Inductive/deductive reasoning Syllogisms Fallacies

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

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
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 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
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
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 Induction 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.

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.

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. OR When the meaning of a word is unclear and used to the advantage of the argument.

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.

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.

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!