Reason as a Way of Knowing

‘We know the truth, not only by the reason, but also by the heart.” ~Blaise Pascal

(Interpret this quote. How does this relate to other things we have examined this semester?)

Deductive Reasoning

“Top-down” or “top to bottom” logic

Deduce = to derive as a conclusion from something known or assumed.

Literary term = ?

Moves from general to particular If given truth of information, the conclusion must

also be true.

All dogs are mammals.Fido is a dog.Therefore Fido is a mammal.

All dogs are mammals. (A)Fido is a dog. (B)Therefore Fido is a mammal. (C)

IF statements A and B are true, we can reason that C is true.

Syllogisms

Two premises and a conclusion

Three terms, each of which occurs twice (“dogs”, “mammals”, “Fido”)

Quantifiers, such as “all”, “some” or “no”

All ostriches are teachers.Mr. Jones is an ostrich.

Therefore Mr. Jones is a teacher.

Both premises are false.The conclusion is ________.

Make your own Syllogisms! Both premises and conclusion are true. (#1)

One true and one false premise with a true conclusion. (#2)

One true and one false premise with a false conclusion. (#3)

Two false premises and a true conclusion. (#4)

Two false premises and a false conclusion. (#5)

Truth vs. Validity

Cats are birds Birds are mammals Therefore, cats are mammals

Dogs are cats Cats are birds Therefore, dogs are birds

Deductive Reasoning

Inductive Reasoning

Certainty not involved the same way as ___________.

“bottom to top”

Probabilistic

90% of humans are right-handed. Joe is a human. Therefore, the probability that Joe is right-handed is 90%.

Inductive Reasoning

Nested Dolls Logic Problem

On a recent trip to St. Petersburg, Cheryl bought a set of Matryoshka, Russian nesting dolls where each holds the doll(s) smaller than it. Each of the five dolls in the set is a caricature of a noted Russian ruler or Soviet leader, and each is decorated in a dominant color scheme, one in green. From the information about opening the set of nesting dolls below, can you order theMatryoshka from largest to smallest, determining which historical Russian is on each doll and its dominant color?

The Lenin doll, which isn't the one with a blue motif, is the middle, or 3rd largest, of the five nesting dolls.

The Ivan the Terrible doll isn't the one done in red.

When the Peter the Great doll is opened, the next doll in the set that is revealed is the gold one.

When the blue-colored doll is opened, the Ivan the Terrible figure is the next to appear.

The Catherine the Great doll is nested immediately inside of the purple-based Matryoshka.

The blue-hued doll isn't the one of Peter the Great.

The gold doll, which isn't the smallest of the five, isn't the one with Mikhail Gorbachev on it.

Homework

Continue to solve (attempt to solve) Matryoshka logic problem

Read “Reason” chapter

ARtT (Due December 17…This is also the day that we will be taking the final.)

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Homework Cont’d informationisbeautiful.net/visualizations/rhetological-fal

lacies/ earlham.edu/~peters/courses/log/tru-val.htm

Visit, read and study

*Closely read and annotate “Reason Destroys…” and “Reason Excludes…” articles. They will be discussed and assignments will be applied to them during our next class. 19

Schools use textbooks.

Textbooks are made of paper.

Paper comes from trees.

We need trees for oxygen.

Therefore, school is killing us.

Nested Dolls Logic Problem (Solution)

I’m so sick of Russian dolls. They are all so full of themselves!

1 (largest) = Peter the Great2 = Catherine the Great3 = Lenin4 = Gorbachev5 (smallest) = Ivan the Terrible

Nested Dolls

What information was most useful in the beginning?

How did you judge the most useful information?

How did you use this information?What was the biggest problem solving the

puzzle?

Truth & Validity

Both premises are false, so the conclusion is ________ ?

(semantic concept of validity)

Both premises are false, so the conclusion is ________ ?

(semantic concept of validity)

Truth Validity

True = in accordance with fact

Valid = having sound basis

semantics

When an argument has true premises and a false conclusion, it must be invalid.

“We should never be misled by true premises or false conclusions to suppose (automatically) that an argument is valid. Nor should we be misled by false premises or false conclusions to suppose that it is invalid. Nor should we be misled by valid reasoning to suppose that statements are true, or by invalid reasoning to suppose that statements are false. If we recognize this, then we have already far surpassed “common sense” in protecting ourselves from deception.”

Soundness basis/foundation

“Truth and validity are combined in the concept of soundness. An argument is sound if (and only if) all its premises are true and its reasoning is valid…” Anything else is unsound. All sound arguments have true conclusions.

Where can soundness be found in arguments 0-7?

True premises do not guarantee validity. (1, 3)

A true conclusion does not guarantee validity. (3, 7)

True premises and a true conclusion together do not guarantee validity. (3)

Invalid reasoning does not guarantee a false conclusion. (3,5)

#4 = A lot of ways to (basically) say the same thing

Valid reasoning does not guarantee a true conclusion.

False premises and a false conclusion together do not guarantee invalidity. (also 6)

A false conclusion does not guarantee invalidity.

(reasoning is valid, but argument is not sound)

False premises do not guarantee invalidity.

#2 = Truth-Bomb!!!

Cats are mammals.

Tigers are cats.

Therefore, tigers are mammals.

(true premises/true conclusion…also, reasoning is valid)

Finally! An argument that has valid reasoning and is sound!

Find validity by testing for invalidity. “We know exactly what invalidity in an argument is: to have true premises and a false conclusion. An argument is valid in a weak sense if it simply is not invalid. This weak sense of validity turns out to suffice for all the purposes of rigorous reasoning in science, mathematics and daily life.”

Enthymeme - Incomplete Argument

Enthymeme = informal syllogism

Jenny goes to Oxford University, so she must be very intelligent.

What is the missing premise?

Fallacies

Formal Fallacy = pattern of reasoning that is always wrong

Informal Fallacy = an error in reason is made; can possess appeal

appeal

ad misericordiamattempt to gain support

by exploiting another’s feelings.

ad hominemLatin - “to the man”argument made personally against an

opponent. an attack.

hasty generalization

appeal to authority

“It must be true – our Theory of Knowledge teacher says so!

unpalatable consequencesarguing that a belief is false because you’d

rather not believe the truth“My son is an honest child. He would never

lie!’

loaded languageemotive language“You want to come to my birthday party,

don’t you?”

appeal to common practiceclaiming something is true because it is

common practice“You shouldn’t pick on me for having my

phone out when others also have theirs out.”

“If everyone jumped off a bridge…

red herring Introducing irrelevant material to distract

and lead towards a different conclusion “I think that we should make the academic

requirements stricter for students. I recommend that you support this because we are in a budget crisis and we do not want our salaries affected.”

straw man misrepresenting your opponent’s position easy to “defeat”

Daughter: I need to eat ice cream every day.

Mother: Eating ice cream every day is not good for you.

Daughter: Do you want me to starve?

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false dilemmablack and white thinking“You’re either for me or against me.”

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ad ignorantiam - appeal to ignorance a claim is true simply because it hasn’t been

proven false

(or vice versa)

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ad bacculam

appeal to force

(literally, “the stick”)

Employee: I don’t think the company

should invest in this project.

Boss: Be quiet or you’re fired.

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contradiction in terms

“It is impossible for written words to communicate anything.”

(intentional = oxymoronic)

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begging the question / circular argument

a statement using its own assertions for

proof

Brian: Unbelief is disobedience to God’s

commands.

Aaron: Says who?

Brian: Says God Himself!

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false cause / post hoc ergo propter hoc

(trans. = after this, therefore because of this)A occurred, then B occurred.

Therefore, A caused B.

(When B is undesirable, the pattern is often

extended in reverse: Avoiding A

will prevent B.)

“Rooster Syndrome”

Create your own!!!(7)

(sentences/situations, illustrations)

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Three part assignment for articles. 1 = Compose your own blog/journal about reason. 2 = Answer 4 questions for “Reason Destroys...” 3 = Answer 4 questions for “Reason Excludes...”

(Notice, blog/journal is separate from 8 total

questions. Avoid using blog/journal to answer

questions. However, it may be used in your

processing thereof.)

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“Reason Destroys Itself”

1. Create another example of circular reasoning and explain it in detail.

2. What is intuition?3. Provide another example of people

putting unreasonable standards on certainty and explain it in detail.

4. How can we be reasonable about Reason?

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Reason Excludes Creativity and Intuition

1. How do you understand and come to terms with the words “rationale” and “counterintuitive”?

2. What is holistic synthesis? How would you describe the way that holistic synthesis has been lost?

3. Why is reason a slow and gradual process?

4. Is reason a good thing or a bad thing? Justify your answer.

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HW

Three part assignment for articlesRead textRead and study websites.

(1.fallacies 2. reason)Read and study 15 fallaciesARtT

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