1. Introduction to Logic Lecture 3 Formalizing an argument By David Kelsey

2. Evaluating an argument Evaluate the argument: –To evaluate an argument is to critique it. Understand the argument: –Before evaluating an argument you must understand it as it’s author does. –Formalize it: break it down into its most simplified form

3. The principle of charity Write what the author intends: –Abide by the principle of charity. –The Bloodhounds example again

4. 3 step process The process (of formalizing) includes several steps: –Write: Simplify and number –Structure: –Evaluate:

5. The structure of an argument The structure rule: –any inference the argument makes follows what it is inferred from. –We must clarify the argument’s structure? An argument’s structure: its pattern of reasoning from the first premise to the conclusion.

6. Clarifying an argument’s structure: #s and symbols First, –Number the propositions of the argument according to the order in which they fall in the text itself. Second, –Clarify the structure with the numbers

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

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:

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: –

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

11. Counter-arguments Symbolizing counter Reasons: –When we have a proposition, P, that is a reason against some other proposition of the argument, Q, we write a downward arrow from P to Q. We then put a slash mark through the arrow. –Like this: Counter reason: –A reason that is evidence against some premise of an argument.

12. Defending against Counter-arguments Defending against a Counter Argument: –Counter argument: an argument that makes use of a counter reason to show some other argument unsound. Show the counter argument is unsound: –You can defend your own argument by showing a counterargument is unsound.

13. 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. Find the premises and conclusion. Look at each sentence and ask: “does this belong in the argument?” Look for premise and conclusion indicator words

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. –1. I don’t think we should get Carlos his own car.

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. –1. I don’t think we should get Carlos his own car. –2. He is not responsible.

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. –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.

17. 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. –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.

18. 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. –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.

19. 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. –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.

20. 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. –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.

21. Simplify Simplify: –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.

22. Structuring the Carlos argument Now clarify the structure of the argument: –What is the relationship between 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. What does the because mean? So is the relationship between 2 and 3: –2 → 3 or –3 → 2

23. Structuring the argument Structuring the argument continued –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 Is the relationship here: –1 → 2 or –2 → 1

24. Structuring the argument Structuring the argument continued: –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. What does ‘since’ indicate about 4 and 5? Is the relationship here: –4 → 5 or –5 → 4

25. Structuring the argument 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 & 7 reasons in favor of 4? –Are 6 and 7 working dependently in favor of 4 or are they supporting 4 independently of each other? –How do we draw the relationship between 6, 7 and 4?

26. Finishing the structure Combining the inferences: –Propositions 6, 7 and 5 are all related to 4. So lets combine the symbolization: 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. The finished structure: –Let’s combine all of our inferences to obtain our finished structure...

27. The finished formalization Here is the numbering we started with: –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. Now Renumber the propositions of the argument to map onto its structure. The argument after it has been renumbered: –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.) Some things to notice: –The parenthesis pick out the argument’s inferences The last step: Evaluate!!!

28. Evaluating formalizations In evaluating a formalization: determine if the argument is good. –Is the argument valid or strong? –Are the premises of the argument reasonable? Do you suspect any of the premises false? Inspect each premise for questions, concerns, weaknesses, etc. A well supported argument has well supported premises. Are the premises well supported?

29. 5 Simple steps to formalizing Here is a quick 5 step process to formalizing arguments: 1. Are there any terms you don’t understand? 2. What is the issue of the passage? 3. Find the conclusion. 4. Find the premises –Work backwards: 5. Arguments for premises?

30. The Argument from Evil Let us now look at the Argument from evil in a passage by J.L. Mackie: In its simplest form the problem is this: God is omnipotent; God is wholly good; and yet evil exists. There seems to be some contradiction between these three propositions, so that if any two of them were true the third would be false. But at the same time all three are essential parts of most theological positions: the theologian, it seems, at once must adhere and cannot adhere consistently to all three...However, the contradiction does not arise immediately; to show it we need some additional premises, or perhaps some quasi-logical rules connecting the terms "good", "evil," and "omnipotent." These additional principles are that good is opposed to evil, in such a way that a good thing always eliminates evil as far as it can, and that there are no limits to what an omnipotent thing can do. From these it follows that a good omnipotent thing eliminates evil completely, and then the propositions that a good omnipotent thing exists, and that evil exists, are incompatible. (This passage is taken from the first page of J.L. Mackie's Evil and Omnipotence.)

31. Formalizing the argument 1. Any terms that you don’t understand? 2. What is the issue? 3. What is the conclusion? Remember this is the answer to the issue. 4. The premises…

32. Evaluating the argument Now that our argument is formalized we must evaluate it –Examine the premises: Does evil really exist? Maybe God has a reason for allowing evil to exist? Questions about freedom of the will… Questions about moral and natural evils… Is omnipotence even possible?