ICT role in 21st century education and it's challenges.
Basic Logical Argument.ppt
1. DEDUCTIVE ARGUMENTS
• Some pigs have wings.
All winged things sing.
Therefore, some pigs sing.
• Everyone has one and only one biological mother.
Full sisters have the same biological mother.
No one is her own biological mother.
Therefore, there is no one whose biological mother is
also her sister.
2. INDUCTIVE ARGUMENTS
• Every ruby discovered thus far has been red.
So, probably all rubies are red.
• Polls show that 87% of 5-year-olds believe in the tooth
fairy.
Marta is 5 years old.
Marta probably believed in the tooth fairy.
• Chemically, potassium chloride is very similar to
ordinary table salt (sodium chloride).
• Therefore, potassium chloride tastes like table salt.
3. THE DIFFERENCE
Key: deductive / inductive
• If the premises are true the conclusion is
necessarily / probably true.
• The premises provide conclusive / good evidence
for the conclusion.
• It is impossible / unlikely for the premises to be
true and the conclusion to be false.
• It is logically inconsistent / consistent to assert
the premises but deny the conclusion.
4. FOUR TESTS
• Four tests allow us to identify deductive /
inductive arguments
The indicator word test
The strict necessity test
The common pattern test
The principle of charity test
5. INDICATOR WORD TEST
Deduction Induction
Certainly Probably
Definitely Likely
Absolutely Plausible
Conclusively Reasonable
This entails that The odds are that
6. CAUTION!
-Arguments may not contain any indicator words.
Pleasure is not the same thing as happiness.
The occasional self-destructive behavior of the rich
and famous confirms this too vividly.
(Tom Morris)
-Arguers may use indicator words incorrectly.
(People very often overstate their cases.)
-In these cases, other tests must be used to determine
whether an argument is deductive or inductive.
7. The Strict Necessity Test
• An argument’s conclusion either follows with
strict logical necessity from its premises or it
does not.
• If an argument’s conclusion does follow with
strict logical necessity from its premises, the
argument should always be treated as deductive.
• if an arguments conclusion does not follow with
strict logical necessity from its premises, the
argument should normally be treated as
inductive.
8. The Strict Necessity Test
• Examples:
• Tola is a father. Therefore Tola is a male.
• Guta is a six-year-old. Therefore, Guta cannot
run a mile in one minute flat.
9. COMMON PATTERN TEST
• Modus ponens (affirming the antecedent)
– If A then B.------A.-------Therefore B.
(A = antecedent; B = consequent)
This is a very common pattern of deductive reasoning.
• Example (modus ponens)
• If we are in Paris, then we are in France.
------A------- -----B-------
• We are in Paris.
--------A---------.Therefore, we are in France.
---------B-----------
10. Exceptions to the Strict Necessity Test
• Examples
1. Magellan’s ships sailed around
the world. It necessarily follows,
therefore, that the earth is a sphere.
(The arguer intended to offer a logically conclusive
argument, so it should be treated as deductive.)
2. If I’m Bill Gates, then I’m mortal. I’m not Bill Gates.
Therefore, I’m not mortal. (The argument has a
pattern of reasoning characteristic of deductive
arguments, so should be treated as deductive.)
11. SUMMARY: How To Distinguish Deductive From
Inductive Arguments
• If the conclusion follows necessarily from the premises =
deductive
• If the conclusion does not follow necessarily from the premises
= inductive, unless
– Language indicates it is deductive
– Argument has deductive pattern of reasoning
• If the argument has a pattern of reasoning that is
characteristically deductive = deductive, unless
– Clear evidence indicates it is intended to be inductive
• If the argument has a pattern of reasoning that is
characteristically inductive = inductive unless
– Clear evidence indicates it is intended to be deductive
• If the argument contains an indicator word
• If still in doubt: Principle of Charity
12. 5 COMMON DEDUCTIVE PATTERNS
• Hypothetical syllogism
• Categorical syllogism
• Argument by elimination
• Argument based on mathematics
• Argument from definition
13. HYPOTHETICAL SYLLOGISM
• A syllogism is a three-line argument with two
premises, one of which is a conditional.
• Modes ponens is a syllogism.
• Other syllogisms are:
–Chain arguments
–Modus tollens (denying the consequent)
–Denying the antecedent
–Affirming the consequent
14. CHAIN ARGUMENT
If A then B.
• If B then C.
Therefore if A then C.
• If you are blue in the face then you are lying.
If you are lying then you can’t be my friend.
Therefore if you are blue in the face then you
can’t be my friend.
15. MODUS TOLLENS
• If A then B.
Not B.
Therefore not A.
• If we’re in Sacramento, we’re in California.
We’re not in California.
Therefore, we’re not in Sacramento.
• If you love me, you’ll come with me to Tibet.
You will not come with me to Tibet.
Therefore you do not love me.
16. DENYING THE ANTECEDENT***
• If A then B.
Not A.
Therefore not B.
*If Tiger Woods won this year’s Masters then he’s a great athlete.
Tiger Woods didn’t win this year’s Masters.
Therefore, Tiger Woods is not a great athlete.
*If Jack comes to the party, Jill will leave.
Jack did not come to the party.
Therefore Jill did not leave.
17. AFFIRMING THE CONSEQUENT***
• If A then B.
B.
Therefore A.
*If we are on Neptune then we are in the solar
system.
We are in the solar system.
Therefore we are on Neptune.
***Affirming the consequent is a fallacious deductive
pattern
18. MODUS PONENS (affirming the antecedent): If A then B.A.
Therefore B.
CHAIN: If A then B. If B then C. Therefore if A then C.
MODUS TOLLENS: If A then B. Not B. Therefore not A.
*DENYING THE ANTECEDENT: If A then B. Not A. Therefore
not B.
*AFFIRMING THE CONSEQUENT: If A then B. B. Therefore
A.
19. PRINCIPLE OF CHARITY
• Attribute an arguer the strongest argument
possible.
Andy told me he ate at JB’s yesterday.
But JB’s was destroyed by a fire a month ago.
It is certain therefore that Andy is eitherlying or
mistaken.
Caution – The Principle of Charity is a principle of
argument interpretation, not a principle of
argument repair.
20. CATEGORICAL SYLLOGISM
• A three-line argument in which each
statement begins with one of the words all,
some, or no.
–Some pigs have wings
All winged things sing.
Therefore some pigs sing.
21. Caution – not all arguments that make
use of numbers and mathematics are
deductive.
DEFINITION
The conclusion follows from the definition of some
key word or phrase in the argument.
Josefina is a drummer.
Therefore Josefina is a
musician.
22. COMMON INDUCTIVE PATTERNS
• There are 6 common inductive patterns:
Inductive generalization
Predictive argument
Argument from authority
Causal argument
Statistical argument
Argument from analogy
23. 1. INDUCTIVE GENERALIZATION
• A generalization attributes some characteristic to
all or most members of a given class.
• Information about some members of the class is
said to license the generalization.
All dinosaur bones discovered thus far have
been more than 65 million years old.
Therefore probably all dinosaur bones are
more than 65 million years old.
24. 2.PREDICTIVE ARGUMENT
• A statement about what will (likely) happen in the
future is defended with reasons.
It has rained in Vancouver every February since
records have been kept.
Therefore it will probably rain in Vancouver next
February.
25. 3.AUTHORITY, CAUSE, STATISTICS
• Argument from Authority
The conclusion is supported by citing some
presumed authority or witness.
• Causal Argument
Asserts or denies that something is the cause
of something else.
• Statistical Argument
Rests on statistical evidence.
26. ANALOGY
• Common Pattern:
Two (or more) things are alike in one way. Therefore they
are probably alike in some further way.
As a man casts off worn-out garments and puts on others
that are new,
similarly, the soul, casting off worn-out bodies, enters
into others, which are new.
(Bhagavad-Gita)
27. VALIDITY
• VALID arguments may have false premises and
false conclusions!
• At issue is the form. If the premises are true the
conclusion must be true.
All circles are squares.
All squares are triangles.
Therefore all circles are triangles.
All fruits are vegetables.
Spinach is a fruit.
Therefore spinach is a vegetable.
28. VALIDITY, CONT’D
• It is not enough that the conclusion happens to
be true. If the conclusion doesn’t follow from the
premises by strict logical necessity, a deductive
argument is invalid.
• All pigs are animals.
Wilber is pink.
Therefore Wilber is a pig.
29. SOUNDNESS
• A deductive argument is sound if it is valid and
has true premises.
• A deductive argument with (at least) one untrue
premise, valid or invalid, is unsound.
30. INDUCTIVE STRENGTH
• A ‘good’ deductive argument is valid.
• A ‘good’ inductive argument is strong.
• An inductive argument is strong if the
conclusion follows probably from the premises.
All recent US presidents have
been college graduates.
It is likely that the next US
president will be a college
graduate.
31. WEAKNESS
• An argument that is not strong is weak.
Most US presidents have been men. It is likely that the
next US president will be a woman.
• In a weak inductive argument, the conclusion does
not follow probably from the premises.
I dream about monsters. You dream about monsters.
Therefore everybody probably dreams about
monsters.
32. INDUCTIVE PROBABILITY
• The premises and conclusion do not have to be True –
The question is:
If the premises were True, would the conclusion
follow?
• Deductive arguments are either 100% valid or 100%
invalid.
• Inductive arguments can be somewhat strong, strong,
very strong, depending on the degree of support the
premises provide for the conclusion.
According the National Weather Service, there is a 60% -
70% - 90% chance of rain today.
It is likely that it will rain today.
33. INDUCTIVE ARGUMENTS
• A valid deductive argument with True Premises is sound.
• A strong inductive argument with True Premises is cogent.
• An inductive argument that is either weak or has at least one
false premise is uncogent.
No US president has been a skateboarding champion.
Therefore the next US president will probably not be a
skateboarding champion. (Cogent)
All previous US presidents have been rocket scientists.
Therefore the next US president will probably be a woman.
(Uncogent)
All previous U.S. Presidents have been Democrats. Therefore
the next U.S. President will be a Democrat. (Uncogent)
