Elements of Sciencemitch/teaching/s11/phil12/lectures/...Elements of Science ... Organization...

Elements of SciencePhil 12: Logic and Decision Making

Spring 2011UC San Diego

3/31/2011

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Thursday, March 31, 2011

Registering your i>clicker

• In order to earn points for your i>clicker responses, you must register your i>clicker online (but don’t worry, you will still get the points from before registration).

• Go to www.iclicker.com/registration, fill in:

- your name

- your PID (student ID) number

- your clicker ID (located on the back of your clicker, below the scan code)

- Finish by clicking ENTER.

Organization

Clickers

Basic operation



In order to earn points for your

i>clicker responses, you must register

your i>clicker online (but don’t worry,

you will still get the points from before

registration).

For this, you will need (your name),

your PID number (starting with an ‘A’),

and your clicker ID (located on the

back of your clicker, below the scan

code).

Christian Wüthrich Topic 0

2


http://www.iclicker.com/registration

http://www.iclicker.com/registration

Using your clickers - Set frequency

• When I ask the first question of each class, set your frequency code to AB

- Instructions found on the back of your clicker:

• hold power button until it blue “power” light flashes twice

• type A then B

• then select A, B, C, D, or E as your vote.

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How do you know your vote was received?

• Check your “Vote Status” Light:

- Green light = your vote was sent and received

- Red flashing light = you need to vote again.

• Not sure you saw the light? Just vote again.

• Want to change your vote? You can vote again as long as the timer is still going.

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Clicker question 1

Practice question: I have registered my clicker online www.iclicker.com.

A. Yes

B. No

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http://www.iclicker.com

http://www.iclicker.com

• One proposal: Scientists observe what happens in the world

- Mendel observed a pattern in the inheritance of traits in peas

- Edmond Halley observed a pattern in the occurrence of a comet

• But they also attempt to explain why things happen as they do

- Mendel proposed factors which accounted for traits

- Halley proposed an orbit for comets

What do scientists do?

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Hypotheses, Laws, and Theories

• A hypothesis is a conjecture about the way some phenomenon in the world is or behaves

- Malaria is transmitted by mosquitoes

- Mental imagery uses the same brain processes as perception

• A law is a hypothesis that seems to be very well supported

• A theory is a systematic set of hypotheses

- Newton’s theory of motion

- Freud’s psychodynamic theory

- Darwin’s theory of evolution

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It is just a theory!?• Hypotheses and theories range from conjectures or guesses

to well-substantiated claims

- When first proposed, most hypotheses are conjectures or proposals—guesses as to how things might be

- What matters is whether appropriate evidence can be marshaled for them

• Hypotheses and theories that were once well-substantiated may turn out to be false!

- The theory that the sun circled the earth was once very well supported

• Because hypotheses and theories go beyond the evidence, they always risk being falsified by future evidence

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Clicker question 2A theory consists in:

A. unsupported speculations about a domain of phenomena

B. false speculations about a domain of phenomena

C. a set of hypotheses that have a lot of evidence in their favor

D. a structured set of hypotheses

E. I’m not sure9


The value of hypotheses and theories

• They give us power and satisfy our curiosity

- Predictions: specific detectable phenomena which we can infer from the hypothesis and to which an hypothesis is committed (false predictions count against the truth of a hypothesis)

• From the hypothesis that mosquitoes transmit malaria, we predict that if we eliminate mosquitoes we will stop the spread of malaria

- Explanations: enable us to understand why something happens and often how to alter it

• From the hypothesis that a disease is produced by a vitamin deficiency, we can figure out how to treat it

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Representations and Phenomena

• Although it is the phenomenon in nature that interest us, we understand it by re-presenting it to ourselves

• Representations are particularly important when our hypotheses and theories go beyond what we can observe to posit factors responsible for what we observe

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Representations and Phenomena

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• Although it is the phenomenon in nature that interest us, we understand it by re-presenting it to ourselves

• Representations esp. important when our hypotheses and theories go beyond what we can observe

• Vehicles of representation:

- Words and sentences

- Diagrams

- Physical models

• All representations emphasize some features of the phenomena and distort others


Statements: Atoms of representation

• A statement is a sentence that has a truth value, i.e., is either true or false (even if we do not know which)

- Today is Thursday

- California is in Europe

- The brain is composed of neurons

• A statement has an internal structure (subject, predicate, etc.), but for our purposes we will not go inside of a statement

- Treat statements as atoms (indivisible)13


Compound Statements

• We can combine statements using logical connectives such that the truth value of the compound is determined solely by the truth value of the components

• Examples of connectives:

- AND

- OR

- IF, THEN

- NOT14


Truth-conditions for compound statements

• AND: true if both components are true

• OR: true if at least one of the components is true

• IF, THEN: true unless the first component is true and the second false

• NOT: true if the component is false

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Types of statements1. Tautologies

2. Contradictions

3. Contingent statements

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Types of statements1. Tautologies: always true (no matter what the

truth value of its components)

- Example: P OR NOT-P

- Definitions are stipulated tautologies, i.e., they are not tautologies by virtue of their form.

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Types of statements2. Contradictions: always false (no matter what

the truth value of its components)

- Example: P AND NOT-P

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Types of statements3. Contingent statements: could be true or could

be false

- when true, they tell us something about what the world is like, what it isn’t like

- Examples:

• P

• P OR Q

• P AND Q

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Classify the following statement:

Humans share an evolutionary ancestor with chimpanzees.

A. Tautology

B. Contingent statement

C. Contradiction

Clicker question 3

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Definitions: Vastly overrated!• Definitions attempt to provide the necessary and sufficient

conditions for being an instance of a word

- Example: An odd number is a positive integer that is not divisible by two without remainder

• Necessary condition = a condition which must be met for something to be an instance of the term

- Example: Being a positive integer is necessary for being an odd number

• Sufficient condition = one which suffices for being an instance

- Example: Being both a positive integer and not being divisible by two is sufficient for being an odd number

- Sufficient conditions are interesting when there are different ways of satisfying a term

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Trying to define ordinary terms• Necessary and sufficient conditions can generally only

be provided for technical terms (e.g., in mathematics or in legal contracts)

• Most ordinary terms defy such definition: For any attempted definition, a counterexample can be found

• A counterexample is either:

1. An example that fits the definition but we would not count as an instance of a term; or

2. An example that does not fit the definition but we would count as an instance of a term

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Define game

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Clicker question 4

Which of the following is a good definition of bird?

A. an animal that can fly

B. an animal with feathers

C. an animal with a beak

D. an animal with feathers and a beak that can fly

E. None of the above

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Define bird• Flying: is every animal that flies a bird?

- Not all birds fly, and most insects do

• Feathers: is every animal with feathers a bird?

- Caudipteryx, Microraptor seem to have had feathers but not be birds

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Doing without definitionsStart with typical cases

Robin Blue jay Sparrow

Extend to unusual cases

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Arguments

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Argument = a set of statements, some of which are offered as support for other statements in the set

- An argument provides reasons to believe something

- An argument need not involve another person: you can construct an argument to demonstrate that something is true without showing it to anyone

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Elements of arguments• Premises: statements offered in support

- Premise indicators: because, since, given that, on account of, etc.

• Conclusion: the statement that is supported

- Conclusion indicators: thus, therefore, this establishes that, etc.

• Example:

Premises

Conclusion

The car has a large dent in it.

Dents don’t just appear in cars.

∴ You had an accident.29


Good and bad arguments

• The goal is not actual persuasion (people can be persuaded for bad reasons), but establishing the truth

• Two factors relevant to the evaluation of arguments:

1. Are the premises true?

2. Is the connection between the premises and the conclusion such that: if the premises were true, would they establish that the conclusion is true?

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Validity• An argument is valid iff it meets the following condition: if

the premises were true, the conclusion must also be true

- A valid argument cannot have true premises and a false conclusion

• This relationship is modal: it tells us what would be the case were certain conditions to be met

- These conditions might not be satisfied in reality

- The definition tells you nothing about what happens when they are not satisfied

• A way to test for validity: if you can imagine a situation in which the premises are true and the conclusion false, then the argument is not valid

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