Reason & Argument

1. Reason & Argument • Lecture 3

2. Lecture Synopsis • Recap: validity, soundness & counter-examples, induction. • Arguing for a should conclusion. • Complications with using should.

3. (1) Recap: validity & soundness • Last week: • Features of a good argument (n.b. technical terms!): • Validity: an argument is valid if and only if when the premises are true, the conclusion is true. • Soundness: an argument is sound if and only if it is valid & its premises are true.

4. (1) Recap Testing & Criticising Arguments • Thus, to show an argument is faulty, you can either show that: • It is invalid: the conclusion does not follow from the premises. • It is unsound: one or more of its premises is false. • (Notice that if an argument is invalid, then it is automatically unsound.)

5. (1) Recap How to... • Testing for & criticising Validity: • Look at the form or pattern of the argument • Does it exemplify a syllogism (always valid)? • Or a fallacy (always invalid)? • OR: Can you produce a counter-example? • i.e. an instance of the argument with true premises but a false conclusion. • Soundness: • Try to think of a counter-example • A case that shows a premise is false.

6. (1) Recap Valid & Invalid Patterns • Valid (Syllogisms): • Modus Ponens • Modus Tollens • Hypothetical Syllogism • Disjunctive Syllogism (and many others...) • Invalid (Fallacies): • Affirming the Consequent • Denying the Antecedent (and many others)

7. (1) Recap Errata • Disjunctive Syllogism: • X or Y • Not – X • So Y • Also a valid instance: • X or Y • Not–Y • So X

8. (1) Recap Errata • Affirming the consequent • (S1) If he is a thief, then he would look uncomfortable. • (S2) He looks uncomfortable. • (S3) So he is a thief. • Named after the second premise! (The same goes for denying the antecedent) • Invalid because: there are other antecedents (‘reasons why’) for the consequent ‘he would look uncomfortable’.

9. (1) Recap Counter-examples • For soundness: • Think of a case that shows a premise is false. • For validity: • Show how the same form or pattern of reasoning, when employed with different (true) premises, can lead to a false conclusion.

10. (1) Recap Induction • Every zebra we have ever observed has black and white stripes. • So all zebras have black and white stripes. • Induction is ampliative, unlike deduction, i.e. it goes beyond or adds to the information in the premises/observations • Strictly invalid, thus it carries no guarantee of the truth of its conclusion (cf. Hume’s famous ‘problem of induction’) • Arguments can still be inductively strong (supported by many observations)

11. Terminology • Sentences or premises can be conditionals (with antecedents & consequents), conjunctions (conjuncts) and disjunctions (disjuncts). • Premises can be true or false. • (Only) arguments can be valid or invalid, sound or unsound. (e.g. premises can’t be valid or invalid, sound or unsound)

12. (1) Recap • Summary • You have learned the meaning of validity & soundness and other technical terms. • You have learned how to use these terms in constructing & criticising arguments. • Now you need to practice identifying and testing for them! • Tutorials: try all the exercises in McKay.

13. (2) Arguing for a ‘should’ conclusion • A special case: • An argument is typically designed to establish a matter of fact. • Sometimes however, you want to establish that someone should or ought to think something or to act in some way. • In some of these cases, the logic is different.

14. (2) Should Exceptions • We are not worried about straightforward cases like this: • If everyone is ready, then we should begin the meeting. • Everyone is ready. • So we should begin the meeting.

15. (2) Should Invalid examples • John should do the work his boss asked him to do. • John can only do his work if he stops playing Tetris. • So John should stop playing Tetris.

16. (2) Should Invalid examples • Paul wants to get a promotion. • Paul will get a promotion if he works really hard. • So Paul should work really hard.

17. (2) Should Invalid examples • George wants to become the company’s CEO. • The only way to become the company’s CEO is to invest heavily in company stock. • So George should invest heavily in company stock.

18. (2) Should Common Features • A premise about what someone wants or should achieve. • A premise about how that thing can be attained or achieved. • A conclusion about what we should do. • What makes a good ‘should’ argument? • Can such arguments be valid?

19. (2) Should The Success Condition • Will the suggested action achieve the outcome? • e.g. working hard may not lead Paul to get a promotion. • (Perhaps someone else is already a shoo-in) • The ‘SC’ here: • Working really hard will lead to Paul getting a promotion.

20. (2) Should The Optimal Means Condition • Is the action you think Paul should perform, the best way for him to achieve the outcome? • e.g. working really hard might not be the best way to get a promotion. • In this case, the ‘OMC’ would be: • Working really hard is the best way to get a promotion.

21. (2) Should The EJM Condition • Does the end justify the means? • Ringo wants a nuclear warhead. • The best way to get a nuclear warhead is to find a black market arms dealer. • Ringo should find a black market arms dealer. • The EJM here: • All things considered, acquiring a nuclear warhead is better than not acquiring one.

22. (2) Should A ‘Should’ Pattern • Combining these three caveats or conditions yields a promising pattern for should arguments: • Success Condition (SC): Doing Y will achieve X. • Optimal Means (OMC): Doing Y is the best way to achieve X. • End Justifies Means (EJM): All things considered, doing Y and achieving X is better than not achieving X.

23. (2) Should A Valid Schema • SC: P’s doing Y will achieve X. • OMC: Person P’s doing Y is the best way to achieve X. • EJM: All things considered, P’s doing Y and achieving X is better than not achieving X. • (To secure validity, we need to add: If OMC, EJM and SC, then P should do Y) • Therefore: P should do Y. • When evaluating should arguments, ask yourself whether each condition is fulfilled.

24. (2) Should Example • We should execute murderers, because doing so will prevent them from killing again: • SC (stated): Executing murderers will prevent them from killing again. • OMC (unstated): Executing murderers is the best way to prevent them from killing again. • EJM (unstated): Executing murderers and preventing them from killing again is better than not preventing them from killing again. • Conclusion: We should execute murderers.

25. (2) Should Example • You should buy a lottery ticket, because you won’t win unless you play. • SC (unstated): If you buy a lottery ticket, you will win. • OMC (directly implied by the stated premise): Buying a lottery ticket is the best (the only) way to win. • EJM (not stated): Buying a lottery ticket and winning is better than not winning. • Conclusion: You should buy a lottery ticket. • That reconstruction has a glaringly false premise. Here is another try.

26. (2) Should A more charitable interpretation... • SC (unstated): If you buy a lottery ticket, you will have a chance to win. • OMC (directly implied by the stated premise): Buying a lottery ticket is the best (the only) way to have a chance to win. • EJM (not stated): Buying a lottery ticket and having a chance to win is better than not having a chance to win. • Conclusion: You should buy a lottery ticket.

27. (2) Should Example • We should release almost all prisoners, because doing so is the only way to cut down on prison costs. • SC (unstated): Releasing almost all prisoners will cut down on prison costs. • OMC (directly implied by the stated premise): Releasing almost all prisoners is the best (the only) way to cut down on prison costs. • EJM (not stated): Releasing almost all prisoners and cutting down on prison costs is better than not cutting down on prison costs. • Conclusion: We should release almost all prisoners.

28. (2) Arguing for a ‘Should’ Conclusion • Summary • In some cases, the logic of ‘should’ is different from standard patterns of validity (the patterns are strictly invalid). • An easy way to construct a strong ‘should’ argument is to follow the pattern: SC, OMC, EJM, therefore... • And evaluating it is easy too: are these conditions present and correct?

29. (3) Complications • Using ‘should’ can get complicated... • Uncertainty • The lottery/job interview case. • Balancing probabilities - risks and rewards. • Evaluative Terms

30. What You Have Learned Today • Recap • Arguments are valid/invalid, sound/unsound; premises are true/false. • Arguing for a should conclusion. • Optimal Means Condition (OMC), End-Justifies-the-Means (EJM), Success Condition (SC), the valid schema. • Complications • Uncertainty, Evaluative Terms.