Fun with Deductive Reasoning What is a syllogism A syllogism is a deductive argument comprising three categorical propositions a major premise a minor premise and the conclusion Categorical propositions have four standard forms ID: 418121
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Slide1
Syllogisms
Fun with Deductive ReasoningSlide2Slide3
What is a syllogism?
A
syllogism is a deductive argument comprising three categorical propositions: a major premise, a minor premise and the conclusion. Categorical propositions have four standard forms:
A = All S are P
E = No S are P
I = Some S are P
O = Some S are not PSlide4
In the mood
The
mood
of a syllogism is defined by which of the forms appear and where. So, for
example:
All
M are
P
Some
S are
M
Therefore
, All S are P
has
the mood: AIA.Slide5
Syllogism overview
A categorical syllogism contains
only
three categorical terms: a major term, minor term and middle term
.
The
major term
appears as the predicate in the conclusion, and only once in the major premise (i.e., the first premise).
The
minor term
appears as the subject in the conclusion, and only once in the minor premise (
i.e
,. the second premise).
The
middle term
appears once in the major premise, once in the minor premise, and once in the conclusion.Slide6
Distribution of terms
A term is said to be distributed when all members of the class denoted by the term are affected by a proposition.
All S are P
S is distributed; P is not distributed
Example “All cows are mammals” tells us something about cows but nothing about mammalsSlide7
Syllogism Examples
Correct Syllogism:
Major Premise: All mammals are warm-blooded animals.
Minor Premise: No lizards are warm-blooded animals.
Conclusion: Therefore, no lizards are mammals.
Correct Syllogism:
Major Premise: All humans are mortal.
Minor Premise: All Greeks are human.
Conclusion: Therefore, all Greeks are mortal.
Descartes’ Syllogism (correct)
Major Premise: Existence has
to
be
true if one is thinking.
Minor Premise: I am thinking.
Conclusion: I think, therefore, I am.Slide8
Syllogisms can be
Valid
or
Invalid
(reasoning in incorrect order)
AND
True
or
False
(reasoning from a faulty major premise)
If a syllogism is both true and valid then it is said to be
soundSlide9
Examples of Faulty Syllogisms
FALSE Syllogism
(not
TRUE
-- false major premise)
Major Premise: Blondes have more fun
Minor Premise: Mary is blonde; Jane is brunette
Conclusion: Mary has more fun than Jane.
INVALID Syllogism
(not
VALID
– order of reasoning is incorrect):
Major Premise: All dogs eat meat
Minor Premise: Bob (a human) eats meat
Conclusion: Bob is a dog.Slide10
Corrections
Syllogism One:
The first faulty syllogism proceeds from a FALSE major premise and therefore can be thrown out entirely.
Syllogism Two:
Major Premise: All dogs eat meat
Minor Premise: Rover is a dog.
Conclusion: Therefore, Rover eats meat.Slide11
Valid or invalid? True or False?
Example One:
Major Premise: When it snows the streets get wet.
Minor Premise: The streets are getting wet.
Conclusion: Therefore, it is snowing.
Example Two:
Major Premise: If you buy a Ferrari, you will instantly be popular.
Minor Premise: Ed just bought a Ferrari.
Conclusion: Ed will achieve instant popularity.
Example Three:
Major Premise: When the battery is dead, the car will not start.
Minor Premise: The car will not start.
Conclusion: Therefore, the battery is dead.Slide12
Corrections: Valid and True
Example One:
Major Premise: When it snows, the streets get wet.
Minor Premise: It is snowing.
Conclusion: Therefore, the streets are getting wet.
Example Two:
Example Two proceeds from the beginning from a FALSE major premise (Ferraris give instant popularity) and therefore can be thrown out entirely.
Example Three:
Major Premise: When the battery is dead, the car will not start.
Minor Premise: The battery is dead.
Conclusion: Therefore, the car will not start.Slide13
Ty
pes
of
valid
syllogisms
Modus
Ponens
(Affirming the antecedent)
Modus
Tollens
(Denying the consequent)
Hypothetical
Syllogism
(Chain argument)
Disjunctive SyllogismSlide14
Modus Ponens
If A then B
A
Therefore, B
Examples:
If it’s spring, then the birds are chirping
It’s spring.
The birds are chirping.
If a world government doesn’t evolve soon, then wars will continue to occur
A world government isn’t going to evolve soon.
Wars will continue to occurSlide15
Modus Tollens
If A then B
Not B
Not A
Example:
If it’s spring then the birds are chirping
The birds aren’t chirping
Therefore, it isn’t spring.Slide16
Hypothetical Syllogism
If A then B
If B then C
If A then C
Example:
If we successfully develop nuclear fusion power, then power will become plentiful and cheap.
If power becomes cheap and plentiful, then the economy will flourish.
If we successfully develop nuclear fusion power, then the economy will flourish.Slide17
Disjunctive Syllogism
A or B
Not A
B
Example:
Either Romney won in 2012 or Obama did.
Romney didn’t win.
Obama did win.Slide18Slide19
Valid or invalid?
Download
Socrative
app or go to
Socrative.com
Room 769815Slide20
Syllogism no-no’s
Syllogisms need to follow 6 rules in order to be valid. If they violate one of these rules then that syllogism commits a formal fallacy and is invalidSlide21
Rule 1
There needs to be three categorical terms and those terms cannot vary in how they are used
A
fallacy of equivocation
occurs when a term is used in a different way within the course of an argument. So, for example:
The priest told me I should have faith.
I have faith that my son will do well in school this year.
Therefore, the priest should be happy with me.
“
faith
”
is being used in two different
ways in this argumentSlide22
Rule 2
The middle term of a valid syllogism is distributed in at least one of the premises. The
fallacy of the undistributed middle
occurs when this doesn't happen. For instance, the middle term (furry animals) in this syllogism
All dogs are furry animals
Some
cats are furry animals
Therefore
,some
dogs are cats
isn't distributed, and the argument is clearly fallacious
Slide23
Rule 3
If a term is distributed in the conclusion it must be distributed in at least one of the premises
All Protestants are Christians
No Catholics are Protestants
Therefore, no Catholics are Christians
doesn't work, because the term "Christians" is distributed in the conclusion, but not in the (major) premise.Slide24
Rule 3
The
fallacy of illicit major
occurs (as above) when the major term is distributed in the conclusion, but not in the (major) premise.
The
fallacy of illicit minor
occurs when the minor term is distributed in the conclusion, but not in the (minor) premise
Slide25Slide26
Rule 4
A valid syllogism can't have two negative
premises
The
fallacy of exclusive premises
occurs when a syllogism has two premises that are negative.
A
negative premise is either an "E" statement ("No S are P") or an "O" statement ("Some S are not P"), and if you've got two of them in your premises, your syllogism isn't valid.Slide27
Rule 5
The conclusion of a syllogism must be negative, if either premise is negative
The
fallacy of
drawing an affirmative conclusion from a negative premise
occurs if this rule is violated. Similarly, if a conclusion is negative, then one of the premises must be negative (which rule, if broken, constitutes the fallacy of
drawing a negative conclusion from an affirmative premise
).Slide28
Rule 6
No particular conclusion can be drawn from two universal premises
This is arguably the most counterintuitive of the rules for validity. An
existential fallacy
occurs whenever a particular conclusion appears with two universal premises (for example, All M are P, All S are M, Therefore, some S are P).