1 Cpan 110 Week 9 Module 1 Creating Valid Arguments Diagramming Arguments.

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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.

Note: One argument is better than another if it's more reliable. Is one of these arguments better than the other?

If Thomas Paine advocates it then somebody questions it.

Somebody is questioning it.

Therefore, Thomas Paine must be advocating it.

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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...

If P then Q

P

Therefore, Q

One argument form is better than the other if it is more reliable. Is one of these argument forms better than the other?

If P then Q

Q

Therefore, P

We'll use these variables...

P - Thomas Paine advocates it.

Q - Somebody questions it.

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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 RThe 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 ArgumentIf 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 PThe 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

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

thusthereforeconsequentlyhencesoit follows thatproves thatindicates thataccordinglyimplies thatfor this reason

Conclusion indicators

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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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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.

Example

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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).

Example

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Examplewhich can be abbreviated as follows:

If A then ONot O

and the negation of clause O is logically equivalent to conclusion (6).Obvious modus tollens:

If 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” 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• 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.”