“Uniformity of Nature” principle

1. “Uniformity of Nature” principle • Inductive inferences make a kind of assumption: unobserved cases will resemble previously observed cases.

2. Hume’s Puzzle • Can we say what would count as evidence that UN is in general a reliable principle to follow? • Same question: Can we state any good reason for thinking inductively?

3. Is UN true? Notice that UN doesn’t always work: 1. I’ve interviewed 100,000 people, and none won the lottery. 2. Unobserved cases will be like observed cases. 3. Therefore, no one has won the lottery. Inference isn’t always successful… but somewhat reliable.

4. Can we give a non-deductive argument for UN? • Why should you rely on the past to predict the future??

5. A “solutions” to Hume’s puzzle • Peter Frederick Strawson: The idea: “Is it rational to do induction? By rational we mean, in part, using induction!” • Asking whether UN is justified is like asking if the law is legal. Being legal means being in accordance with what the law says. Asking whether the law is in accordance with what the law says doesn’t make any sense.

6. Strawson’s Idea • Induction doesn’t need a justification. It is one of the rules that, if followed, gives beliefs justification. • This logical move has actually been made before.

7. Understanding Strawson Let’s talk about deduction. • “What the Tortoise Said to Achilles” from Lewis Carroll. Achilles: “(1) All A are B (2) All B are C (3) So, All A are C” • Tortoise: “By what reason does 3 follow from 1 and 2?”

8. Tortoise/Achilles Achilles: “The reason that the conclusion follows is “IF ‘All A are B,’ AND ‘All B are C,’ THEN “All A are C.” Tortoise: You are quite right! That is the reason the conclusion follows. And the premises are reasons to accept the conclusion, you should add this missing premise into the set of premises where it belongs.” Achilles: (1) All A are B. (2) All B are C (3) If All A are B and All B are C, then All A are C. (4) So, All A are C. Tortoise: Wait, what’s the reason (4) follows from (1)-(3)? It’s missing!

9. Lewis Carroll is pointing out that there are premises, and on the other hand there are explicitly defined inference rules. Inference rules are not premises, they connect premises to conclusions. • Carroll’s point: “successful deductive reasoning” isfollowing a certain set of rules; can we say the same for successful inductive reasoning?

10. Induction is not formally defined like deductive validity • “We’ve observed 1,000 cases of rats being injected with 1 mg of substance X, and in all cases none lived, therefore no rats injected with 1 mg of substance X will live.” • “We’ve observed 1,000 swans, and in all cases, none of them were black, therefore no swans are black.” • These inferences have the same form! But one is successful while the other isn’t.

11. Summary so far • Doesn’t seem to be a non-question begging way to answer Hume’s riddle here. • We might wonder: if we can’t make any progress on this question/puzzle, then maybe there is something wrong with the question…

12. Re-understanding the problem • “Why will unobserved cases be like observed cases (in general)?” “Why will the future be like the past (in general) ?” • Strange questions … because they seems wrong.

13. The Right Question: • We shouldn’t be asking why are unobserved cases like observed cases generally, or why is the future like the past generally, but rather: • In which ways/respects will unobserved cases be like observed cases? (or, in which respects ways will the future be like the past?). This new question is called: “the new riddle of induction.”

14. The New Riddle of Induction • “How will unobserved cases be like observed cases? In what respect?” Notice: in any particular case, this is a scientific question! Ex: curve-fitting problem:

15. ``Simplest” curve is the best?

16. …or could be a relationship like this:

17. …or any of these:

18. The Point of all the Funny Curves: • For any set of data points, there is an infinite number of possible curves which fit the data (are consistent with the data). • Solution: just get more data, right? • Point: inductive projection depends on more than just data (for example, background assumptions).

19. Not just about curves of course • Very real world problem that any being that learns from experience somehow solves every day: • Ex: Last Friday my dog poops in the house, so I scold him. • What does my dog take the lesson here to be? • Don’t poop inside? • Don’t poop inside on Fridays? • Pee but don’t poop inside? • Don’t poop in the living room? • Use the roll of Charmin and the toilet like a human!? The point: the data in hand does not determine what “theory” is the right one to project given the data.

20. Correlation / Causation

21. How projection happens? • What is the relevant property or pattern for projecting from observed cases into unobserved ? • Answer is, unequivocally: it depends. • Ex 1 : “Typed papers get better grades.” • Exceptions exist of course. But seems true. • Ex: “Smokers more often get lung cancer.” • Exceptions of course. Butt true.

22. Example 1: Typing vs. Grades • How should I project into the future based on this pattern? • “Will I get a worse grade if I hand-write?” • Depends, right? What explains the correlation/pattern? • (1) Maybe: Typing causes better grade. (changes grader’s mind about the goodness of the paper directly, i.e. easier to read). • (2) Or: good students take the time to type and revise, thus having the most presentable paper. • So , if writing long-hand causes worse grades, seems like I should type. But if not, shouldn’t expect a real significant effect.

23. A A B X B Might be a “hidden variable” at work… Causation vs. “Correlation via common cause” “Correlation does not imply causation.” Taken another example: smoking and getting lung cancer…

24. Smoking and Lung Cancer • Tobacco companies: “we do not deny that smoking and lung cancer are correlated.” • Could be a genetic predisposition • Of course, we now have the data that rules this out this particular possibility. Experiments with rats: you put them a cage and they either get smoke or not, it’s not like they get to chose their cage. Also, introducing smoking into a population increases cancer.

25. SMOKE HEART ATTACK Correlated but not causing COFFEE Coffee Drinking and Heart Attacks • Correlation: coffee drinkers get more heart attacks. • Question: “should I stop drinking coffee if I want to reduce risk of a hear attack?” Kind of causal pattern: effect of a non-causal correlate.

26. HEAT POLIO ICE CREAM Another effect of an uncaused correlate: • Both polio and ice cream consumption spiked during summers (only kids get polio).

27. H-user Need-$ Crime Another kind of hidden variable case: • Heroin users commit more property crime. • Should you think that if you use heroin, there is an increased chance of you breaking into someone’s home and taking their stuff? Maybe… it depends. • Effect of an intervening cause:

28. Country music and suicide • There are higher rates of suicide in parts of the country where there is more country music on the radio!

29. Uninteresting Moral: correlation does not imply causation

30. More Significantly… • If you want to make a good inductive projection of a pattern (to all cases, or the next case, or your case), seems like you need to know what explains the correlation. • Idea: maybe explanation is “more basic” than induction, because you need good explanations to make good inductions.