SYL L OGIS TIC REASONING

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SYL L OGIS TIC REASONING. PART 2 Properties and Rules . SYL L OGIS TIC REASONING. The 4 types of quantifiers The 4 types of causes The proof by the effects The rules of syllogism . The 4 types of quantifiers. P R O P E R T I E S. 1. Universal affirmative: ALL S are P.

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### SYLLOGISTICREASONING

PART 2

Properties and Rules

### SYLLOGISTICREASONING

The 4 types of quantifiers

The 4 types of causes

The proof by the effects

The rules of syllogism

The 4 types of quantifiers

PROPERTIES

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 P

The 4 types of causes

PROPERTIES

Material cause:

Because S is made of M

Why can menbreathe?

Because everything with lungs can breathe

And because all men have lungs

Thus, all men can breathe

The 4 types of causes

PROPERTIES

2. Efficient cause:

Because S is moved by M

Why can menbreathe?

Because everything that inhales & exhales can breathe

And because all men can inhale & exhale

Thus, all men can breathe

The 4 types of causes

PROPERTIES

3. Formal cause:

Because S is an M

Why can menbreathe?

Because all mammals can breathe

And because all men are mammals

Thus, all men can breathe

The 4 types of causes

PROPERTIES

4. Final cause:

Because S is for M

Why can menbreathe?

Because all that must live on earth can breathe

And because all men are for life on earth

Thus, all men can breathe

The 4 types of causes

Some Practice

PROPERTIES

Why can humansbereligious?

1. Proof by the materialcause:

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

The proof by the effects

PROPERTIES

Because the effect of S is M

Why can menbreathe?

Because what rejects water & CO2 can breathe

And because all menrejects water & CO2

Thus, all men can breathe

RULES

# 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 ► Sis M ► Sis P

RULES

# 2: The quantifiers

No valid conclusion with 2 negativepremises

Because nohuman is an angel

And because noseraphim ishuman

Thus, no seraphim is an angel

INVALID

RULES

# 2: The quantifiers

. No valid conclusion with 2 negative premises

. No valid conclusion with 2 particular premises

Because someAmericans are saints

And because somehumans are American

Thus, some humans are saints

INVALID

RULES

# 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 allsaints are human

Thus, no saints are from the moon

RULES

# 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 some rational creatures are happy

And because allhumans are rational creatures

Thus, some humans are happy

RULES

# 3: Validity & Truth

A valid syllogism can be false if a premise is false

Because allsaints arehumans

And because all angels aresaints

VALID

Thus, all angels are humans

FALSE

RULES

# 3: Validity & Truth

. A valid syllogism can be false if a premise is false

. A true conclusion can follow an invalid syllogism

Because allsaints arehumans

And because some saints areChristians

Thus, all Christians are humans

INVALID

TRUE