Reason and Logic 2 Inductive/deductive reasoning Syllogisms Fallacies Slide 2 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 Slide 3 Venn Diagrams and Eulers Circles Slide 4 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. Slide 5 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 Slide 6 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. Slide 7 Example syllogism: I like all green things. Kermit the Frog is green. I like Kermit the Frog. Slide 8 3 types of syllogisms Categorical 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 statement Slide 9 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. Slide 10 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. Slide 11 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 Slide 12 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? Slide 13 When do we use inductive reasoning? Slide 14 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. Slide 15 The moral Assuming things will always be as they have been can be a dangerously comfortable place! Slide 16 Inductive Syllogism Annie is a nerd. Annie is in TOK. All kids in TOK are nerds. Slide 17 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. Slide 18 Deductive reasoning From the general to the specific. For example: All dogs are mammals. Fido is a dog. Fido is a mammal. Slide 19 Deductive reasoning we tend to believe is based more on logic than inductive reasoning. Can you think of examples? Slide 20 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 classificationwhich is impossible. Everything is always changingyou cannot step into the same river twice. Slide 21 Strengths Deduction Uniformity Repetition Validity/correctness Propositional Offers certainty Induction Trust your gut Experience as a way of knowing. Functionality Slide 22 Fallacies Fallacies are invalid arguments, syllogisms, and generalizations. Slide 23 1.Post hoc ergo propter hoc: assumes that because of A follows B. Assumes correlation = causality, which is not true. Slide 24 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. Slide 25 3. Circular reasoning Vicious 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. Slide 26 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. Slide 27 5. Equivocation or Ambiguity When a word is used in two different senses in an argument. OR When the meaning of a word is unclear and used to the advantage of the argument. Slide 28 6. Argument ad ignorantium Claiming something is true on the grounds that there is no evidence that it is NOT true. Slide 29 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? Slide 30 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. Slide 31 9. Loaded question/complex question A biased question with a built in assumption. You dont want to waste your money going to prom, do you? Slide 32 10. Nominal Fallacy Assuming that youve explained something just by naming it. How does that work? Its a radio. Okaybut how does it work? Slide 33 11. Appeal to sympathy Trying to win an argument by using emotional appeal. Watch for emotive words and connotation here! Slide 34 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. Slide 35 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! Slide 36 14. Dicto Simpliciter Not taking genuine exceptions into account Slide 37 15. Hasty Generalizations Concluding from too few instances. Slide 38 Monty Python Its a witch!