Reason and Logic 2

Reason and Logic 2Inductive/deductive reasoningSyllogismsFallacies4 Relationships in LogicAll x is y: total inclusionNo x is y: total exclusionSome x is y: partial inclusionSome x is not y: partial exclusionVenn Diagrams and Eulers Circles

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

Pretend you are on another planet where all things can be true. SyllogismsThe Aristotelian system of logicRequires:Two premises and a conlcusionThree terms used twiceQuantifiers

More on page 68-69 of gold packetPlato is mortal. This is the only true syllogism, and it is an ENTHYMEMEA 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 syllogismsCategorical Syllogismsone that makes assertions.Hypothetical syllogismplaces an if condition. (If he fails the exam, he wont graduate. He failed the exam, thus he wont graduate.)Disjunctive syllogismeither/or statementAristotelian LogicAll x is ySome 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 syllogismsAnything 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 ReasoningFrom the particular to the generalUsually 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 bookBeware of when using inductionHasty generalizationsInsufficient evidenceSuperstitionUnexamined prejudicesConfirmation 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 moralAssuming things will always be as they have been can be a dangerously comfortable place! Inductive SyllogismAnnie is a nerd.Annie is in TOK.All kids in TOK are nerds. Doubting inductive reasoningEven 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 reasoningFrom 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 reasoningDo 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 classificationwhich is impossible.Everything is always changingyou cannot step into the same river twice. StrengthsDeductionUniformityRepetitionValidity/correctnessPropositionalOffers certaintyInductionTrust your gutExperience as a way of knowing.Functionality

21FallaciesFallacies are invalid arguments , syllogisms, and generalizations. Post hoc ergo propter hoc: assumes that because of A follows B.

Assumes correlation = causality, which is not true. 2. Ad hominem fallacyAttacking or supporting the person rather than the argument. This happens often when the attacker or supporter has a vested interest. 3. Circular reasoningVicious circle, assuming the truth of something youre supposed to be proving. Reassertion or rewording of position as argument.

We often do this in our writing. 4. Special pleading/double standardMaking exceptions when convenient or for selfish reasons that you would not allow ifi t came to someone else. Hypocrisy. 5. Equivocation or AmbiguityWhen 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 ignorantiumClaiming something is true on the grounds that there is no evidence that it is NOT true. 7. False analogyBeware 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 dilemmaAssuming 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 questionA biased question with a built in assumption.

You dont want to waste your money going to prom, do you?

10. Nominal FallacyAssuming that youve explained something just by naming it.

How does that work?Its a radio.Okaybut how does it work?

11. Appeal to sympathyTrying to win an argument by using emotional appeal. Watch for emotive words and connotation here!12. Ad populumBased 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 SimpliciterNot taking genuine exceptions into account15. Hasty GeneralizationsConcluding from too few instances.Monty PythonIts a witch!