Reason and Logic 2

Inductive/deductive reasoningSyllogismsFallacies

4 Relationships in Logic

• All x is y: total inclusion• No x is y: total exclusion• Some x is y: partial inclusion• Some x is not y: partial exclusion

Venn Diagrams and Euler’s Circles

VALID syllogism does not necessarily mean TRUE conclusion. It can follow a VALID process (see the Euler’s circle on previous slide).

Pretend you are on another planet where all things can be true.

Syllogisms

• The Aristotelian system of logic• Requires:– Two premises and a conlcusion– Three terms used twice– Quantifiers

• More on page 68-69 of gold packet

• Plato is mortal. – This is the only true syllogism, and it is an

ENTHYMEME…• A syllogism or other argument in which a premise or

the conclusion is unexpressed. Maxims are another example of enthymemes.

Example syllogism:I like all green things.Kermit the Frog is green.I like Kermit the Frog.

3 types of syllogisms

• Categorical Syllogisms—one that makes assertions.

• Hypothetical syllogism—places an ‘if’ condition. (If he fails the exam, he won’t graduate. He failed the exam, thus he won’t graduate.)

• Disjunctive syllogism—either/or statement

Aristotelian Logic

• All x is y• Some x is not y

• If either is true, the other is false.• If either is false, the other is true.

Chain argument: a chain of syllogisms

Anything that has life has a soul.All things that breathe have life.

All things that breathe have a soul.Every animal is a thing that breathes.

Every animal has a soul.Man is an animal.Man has a soul.John is a man.

John has a soul.

Inductive Reasoning

• From the particular to the general• Usually involves a premise we believe to be

true based on experience and repetition. – If I turn this key my car will start.

Assumptions based on: past experience, inference, expectation, and classification. *Chart on page 121 of book

Beware of when using induction

• Hasty generalizations• Insufficient evidence• Superstition• Unexamined prejudices• Confirmation bias

• Where does inductive reasoning fit on the certainty scale for you?

• When do we use inductive reasoning?

Once upon a time there was a farmer who had chickens. Every morning he would go out to feed his chickens; they would hear him coming and start gathering, clucking happily with excitement. One day, the farmer went out to the chicken coop, the chickens gathered, clucking away. He grabbed two by the necks and chopped their heads off.

The moral…

Assuming things will always be as they have been can be a dangerously comfortable place!

Inductive Syllogism

Annie is a nerd.Annie is in TOK.All kids in TOK are nerds.

Doubting inductive reasoning

• Even well confirmed generalizations can fail.• Lateral thinking: looking elsewhere, not the

same old hole, for information.• Prison of consistency: trapped in a way of

thinking, lack of intellectual flexibility.

Deductive reasoning

• From the general to the specific. For example:All dogs are mammals.Fido is a dog.Fido is a mammal.

Deductive reasoning we tend to believe is based more on logic than inductive reasoning. Can you think of examples?

Doubting deductive reasoning

• Do laws of logic apply to the way we think or the way the universe is? Do our thoughts relate to reality at all?

• Logic relies on language which assumes clear classification—which is impossible.

• Everything is always changing—you cannot step into the same river twice.

Strengths

• Deduction– Uniformity– Repetition– Validity/correctness– Propositional– Offers certainty

• Induction– Trust your gut– Experience as a way of

knowing.– Functionality

Fallacies

Fallacies are invalid arguments , syllogisms, and generalizations.

1. Post hoc ergo propter hoc: assumes that because of A follows B.

Assumes correlation = causality, which is not true.

2. Ad hominem fallacy

• Attacking or supporting the person rather than the argument. This happens often when the attacker or supporter has a vested interest.

3. Circular reasoning

• Vicious circle, assuming the truth of something you’re supposed to be proving. Reassertion or rewording of position as argument.

We often do this in our writing.

4. Special pleading/double standard

Making exceptions when convenient or for selfish reasons that you would not allow ifi t came to someone else. Hypocrisy.

5. Equivocation or Ambiguity

When a word is used in two different senses in an argument. ORWhen the meaning of a word is unclear and used to the advantage of the argument.

6. Argument ad ignorantium

• Claiming something is true on the grounds that there is no evidence that it is NOT true.

7. False analogy

Beware of the fluffy metaphor!

Assuming that because things are similar in one respect they are similar in further (or every) respect.

Like sands through the hourglass, so are the days of our lives. So our days must also be miniscule and insignificant?

8. False dilemma

Assuming that only two black and white arguments exist; binary thinking.

IB is at Hellgate and costs money; so money is being taken away from other students.

9. Loaded question/complex question

A biased question with a built in assumption.

You don’t want to waste your money going to prom, do you?

10. Nominal Fallacy

Assuming that you’ve explained something just by naming it.

How does that work?It’s a radio.Okay…but how does it work?

11. Appeal to sympathy

Trying to win an argument by using emotional appeal. Watch for emotive words and connotation here!

12. Ad populum

Based on the idea that “everyone does it, so should I!”

Everyone in Montana owns guns, so it would be wrong of you to vote against gun ownership.

13.Ad Verecundium

• False authority

I saw on TV that 4 out of 5 dentists recommend Colgate for 25% fewer cavities, so I am going to go buy ten cases!

14. Dicto Simpliciter

Not taking genuine exceptions into account

15. Hasty Generalizations

Concluding from too few instances.

Monty Python

It’s a witch!