Philosophy 2301

1. Philosophy 2301 Class 4

2. Last Class • Introduced three areas of philosophy of science, dealing with: • The problem of discovery • The problem of justification/evaluation • The problem of explanation • In the middle of discussing the problem of evaluation- direct and indirect tests.

3. Indirect Test • Hypothesis: The earth is round • Implication: If a sailing ship moves closer and closer to shore, then the height of the mast of the ship will get higher and higher.

4. The problem with auxiliary hypotheses • Hypothesis: The earth is round • Implication: If a sailing ship moves closer and closer to shore, then the height of the mast of the ship will get higher and higher.

5. Auxiliary Hypotheses • Hypotheses: • The earth is round • Light travels in a straight line • Implication: If a sailing ship moves closer and closer to shore, then the height of the mast of the ship will get higher and higher.

6. Auxiliary Hypotheses • Hypotheses: • The earth is round • Light travels in a curved line • Implication: If a sailing ship moves closer and closer to shore, then the height of the mast of the ship will stay the same.

7. Back to Copernicus… Deduction: We should see the position of the stars relative to the sun change as the earth moves. • Hypothesis: The earth is spinning around the sun.

8. The earth moves around the sun Therefore, we should be able to measure the stars’ shift However, we don’t observe the stars’ shifting (Therefore the earth does not move around the sun) The earth moves around the sun The earth is very close to the sun Therefore, we should be able to measure the stars’ shift However, we don’t observe the stars’ shifting (Therefore the earth does not move around the sun) The earth moves around the sun The earth is very far away from the sun Therefore, the stars’ shifting is too small to be measured with our instruments Therefore we don’t observe the stars’ shifting

9. This might seem okay… But what if Copernicus really had been wrong…

10. Another challenge… • Hypothesis: The earth is spinning on its axis • Deduction: Objects that are falling should end up to the left or the right of the point where they are dropped, since the earth is spinning underneath them. YES NO

11. The earth is spinning. If I drop a rock from the tower it should land to the left or right of the tower The earth is spinning When I drop the rock it is completely disconnected from the earth If I drop a rock from the tower it should land to the left or right of the tower FALSE! The earth is spinning The air connects the earth and the rock If I drop a rock from the tower it should land at the bottom of the tower. TRUE!

12. The problem with auxiliary hypotheses • It’s too easy to get your main hypothesis out of trouble- even if it is actually false • Similarly- it’s too easy cast doubt on true hypothesis (e.g. church and telescope). • You can no longer use observations and indirect tests to conclusively prove or disprove a hypothesis. • That’s bad!

13. Multiple Hypotheses (Crucial Tests)

14. Hypothesis One: The sun moves around the earth Hypothesis Two: The earth moves around the sun contrary hypotheses

15. Hypothesis One: The earth is stationary Hypothesis Two: The earth rotates on an axis. contrary observations Expected Observation: Stone falls straight down Expected Observation: Stone falls left or right

16. Hypothesis One: The sun moves around the earth Hypothesis Two: The earth moves around the sun crucial test Expected Observation: Stone falls straight down Expected Observation: Stone falls left or right

17. But because of auxiliary hypotheses, it doesn’t work… crucial test Copernicus adds an auxiliary hypothesis- now both theories predict the exact same observation.

18. Salvaging Indirect Tests • Indirect tests are very useful to science! • They need to be saved! • Is there some way to make them more reliable? Less vulnerable to these problems we have just discussed?

19. Any suggestions?

20. Karl Popper (1902-1994) • He might have some solutions for us…

21. Before Solutions… More Problems! • Another problem of evaluation… • The problem of universal statements • The problem of inductive logic

22. Some Hypotheses • All snowflakes are unique • You cannot divide any prime number by another number • Mass cannot be created or destroyed • It's cold outside • The earth is round • The Universe never ends • The sun is responsible for all life on earth • For every action there is an equal and opposite reaction • Some Categories • physically observable • analytic (a prior true, no observation required) • easily tested • Can be proven false, but not true • more or less clearly falsifiable

23. Singular: The earth is round Singular: All planets in the solar system are round. Universal: All planets are round Universal: Planets are round Singular and Universal Statements:

24. Indirect Test • Hypothesis: All swans are white. John the swan

25. Indirect Test Swan 1 is white Swan 2 is white Swan 3 is white … Swan n is white • Hypothesis: All swans are white. John the swan

26. Indirect Test Swan 1 is white Swan 2 is white Swan 3 is white … Swan n is black • Good Bye Hypothesis! It is false that all swans are white. Roxanne the swan

27. My neighbour’s pet has four legs, sharp teeth, barks, and it bit me! • My aunt's pet has four legs, sharp teeth, barks and it bit me! • The animal we met in the park had four legs, sharp teeth, barked and it bit me! • That animal by the coffee table has four legs, sharp teeth and is barking. Therefore: • That animal is going to bite me! Induction by Analogy: Four legs, sharp teeth, barks…

28. Another example… Deductive: • Matter attracts matter • Apples are matter • The earth is matter Therefore • Apples are attracted to the earth. Inductive: • Apple 1, when unsupported falls to the ground • Apple 2, when unsupported falls to the ground • Apple 3, when unsupported falls to the ground Therefore • All apples when unsupported fall to the ground An important difference!

29. But there are some just plain bad arguments… • Swan A is white • Swan C is purple. • Therefore • All swans are white.

30. Philosophers Disagree about the roles of induction and deduction… Deduction Induction Easy to make observations Generate Powerful Statements Conclusions could be false Hard to generate arguments Difficult to find premises you can be sure are true Conclusions almost certainly true.

31. Philosophers Disagree about the roles of induction and deduction… Deduction Induction Easy to make observations Generate Powerful Statements Conclusions could be false Weaker? Generative? Hard to generate arguments Difficult to find premises you can be sure are true Conclusions almost certainly true. Stronger? Non-Ampliative?

32. Non-Ampliative? • Tom is a black dog • Therefore • Tom is a dog. • Lions are carnivores • Carnivores have no molars • Therefore • Lions have no molars.

33. A schism between philosophy and science!

34. Example: Method of Agreement A number of students in a dormitory fall ill. The doctor questions four of them and finds the following: John Stuart Mill1806-1873 Developed five inductive methods: Mills Methods… The students became sick because they ate the soup in the cafeteria

35. Statistics!

36. Why Statistics? • Scientists want to: • use inductive methods to investigate nature • minimize the problems associated with these methods. • Statistics was developed to achieve these two goals.

37. 10 minute break… (while I set up our statistical example…)

38. Note: If your attention wanders and you lose track, ask me to go back!

39. Learning about the people in Philosophy 2301- using statistics!

40. Some new knowledge: • Number of people of each age • how many people fall below this age and how many fall above it • For which age is there an even number of people below and above this age • One number to describe our class. Add together all of the ages, take the mean, or average • These are ‘global properties’ of the class.

41. Population and Samples Suppose we didn’t have time to make observations about everyone in the class… Population: People in philosophy 2301 today Sample: Group of five people chosen from the class Oldest Age in Sample: 27 Oldest Age in class: 74

42. A few more groups of five… Group One: Oldest: 27 Youngest: 20 Average Age: 22.7 Whole Class: Oldest: 74 Youngest: 18 Average Age: 23 Group Two: Oldest: 27 Youngest:19 Average Age: 21.8

43. Average Age for each of 100 groups of five Average Age Group 1 21.8 20.4 20.2 31.4 22.2 22.6 22 22.8 31.2 31.8 21.2 22.6 22.6 21.6 34 22 19.8 21.2 22.2 Group 2 Group 3 … Group 100

44. Looking at the average age for each group of five: What can we learn? Xxx graph here 21.8 20.4 20.2 31.4 22.2 22.6 22 22.8 31.2 31.8 21.2 22.6 22.6 21.6 34 22 19.8 21.2 22.2

45. Chance of picking a group that is close to the right value: Real Class Average: 23.3 Number of group averages within +- 3 of real value: 80 Number of group averages outside +- 3 of real value: 20 Chance of getting a ‘close group’: 80% Chance of getting a ‘way off group’: 20%g New Hypothesis: If I randomly pick one of the groups of five people from my list of 100 groups, there is a 80% chance that the real value will be within +- 3 of the value I pick. This is deductive logic- not inductive logic!

46. Original Hypotheses: The average age of the class is 23 New Hypothesis: If I randomly pick a group of five people from the class, there is a 80% chance that the real average age will be within +- 3 of the value I pick. Combined: There is a 80% chance that the average of the class is 23 +- 3

47. How science uses statistics in the ‘real word’… We could only find our new hypothesis (with probabilities) because we knew the real average age of the class! To draw similar conclusions about real populations, scientists need to make assumptions about the population. Once they have done that, they can draw their conclusions…

48. To collect data for the survey, CareerBuilder.com commissioned SurveySite to use an e-mail methodology whereby individuals who are members of SurveySite Web Panel were randomly selected and approached by e-mail invitation to participate in the online survey. The results of this survey for retail workers are accurate within +/- 4.34 percent (19 times out of 20) Compare: There is a 80% chance that the average of the class is 23 +- 3

49. Some potential problems with statistics: • The assumption about random selection from the entire population can be false… • Need to ask: what population are we drawing randomly from? • Telephone book example… • The population may be an atypical population- breaking another assumption. The bell curve… • Daycare example…

50. Where are we at? • Statistics is important for science • It still has problems though… a current area of research! • Scientists are trying to get around the flaws in inductive logic • Bottom line- still uncertainty associated with these methods • Scientists can’t get too confident- although sometimes they do!