some other proposition of the argument, R:
P+Q → R

9. Symbolizing Independent premises
Independent Premises: when we have two or more propositions, P and Q, that independently support some third proposition of the argument, R: P ↘
Q → R

10. 1 proposition supporting more than one.
1 Proposition Supporting 2: When we have a proposition, P, that supports more than one proposition of the argument, Q and R, we write:
P → Q ↘ R

11. Dependent & Independent Reasons
Dependent & Independent Premises: When we have two propositions, P and Q, that dependently support another, S, and we also have a fourth proposition, R, that independently supports S we write: R ↘
P+Q → S

12. The Carlos example An example passage:
I don’t think we should get Carlos his own car. As a matter of fact, he is not responsible because he doesn’t care for his things. And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet. Last week you yourself complained about our financial situation, and you never complain without really good reason.
First list any claim that the author is using to make his or her argument.
To compose the list look for premise and conclusion indicator words…

13. The Carlos example
Now we will begin to pull out the sentences or claims that look to be required for the argument given…
I don’t think we should get Carlos his own car. As a matter of fact, he is not responsible because he doesn’t care for his things. And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet. Last week you yourself complained about our financial situation, and you never complain without really good reason.
First, it looks apparent from the passage that the first sentence has some importance. So we include it.
1. I don’t think we should get Carlos his own car.

14. The Carlos example The passage:
I don’t think we should get Carlos his own car. As a matter of fact, he is not responsible because he doesn’t care for his things. And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet. Last week you yourself complained about our financial situation, and you never complain without really good reason.
The ‘because’ in the second sentence tells us the claim before and after it are important. So we get:
1. I don’t think we should get Carlos his own car.
2. He is not responsible.
3. He doesn’t care for his things.

15. The Carlos example The passage:
I don’t think we should get Carlos his own car. As a matter of fact, he is not responsible because he doesn’t care for his things. And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet. Last week you yourself complained about our financial situation, and you never complain without really good reason.
The ‘since’ in the 3rd sentence tells us the 2 claims in that sentence belong in the argument. So we get:
1. I don’t think we should get Carlos his own car.
2. He is not responsible.
3. He doesn’t care for his things.
4. We don’t have enough money for a car.
5. Even now we have trouble making ends meet.

16. The Carlos example The passage:
I don’t think we should get Carlos his own car. As a matter of fact, he is not responsible because he doesn’t care for his things. And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet. Last week you yourself complained about our financial situation, and you never complain without really good reason.
The ‘and’ in the last sentence tells us we have 2 more claims to add:
1. I don’t think we should get Carlos his own car.
2. He is not responsible.
3. He doesn’t care for his things.
4. We don’t have enough money for a car.
5. Even now we have trouble making ends meet.
6. Last week you yourself complained about our financial situation.
7. You never complain without really good reason.

17. Simplify Now just simplify the list a bit:
1) We shouldn’t get Carlos his own car.
2) Carlos is not responsible.
3) Carlos doesn’t care for his things.
4) We don’t have enough money for a car.
5) We have trouble making ends meet.
6) Last week you complained about our financial situation.
7) You never complain without really good reason.

18. Structuring the Carlos argument
Now we need to clarify the structure of the argument.
We will use the numbers in our list to represent the sentences in the list.
What is the relationship between sentences 2 and 3?
2) Carlos is not responsible.
3) Carlos doesn’t care for his things
Here is the sentence in which they occur: As a matter of fact, he is not responsible because he doesn’t care for his things.
The because means that what follows it is a reason for what precedes it. Thus, 3 is a reason for 2. So we get:
3 → 2

19. Structuring the argument
What is the relationship between 2 and 1?
1. I don’t think we should get Carlos his own car.
2. He is not responsible.
Here is how they occur in the passage: I don’t think we should get Carlos his own car. As a matter of fact, he is not responsible
Isn’t it that Carlos’ not being responsible is a reason for us to not get him his own car. Thus, 2 is a reason for 1. And so we get:
2 → 1

20. Structuring the argument
What is the relationship between 4 and 5?
4) We don’t have enough money for a car.
5) We have trouble making ends meet.
Here is how they look in the passage:
And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet.
The since indicates that what follows it is a reason for what precedes it. Thus, 5 is a reason for 4. So we get:
5 → 4

21. Structuring the argument
Lastly, what is the relationship between 6, 7 and 4?
4. We don’t have enough money for a car.
6. Last week you yourself complained about our financial situation.
7. You never complain without really good reason.
Are 6 and 7 reasons in favor of 4? If so, are they dependent or independent reasons for 4?
To answer this look at the passage. There you see the premise indicator ‘and’ that joins 6 and 7.
Here is the sentence in the passage: Last week you yourself complained about our financial situation, and you never complain without really good reason.
Thus, we get:
6+7 → 4

22. Combining the inferences
Propositions 6, 7 and 5 are all related to 4. So lets combine the symbolization:
5 → 4
6+7 → 4
And claims 1, 2 and 3 are all related so lets combine the symbolization:
3 → 2
2 → 1
Combining all of it we get:
↓ ↓
2 4 ↓ 1

23. Finishing the Formalization
But what is the relationship between 4 and 1?
1. I don’t think we should get Carlos his own car.
4. We don’t have enough money for a car.
We see here that not having enough money for a car is a reason for not getting Carlos one.
Thus, 4 is a reason for 1.
Thus we get: 4 → 1
Now we can add on this final inference to complete the structure:
↓ ↓
2 4 ↓ 1

24. Renumbering and the Finished Formalization
Before renumbering
After renumbering
1) We shouldn’t get Carlos his own car.
2) Carlos is not responsible.
3) Carlos doesn’t care for his things
4) We don’t have enough money for a car.
5) We have trouble making ends meet.
6) Last week you complained about our financial situation.
7) You never complain without really good reason.
1) Carlos doesn’t care for his things.
Thus, 2) Carlos isn’t responsible. (from 1)
3) Last week you complained about our financial situation.
4) You never complain without really good reason.
5) We have trouble making ends meet now.
Thus, 6) We don’t have enough money for a car. (from 3&4 and 5.)
Thus, 7) We shouldn’t get Carlos his own car. (from 2 and 6.)