Philosophy 2301

Class 4

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.

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.

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.

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.

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.

•Hypothesis: The earth is spinning around the sun.

Deduction: We should see the position of the stars relative to the sun change as the earth moves.

Back to Copernicus…

The earth moves around the sunTherefore, we should be able to measure the stars’ shiftHowever, we don’t observe the stars’ shifting(Therefore the earth does not move around the sun)

The earth moves around the sunThe earth is very close to the sunTherefore, we should be able to measure the stars’ shiftHowever, we don’t observe the stars’ shifting(Therefore the earth does not move around the sun)

The earth moves around the sunThe earth is very far away from the sunTherefore, the stars’ shifting is too small to be measured with our instrumentsTherefore we don’t observe the stars’ shifting

This might seem okay…

But what if Copernicus really had been wrong…

•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.

NOYES

Another challenge…

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 spinningWhen I drop the rock it is completely disconnected from the earthIf I drop a rock from the tower it should land to the left or right of the tower

FALSE!

The earth is spinningThe air connects the earth and the rockIf I drop a rock from the tower it should land at the bottom of the tower.

TRUE!

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!

Multiple Hypotheses

(Crucial Tests)

Hypothesis One: The sun moves around the earth

Hypothesis Two: The earth moves around the sun

contrary hypotheses

Hypothesis One: The earth is stationary

Hypothesis Two: The earth rotates on an axis.

Expected Observation: Stone falls straight down

Expected Observation: Stone falls left or right

contrary observations

Hypothesis One: The sun moves around the earth

Hypothesis Two: The earth moves around the sun

Expected Observation: Stone falls straight down

Expected Observation: Stone falls left or right

crucial test

But because of auxiliary hypotheses, it doesn’t work…

Copernicus adds an auxiliary hypothesis- now both theories predict the exact same observation.

crucial test

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?

Any suggestions?

Karl Popper (1902-1994)

• He might have some solutions for us…

Before Solutions… More Problems!

• Another problem of evaluation…– The problem of universal statements– The problem of inductive logic

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

Singular and Universal Statements:

Singular: The earth is round

Singular: All planets in the solar system are round.

Universal: All planets are round

Universal: Planets are round

Indirect Test

•Hypothesis: All swans are white.

John the swan

Indirect Test

•Hypothesis: All swans are white. John the swan

Swan 1 is whiteSwan 2 is whiteSwan 3 is white…Swan n is white

Indirect Test

•Good Bye Hypothesis! It is false that all swans are white.

Roxanne the swan

Swan 1 is whiteSwan 2 is whiteSwan 3 is white…Swan n is black

•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…

Deductive:•Matter attracts matter•Apples are matter•The earth is matterTherefore•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 groundTherefore•All apples when unsupported fall to the ground

An important difference!

Another example…

•Swan A is white•Swan C is purple.Therefore•All swans are white.

But there are some just plain bad arguments…

Philosophers Disagree about the roles of induction and deduction…

Induction Deduction

Easy to make observationsGenerate Powerful StatementsConclusions could be false

Hard to generate argumentsDifficult to find premises you can be sure are trueConclusions almost certainly true.

Philosophers Disagree about the roles of induction and deduction…

Induction Deduction

Easy to make observationsGenerate Powerful StatementsConclusions could be falseWeaker?Generative?

Hard to generate argumentsDifficult to find premises you can be sure are trueConclusions almost certainly true.Stronger?Non-Ampliative?

•Tom is a black dogTherefore•Tom is a dog.

•Lions are carnivores•Carnivores have no molarsTherefore•Lions have no molars.

Non-Ampliative?

A schism between philosophy and science!

John Stuart Mill 1806-1873

Developed five inductive methods: Mills Methods…

Student 1 Ate in cafeteria, ate potatoes, ate meatballs, ate soup

Student 2 Ate in cafeteria, ate salad, ate spaghetti, ate soup

Student 3 Ate in cafeteria, ate soup, ate ice cream

Student 4 Ate in cafeteria, ate potatoes, ate spaghetti, ate soup

A number of students in a dormitory fall ill. The doctor questions four of them and finds the following:

Example: Method of Agreement

The students became sick because they ate the soup in the cafeteria

Statistics!

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.

10 minute break…

(while I set up our statistical example…)

Note: If your attention wanders and you lose track, ask me to go

back!

Learning about the people in Philosophy 2301- using statistics!

• 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.

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

Population and Samples

A few more groups of five…

Group One:Oldest: 27Youngest: 20Average Age: 22.7

Group Two:Oldest: 27Youngest:19Average Age: 21.8

Whole Class:Oldest: 74Youngest: 18Average Age: 23

Average Age for each of 100 groups of five

Group 1

Group 2

Group 3

Group 100

…

Average Age

21.820.420.231.422.222.62222.831.231.821.222.622.621.6342219.821.222.2

Looking at the average age for each group of five:What can we learn?

Xxx graph here

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21.820.420.231.422.222.62222.831.231.821.222.622.621.6342219.821.222.2

Chance of picking a group that is close to the right value:

Real Class Average: 23.3Number of group averages within +- 3 of real value: 80Number 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!

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1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

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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

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…

How science uses statistics in the ‘real word’…

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

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…

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!

The big picture

• Several problems for science when it comes to testing hypotheses:

• Problems of direct testing- biased observations, observations not possible

• Problems of indirect testing- Auxiliary Hypotheses, Use of Inductive methods.

• After reading week… Some solutions to these problems?

Questions?

• Was there anywhere where you lost track of what was going on?

• Is there anything you want me to go over again?

• Any questions about any of the material we discussed today?

Midterm Questions?

• First class- ways to come up with answers, ways to evaluate answers, philosophers’ opinions…

• Second class- universal human behaviours, ideas traveling through history, beginnings of science. Philosophical Methodology- arguments, logic

• Third Class- origin of science. Difference between science and philosophy. Our first philosophy of science problems. Discovery and Evaluation.Auxiliary hypotheses

• Fourth Class- More on Auxiliary Hypotheses, deductive and inductive logic, statistics