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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.
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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 menbreath? 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
