1. Inductive/deductive reasoning Syllogisms Fallacies
Reason and Logic 2
Inductive/deductive reasoning
Syllogisms
Fallacies

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

3. Venn Diagrams and Euler’s Circles

4. VALID syllogism does not necessarily mean TRUE conclusion
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.

5. Syllogisms The Aristotelian system of logic Requires:
Two premises and a conlcusion
Three terms used twice
Quantifiers
More on page of gold packet

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.

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

8. 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

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.

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.

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

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?

13. When do we use inductive reasoning?

14. Once upon a time there was a farmer who had chickens
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.

15. The moral…
Assuming things will always be as they have been can be a dangerously comfortable place!

16. Inductive Syllogism
Annie is a nerd. Annie is in TOK. All kids in TOK are nerds.

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.

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

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

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 classification—which is impossible.
Everything is always changing—you cannot step into the same river twice.

21. Strengths Deduction Induction Uniformity Repetition
Validity/correctness
Propositional
Offers certainty
Induction
Trust your gut
Experience as a way of knowing.
Functionality

22. Fallacies
Fallacies are invalid arguments , syllogisms, and generalizations.

23. Post hoc ergo propter hoc: assumes that because of A follows B.
Assumes correlation = causality, which is not true.

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.

25. 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.

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.

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.

28. 6. Argument ad ignorantium
Claiming something is true on the grounds that there is no evidence that it is NOT true.

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?

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.

31. 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?

32. 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?

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

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.

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!

36. 14. Dicto Simpliciter
Not taking genuine exceptions into account

37. 15. Hasty Generalizations
Concluding from too few instances.

38. Monty Python
It’s a witch!