Suppressed premises in real life. Philosophy and Logic Section 4.3 & Some Exercises

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1 Suppressed premises in real life Philosophy and Logic Section 4.3 & Some Exercises

2 Analyzing inferences: finale Suppressed premises: from mechanical solutions to elegant ones Practicing on some real-life argumentative passages

3 Two kinds of suppressed premise problem On p. 1: Short arguments based on standard forms. The mechanical solution works fine for these! On pp. 2-4: in a real-life argument Here we strive for elegance, beauty, and wit, in addition to sound inference The mechanical solution needs step 2, editing, to do this.

4 Standard form problems The following short arguments are based on standard forms. For each one (a) indicate the conclusion by putting it in bold (2 pts each) then (b) write down the suppressed premise in a complete sentence. (6 pts each): Winter is not over, because if winter were over, the snow would be gone.

5 Standard form problems Winter is not over, because if winter were over, the snow would be gone.

6 Standard form problems Winter is not over, because if winter were over, the snow would be gone.

7 Standard form problems Winter is not over, because if winter were over, the snow would be gone. We have: If W then G ~ W

8 Standard form problems Winter is not over, because if winter were over, the snow would be gone. We have: modus tollens! If W then G ~ W

9 Standard form problems Winter is not over, because if winter were over, the snow would be gone. We have: modus tollens! If W then G ~ W Needs: ~G. The snow is not gone.

10 If the Seventh fleet is sent into the straits of Taiwan, the Chinese missile tests will cease. So if the Seventh fleet is sent into the straits of Taiwan, the security of east Asia will be enhanced.

11 If the Seventh fleet is sent into the straits of Taiwan, the Chinese missile tests will cease. So if the Seventh fleet is sent into the straits of Taiwan, the security of east Asia will be enhanced.

12 If the Seventh fleet is sent into the straits of Taiwan, the Chinese missile tests will cease. So if the Seventh fleet is sent into the straits of Taiwan, the security of east Asia will be enhanced. We have: If S then C If S then E

13 If the Seventh fleet is sent into the straits of Taiwan, the Chinese missile tests will cease. So if the Seventh fleet is sent into the straits of Taiwan, the security of east Asia will be enhanced. We have: hypothetical syllogism! If S then C If S then E

14 If the Seventh fleet is sent into the straits of Taiwan, the Chinese missile tests will cease. So if the Seventh fleet is sent into the straits of Taiwan, the security of east Asia will be enhanced. We have: hypothetical syllogism! If S then C * If C then E If S then E

15 If the Seventh fleet is sent into the straits of Taiwan, the Chinese missile tests will cease. So if the Seventh fleet is sent into the straits of Taiwan, the security of east Asia will be enhanced. Answer: if the Chinese missile tests cease, then the security of east Asia will be enhanced If S then C * If C then E If S then E

16 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation.

17 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation.

18 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. We have: Either S or H If H then B B

19 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. We have: Dilemma! The weakest addition is: Either S or H If H then B B

20 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. We have: Dilemma! The weakest addition is: Either S or H If H then B * If S then B B

21 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. Answer: If I stay in Storrs, I will have a boring vacation. Either S or H If H then B * If S then B B

22 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. Slightly Worse Answer: I will go home. Either S or H If H then B H B

23 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. Another Slightly Worse Answer: I won t stay in Storrs. Either S or H If H then B ~S B

24 Either I will stay in Storrs or go home. If I go home, I will have a boring vacation. Hence I will have a boring vacation. The weakest, least committed answer: If I stay in Storrs, I will have a boring vacation. Either S or H If H then B If S then B (And it is obviously true!) B

25 Real-life arguments also need step 2: 1 Produce a mechanical (truth table) solution. (Done!) 2 Edit the mechanical solution. Try to make the claim you have produced as weak as possible (as plausible as possible) while retaining the validity of the argument.

26 Our Rule of Charity Add the minimum necessary to make the argument valid. 1 Add the weakest premise that you can. Def: One statement is weaker than another if it commits the author to less. It is harder to refute. Add hedges, qualifications, guarding terms. Note: weak argument vs. weak statement

27 The minimum necessary 2 Try to add only obvious or uncontroversial claims. (eg, of type a). 3 Add premises that the author seems to take for granted, or that seem to be implicit in the statements of the author. (The author at least should agree with them!) 4 If possible, only add premises that are true, or at least plausible.

28 The Editing step 2 Look at your mechanical solution: a. See if there are any other repeated elements in the premises that you could exploit. b. Are there phrases in the premises that are not identical, but have very similar meanings? These can provide additional repeated elements c. Stay close to the actual words of the text. d. Adjust your wording until the claim is the weakest you can make it.

29 Applied to real-life: Underline the inference indicators. (2 pts each) Bracket and number the statements in the argument. (5 pts each) Write out the argument schema, as abbreviated. (5 pts.) Diagram the entire argument, including any sub-arguments. (20 pts) What is the suppressed premise needed in the inference to (the main conclusion)?

30 Ernest van den Haag in Taking Sides, p 280 If capital punishment is immoral, no distribution of it among the guilty could make it moral. If capital punishment is moral, no distribution could make it immoral. So improper distribution cannot affect the moral quality of what is distributed. Discriminatory distribution thus could not justify abolition of the death penalty.

31 [(1) If capital punishment is immoral, no distribution of it among the guilty could make it moral.] [(2) If capital punishment is moral, no distribution could make it immoral.] So [(3) improper distribution cannot affect the moral quality of what is distributed.] [(4) Discriminatory distribution thus could not justify abolition of the death penalty.] (1) (2) (3) (4)

32 [(1) If capital punishment is immoral, no distribution of it among the guilty could make it moral.] [(2) If capital punishment is moral, no distribution could make it immoral.] So [(3) improper distribution cannot affect the moral quality of what is distributed.] [(4) Discriminatory distribution thus could not justify abolition of the death penalty.] In the inference to his main conclusion, van den Haag has at least one suppressed premise. Write it down as a complete sentence.

33 [(1) If capital punishment is immoral, no distribution of it among the guilty could make it moral.] [(2) If capital punishment is moral, no distribution could make it immoral.] So [(3) improper distribution cannot affect the moral quality of what is distributed.] [(4) Discriminatory distribution thus could not justify abolition of the death penalty.] The inference in question: From (3) to (4).

34 [(1) If capital punishment is immoral, no distribution of it among the guilty could make it moral.] [(2) If capital punishment is moral, no distribution could make it immoral.] So [(3) improper distribution cannot affect the moral quality of what is distributed.] [(4) Discriminatory distribution thus could not justify abolition of the death penalty.] The inference in question: (3) Improper distribution cannot affect the moral quality of what is distributed (4) Discriminatory distribution could not justify abolition of the death penalty.

35 The inference in question: (3) Improper distribution cannot affect the moral quality of what is distributed (4) Discriminatory distribution could not justify abolition of the death penalty.

36 The inference in question: (3) Improper distribution cannot affect the moral quality of what is distributed (4) Discriminatory distribution could not justify abolition of the death penalty. Mechanical solution: if (3), then (4) : If improper distribution cannot affect the moral quality of what is distributed, then discriminatory distribution could not justify abolition of the death penalty.

37 The inference in question: (3) Improper distribution cannot affect the moral quality of what is distributed (4) Discriminatory distribution could not justify abolition of the death penalty. Editing notes: if (3), then (4) : We go from improper distribution to discriminatory distribution The conclusion is confined to the death penalty There is an assumption that if moral quality is unaffected, there is no justification for a policy.

38 The inference in question: (3) Improper distribution cannot affect the moral quality of what is distributed (4) Discriminatory distribution could not justify abolition of the death penalty. An edited version of: if (3), then (4) : If the moral quality of the death penalty is unaffected by discriminatory distribution, then such distribution cannot justify abolition of the the death penalty.

39 Summary: Analyzing inferences 1 Underline the indicators. 2 Bracket each statement. 3 Number them. One statement per number, one number per statement. 4 Write out the schema. Make sub diagrams. 5 Put the main conclusion at the bottom.

40 Summary (cont) 6 Connect them together. Sometimes you need to try various options. Think about what would be the best way to argue, if it were your argument. 7 Check the result. Check each inference to see if it makes sense. Check to see if any claims could be better used somewhere else in your diagram. Rearrange as needed. 8 Add suppressed premises.

41 Jean Jacques Rousseau, Social Contract, I, chap VI Whoso gives himself to all gives himself to none. And, since there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him, it follows that we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have.

42 [(1) Whoso gives himself to all gives himself to none.] And, since [(2) there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him], it follows that [(3) we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have.] (1). And, since (2), it follows that (3). (2) (1) (3)

43 [(1) Whoso gives himself to all gives himself to none.] And, since [(2) there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him], it follows that [(3) we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have.] In the inference to his main conclusion, Rousseau needs a suppressed premise. What is it? (2) (1) (3)

44 [(1) Whoso gives himself to all gives himself to none.] And, since [(2) there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him], it follows that [(3) we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have.] In the inference to his main conclusion, Rousseau needs a suppressed premise. What is it? (1) Whoso gives himself to all gives himself to none, (2) there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him (3) we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have

45 In the inference to his main conclusion, Rousseau needs a suppressed premise. What is it? If (1) and (2) then (3). (1) Whoso gives himself to all gives himself to none (2) there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him (3) we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have

46 In the inference to his main conclusion, Rousseau needs a suppressed premise. What is it? The mechanical solution: If (1) and (2) then (3). If whoso gives himself to all gives himself to none, and there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him, then we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have

47 More examples are in the class handouts "Some arguments to analyze", sides 1a and 1b. "Some more arguments to analyze", sides 2a and 2b. Answers are in four separate slideshows on the website.

48 In the inference to his main conclusion, Rousseau needs a suppressed premise. What is it? If whoso gives himself to all gives himself to none, and there is no member of the social group over whom we do not acquire precisely the same rights as those over ourselves which we surrendered to him, then we gain the exact equivalent of what we lose, as well as an added power to conserve what we already have. Edited somewhat: If each of us gain over others precisely the same rights as those they gain over us, then we all gain exactly as many rights as we lose, but we also gain an added power to conserve what we already have

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