Transcript Chapter 3

Cpan 110 Week 12
Creating Valid Arguments
Diagramming Arguments
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Consider these arguments...
If Thomas Paine advocates it then somebody questions it.
Thomas Paine advocates it.
Therefore, somebody will question it.
If Thomas Paine advocates it then somebody questions it.
Somebody is questioning it.
Therefore, Thomas Paine must be advocating it.
Note: One argument is better than another if it's more
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reliable. Is one of these arguments better than the other?
Consider using claim variables...
A claim variable is a letter or other symbol that
stands for a claim.
For example...
P - Thomas Paine advocates it.
Q - Somebody questions it.
R - Paul Revere advocates it.
P, Q, and R are claim variables representing three
different sentences.
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Consider these arguments formally...
We'll use these variables...
P - Thomas Paine advocates it.
Q - Somebody questions it.
If P then Q
If P then Q
P
Q
Therefore, Q
Therefore, P
One argument form is better than the other if it is more
reliable. Is one of these argument forms better than the
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other?
Modus Ponens
If P then Q
P
Therefore, Q
Modus Ponens is a valid deductive form.
Any argument that is in this form and has true
premises will have a true conclusion.
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Modus Ponens
If the glove don't fit, you must acquit.
The glove don't fit.
Therefore, you must acquit.
But if there is an untrue premise, the conclusion could be
false.
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IMPORTANT POINT
• A valid argument is perfectly reliable.
• This means that if the premises of an
argument are true, the conclusion must be
true.
• "Valid" is a word that describes reliable
logic.
•It does not mean the premises or conclusion
must actually be true.
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Affirming the Consequent
If P then Q
Q
Therefore, P
Affirming the Consequent is an invalid form.
An argument that is in this form and has true
premises may or may not have a true conclusion.
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Invalid arguments are not completely reliable.
Affirming the Consequent
If God wanted to test our faith, there would be
a fossil record to make it look like evolution
occurred.
There is a fossil record that makes it look like
evolution has occurred.
Therefore, God wants to test our faith.
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Modus Tollens
If P then Q
~Q
Therefore, ~P
Modus Tollens is a valid deductive form.
Any argument that is in this form and has true
premises will have a true conclusion.
The "~" means "not".
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Modus Tollens
If people had an ounce of sense, they
would not dump sewage into their
drinking water.
People dump sewage into their drinking
water regularly.
Therefore, people do not have an ounce of
sense.
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Denying the Antecedent
If P then Q
~P
Therefore, ~Q
Denying the Antecedent is an invalid form.
An argument that is in this form and has true
premises may or may not have a true conclusion.
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Invalid arguments are not completely reliable.
Denying the Antecedent
If someone thinks alcohol should be legal,
then they agree with the principle that some
mind-altering substances should be legal.
But you don't think alcohol should be legal.
So that means you don't agree that some mind
altering substances should be legal.
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Invalid arguments are not completely reliable.
Chain Argument
If P then Q
If Q then R
So, if P then R
The Chain Argument is a valid deductive form.
Any argument that is in this form (including any
number of premises, as long as they can be arranged
as a chain) and has true premises will have a true
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conclusion.
Chain Argument
If there's a chance we can balance the budget,
we should keep meeting.
If we keep meeting, I'll get home late for dinner.
If I get home late for dinner, I won't be able to
help little Jimmy with his homework.
If I don't help little Jimmy with his homework,
he will cry himself to sleep.
So, if there's a chance we can balance the
budget, little Jimmy will cry himself to sleep.
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Reversed Conclusion
Chain Argument
If P then Q
If Q then R
So, if R then P
The Reversed Conclusion Chain Argument is an
invalid (i.e., unreliable) form. An argument that is in
this form may have true premises and (unlike a valid
form) still have a false conclusion.
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Diagramming Arguments
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Diagramming Arguments
•
•
Analyzing the structure of arguments is
clarified by representing the logical
relations within an argument in diagram
form.
In order to analyze arguments, we will
construct a diagram of the argument that
details the relations among the premises
and conclusions.
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Find the Conclusion
•
•
In analyzing the structure of an argument,
the all-important first step is to find the
conclusion.
Here are some specific suggestions as to
how to find the conclusion.
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The sequence of sentences is often
an indication of the conclusion
Example:
(1) John didn't get much sleep last night.
(2) He has dark circles under his eyes.
(3) He looks tired.
The conclusion is the first sentence in the
passage.
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Premise indicators
for
since
as
because
for the reason
follows from
after all
in light of the fact
for the reason
Conclusion
indicators
thus
therefore
consequently
hence
so
it follows that
proves that
indicates that
accordingly
implies that
for this reason
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Example
(1) Studies from rats indicate that neuropeptide
Y in the brain causes carbohydrate craving,
and
(2) galanin causes fat craving.
(3) Hence, I conclude that food cravings are tied
to brain chemicals
(4) because neuropeptide Y and galanin are
brain chemicals
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Example Argument:
(1)The graphical method for solving a
system of equations is an approximation,
(2) since reading the point of intersection
depends on the accuracy with which the
lines are drawn and on the ability to
interpret the coordinates of the point.
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Example
(1) No one has directly observed a chemical
bond,
(2) so scientists who try to envision such
bonds must rely on experimental clues and
their own imaginations.
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Conjunctives
• Conjunctives (including conjunctive
adverbs) often indicate equal status for
clauses or sentences.
• Noticing these conjuncts is especially
helpful for argument analysis if one of the
elements has already been identified.
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Indicators of clauses of equal status:
and
but
yet
however
moreover
in addition
nevertheless
(and also the semicolon ";")
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Example
(1) Some students absent today are
unprepared for this test,
since (2) the law of averages dictates that
only 10% of students are absent due to
illness, and (3) more than 10% are absent.
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Example
(1) Lenses function by refracting light at their
surfaces.
(2) Consequently, not only does their action
depends on the shape of the lens surfaces
but also
(3) it depends on the indices of refraction of
the lens material and the surrounding
medium.
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When working with complex arguments, it
is often helpful to reconstruct the argument
backwards from the conclusion.
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Example
(1) If students were environmentally aware,
they would object to the endangering of any
species of animal. (2) The well-known
Greenwood white squirrel has become
endangered (3) as it has disappeared from the
Lander Campus (4) because the building of the
library destroyed its native habitat. (5) No
Lander students objected. (6) Thus, Lander
students are not environmentally aware.
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Example
The premiss indicators
suggest that (2) is a
subconclusion of (3) since
the indicator "as" connects
them, and (3), in turn, is a
subconclusion of (4) since
the indicator "because"
connects those two
statements.
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Example
Intuitively, the structure of the first statement (1)
together with statement (5) is a common argument
form:
If students were environmentally Aware, they
would Object to the endangering of any species of
animal.
No student Objected (to the endangering of the
Greenwood white squirrel).
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Example
which can be abbreviated as follows:
If A then O
Not O
and the negation of clause O is logically equivalent
to conclusion (6).
Obvious modus tollens:
If A then O
Not O
_____________
Not A (which is the same statement as (6)).
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Hence the whole argument can now
be pieced together as:
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Scientific reasoning
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Scientific reasoning is for everyone
• Science in everyday life
– Technical troubleshooting, health
• Personal dimension
– Investment, personal relationships
• Commerce
– Sales and marketing, logistics
• Law
– Causation and liability
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Four basic principles
• Rational belief need not be certain.
• Rational belief should take into account both
positive and negative evidence.
• Always consider alternative explanations.
• Extraordinary beliefs require extraordinary evidence.
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1. Rational belief need not be certain.
• Scientific reasoning is often inductive.
– We need to act on the basis of probability rather than
absolute certainty.
• Predictions about the future.
• Inferences from observed cases to unobserved cases.
• Best case: uncertain but beyond reasonable doubt
– “Uncertain” doesn’t mean “reasonable to deny”.
• The earth is not flat.
• Holocaust.
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Bad argument
• “We should not accept the theory
of evolution because it is only a
theory / hypothesis and there is no
proof.”
• Two senses of “proof”
– Highly compelling evidence
– Absolutely irrefutable evidence
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2. Rational belief requires evidence
• Evidence and probability
– Confirming evidence for H increases probability of H.
– Disconfirming evidence for H decreases probability of H.
• Fingerprint on murder weapon vs. alibi.
– Neutral evidence
• What counts as good evidence?
–
–
–
–
Publicly observable
Repeatable
Described in neutral terms
NOT: Faith, intuition
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Confirmation bias
• We tend to focus more on evidence that confirms our
expectations.
– Horoscope predictions
• Motivation biases memory.
Man prefers to believe what
he prefers to be true.
- Francis Bacon (1561-1626)
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3. Always consider alternative explanation
The SEARCH Formula
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•
•
•
State the claim.
Examine the Evidence for the claim.
Consider Alternative hypotheses.
Rate, according to the Criteria of adequacy, each
Hypothesis.
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Alien sculpture on Mars
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David Blaine
Intuition may have a good track record
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Ignorance is not truth
• There might be many explanations for an
observation, even if you cannot think of any
yourself.
– Being stubborn
– Lack of knowledge and imagination
– Lack of further information
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Telescope photo of UFO
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Some lessons
• Beware of
– Newspaper reports of scientific experiments
– Reports invoking personal testimonies
– Reports of experiments which lack follow-up
information.
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4. Extraordinary claims require
extraordinary evidence
• Supernatural phenomena
– ESP, OBE, ghosts, etc.
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Miracle cures
• Quality of evidence
– How many studies?
– Peer-review?
– “Some doctors believe P.”
• Vagueness
– “This MAY fight cancer.”
– “Revitalizes the body.”
• Qualifications
– “Requires balanced diet etc.”
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