SYLLOGISTIC
REASONING
PART 2
Properties and Rules
SYLLOGISTIC
REASONING
The 4 types of quantifiers
The 4 types of causes
The proof by the effects
The rules of syllogism
P
R
O
P
E
R
T
I
E
S
The 4 types of quantifiers
1. Universal affirmative:
NO S is P
2. Universal negative:
3. Particular affirmative:
4. Particular negative:
ALL S are P
SOME S are P
SOME S are NOT P
P
The 4 types of causes
R
O 1. Material cause:
P Because S is made of / has M
E
Why can men breathe?
R
Because everything with lungs can breathe
T
And because all men have lungs
I
Thus, all men can breathe
E
S
P
The 4 types of causes
R
O 2. Efficient cause:
P Because S is effected by / effects M
E
Why can men breathe?
R
T Because everything that inhales & exhales can breathe
I And because all men can inhale & exhale
Thus, all men can breathe
E
S
P
The 4 types of causes
R
O 3. Formal cause:
P Because S is a M
E
Why can men breathe?
R
Because all mammals can breathe
T
And because all men are mammals
I
Thus, all men can breathe
E
S
P
The 4 types of causes
R
O 4. Final cause:
P Because S is for M
E
Why can men breathe?
R
T Because all that must live on earth can breathe
I And because all men are for life on earth
Thus, all men can breathe
E
S
P
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P
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The 4 types of causes
Some Practice
Why can humans be religious?
1. Proof by the material cause:
Because all spiritual souls can be religious
2. Proof by the efficient cause:
Because all that God attracts can be religious
3. Proof by the formal cause:
Because all that is in God’s image can be religious
4. Proof by the final cause:
Because all that is for God can be religious
P
R
O
P
E
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S
The proof by the effects
Because the effect of S is M
Why can men breathe?
Because what rejects water & CO2 can breathe
And because all men reject water & CO2
Thus, all men can breathe
R
U
L
E
S
# 1: The BARBARA formula
. 2 premises
Major: M is P – Minor: S is M
. 1 conclusion
S is P
. 3 terms twice
S twice subject (minor & conclusion)
M once subject of the major and once
predicate of the minor
P twice predicate (major & conclusion)
… in good order
M is P ► S is M ► S is P
R
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S
# 2: The quantifiers
No valid conclusion with 2 negative premises
Because no human is an angel
And because no seraphim is human
Thus, no seraphim is an angel
R
U
L
E
S
# 2: The quantifiers
. No valid conclusion with 2 negative premises
. No valid conclusion with 2 particular premises
Because some Americans are saints
And because some humans are American
Thus, some humans are saints
R
U
L
E
S
# 2: The quantifiers
. No valid conclusion with 2 negative premises
. No valid conclusion with 2 particular premises
. 1 negative premise = a negative conclusion
Because no human is from the moon
And because all saints are human
Thus, no saints are from the moon
R
U
L
E
S
# 2: The quantifiers
. No valid conclusion with 2 negative premises
. No valid conclusion with 2 particular premises
. 1 negative premise = a negative conclusion
. 1 particular premise = a particular conclusion
Because all humans are mammals
And because some 2 legged creatures are human
Thus, some 2 legged creatures are mammals
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# 3: Validity & Truth
A valid syllogism can be false if a premise is false
Because all saints are humans
And because all angels are saints
Thus, all angels are humans
VALID
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# 3: Validity & Truth
. A valid syllogism can be false if a premise is false
. A true conclusion can follow an invalid syllogism
Because all saints are humans
And because some saints are Christians
Thus, all Christians are humans
TRUE