Philosophy 2301

1
Philosophy 2301

• Class 4

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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.

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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.

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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.

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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.

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The earth moves around the sun Therefore, we
should be able to measure the stars
shift However, we dont 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 dont
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 dont observe the stars
shifting
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This might seem okay

• But what if Copernicus really had been wrong

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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.

NO
YES
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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!
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The problem with auxiliary hypotheses

• Its too easy to get your main hypothesis out of
  trouble- even if it is actually false
• Similarly- its 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.
• Thats bad!

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Multiple Hypotheses

• (Crucial Tests)

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Hypothesis One The sun moves around the earth
Hypothesis Two The earth moves around the sun
contrary hypotheses
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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
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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
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But because of auxiliary hypotheses, it doesnt
work
crucial test
Copernicus adds an auxiliary hypothesis- now both
theories predict the exact same observation.
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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?

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Any suggestions?
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Karl Popper (1902-1994)

• He might have some solutions for us

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Before Solutions More Problems!

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

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• 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

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Singular and Universal Statements
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Indirect Test

• Hypothesis All swans are white.

John the swan
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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
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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
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Induction by Analogy Four legs, sharp teeth,
barks
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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!
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But there are some just plain bad arguments

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

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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.
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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?
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Non-Ampliative?

• Tom is a black dog
• Therefore
• Tom is a dog.

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

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A schism between philosophy and science!
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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
The students became sick because they ate the
soup in the cafeteria
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Statistics!
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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.

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10 minute break

• (while I set up our statistical example)

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Note If your attention wanders and you lose
track, ask me to go back!
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Learning about the people in Philosophy 2301-
using statistics!
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• 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.

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Population and Samples
Suppose we didnt 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
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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 Youngest19 Average Age
21.8
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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
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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
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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 20g
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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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
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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
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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
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• 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

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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 cant get too confident- although
  sometimes they do!

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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?

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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?

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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