Reason and Logic 2
Inductive/deductive reasoning
Syllogisms
Fallacies
4 Relationships in Logic
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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
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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
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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.
OR
When 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!