Cpan 110 Week 9

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Cpan 110 Week 9

• Module 1
• Creating Valid Arguments
• Diagramming Arguments

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Consider these arguments...
If Thomas Paine advocates it then somebody
questions it. Thos 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 reliable. Is one of these arguments better
than the other?
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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 P Therefore, Q
If P then Q 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 other?
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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.
Invalid arguments are not completely reliable.
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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.
Invalid arguments are not completely reliable.
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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.
Invalid arguments are not completely reliable.
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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 conclusion.
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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
Conclusion indicators
thusthereforeconsequentlyhencesoit follows
thatproves thatindicates thataccordinglyimplie
s thatfor this reason

• forsinceasbecausefor the reason follows
  fromafter allin light of the factfor the 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

• andbutyethowevermoreoverin
  additionnevertheless(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 formIf 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 followsIf A then
  ONot O
• and the negation of clause O is logically
  equivalent to conclusion (6).
• Obvious modus tollensIf A then ONot
  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 doesnt 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
• 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.