syllogistic reasoning part 2 properties and rules part 2 properties and rules
DESCRIPTION
PROPERTIESPROPERTIES PROPERTIESPROPERTIES The 4 types of quantifiers 1. Universal affirmative: ALL S are P 2. Universal negative: NO S is P 3. Particular affirmative: SOME S are P 4. Particular negative: SOME S are NOT PTRANSCRIPT
SYLLOGISTICREASONING
PART 2Properties and Rules
SYLLOGISTICREASONINGThe 4 types of quantifiers
The 4 types of causesThe proof by the effectsThe rules of syllogism
PROPERTIES
The 4 types of quantifiers
1. Universal affirmative: ALL S are P
2. Universal negative: NO S is P3. Particular affirmative: SOME S are P
4. Particular negative: SOME S are NOT P
PROPERTIES
The 4 types of causes1. Material cause:
Because S is made of M
Why can men breathe?
Because everything with lungs can breatheAnd because all men have lungsThus, all men can breathe
PROPERTIES
The 4 types of causes2. Efficient cause:
Because S is moved by M
Why can men breath?
Because everything that inhales & exhales can breatheAnd because all men can inhale & exhale Thus, all men can breathe
PROPERTIES
The 4 types of causes3. Formal cause:
Because S is an M
Why can men breathe?
Because all mammals can breathe
And because all men are mammalsThus, all men can breathe
PROPERTIES
The 4 types of causes4. Final cause:
Because S is for M
Why can men breathe?
Because all that must live on earth can breatheAnd because all men are for life on earth
Thus, all men can breathe
PROPERTIES
The 4 types of causesSome Practice
Why can humans be religious?
Because all spiritual souls can be religious1. Proof by the material cause:
Because all that God attracts can be religious2. Proof by the efficient cause:
Because all that is in God’s image can be religious3. Proof by the formal cause:
Because all that is for God can be religious4. Proof by the final cause:
PROPERTIES
The proof by the effects
Because the effect of S is M
Why can men breathe?
Because what rejects water & CO2 can breatheAnd because all men rejects water & CO2
Thus, all men can breathe
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2 premisesMajor: M is P – Minor: S is M
# 1: The BARBARA formula
1 conclusionS is P 3 terms twiceS twice subject (minor & conclusion)
… in good order M is P ► S is M ► S is P
M once subject of the major and once predicate of the minorP twice predicate (major & conclusion)
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No valid conclusion with 2 negative premises
# 2: The quantifiers
Because no human is an angel
And because no seraphim is humanThus, no seraphim is an angel
INVALID
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No valid conclusion with 2 negative premises
# 2: The quantifiers
Because some Americans are saintsAnd because some humans are AmericanThus, some humans are saints
No valid conclusion with 2 particular premises
INVALID
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No valid conclusion with 2 negative premises
# 2: The quantifiers
Because no human is from the moon
And because all saints are human
Thus, no saints are from the moon
No valid conclusion with 2 particular premises 1 negative premise = a negative conclusion
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No valid conclusion with 2 negative premises
# 2: The quantifiers
Because some rational creatures are happy
And because all humans are rational creatures
Thus, some humans are happy
No valid conclusion with 2 particular premises 1 negative premise = a negative conclusion
1 particular premise = a particular conclusion
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A valid syllogism can be false if a premise is false
# 3: Validity & Truth
Because all saints are humans And because all angels are saintsThus, all angels are humans
FALSE
VALID
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A valid syllogism can be false if a premise is false
# 3: Validity & Truth
Because all saints are humans
And because some saints are Christians Thus, all Christians are humans
INVALIDTRUE
A true conclusion can follow an invalid syllogism