FORM/STRUCTURE
These are included in a Logical Proposition.
Chap 5
Subject, predicate, quantifier (all, no, some), compliment (class of things added to predicate - All taxpayers are poor people.), copula
The First Figure moods.
Chap 2
BARBARA, CELARENT, DARII, FERIO
Construct syllogism: BRAMANTIP where Brilliant (M), Philosophers (P), Smart (S)
All philosophers are brilliant.
All brilliant people are smart.
Some smart people are philosophers.
This is how you check validity.
Chap 2
Step #1: Determine the figure
Step #2: Determine the mood
Step #3: Determine whether the mood is included in the mnemonic verse.
Terminological Rules
There must be 3 terms only.
The middle term must not occur in the conclusion.
This is the form of a Goclenian Sorite.
Chap 11
All D is E
All C is D
All B is C
All A is B
Therefore, all A is E
These are valid and invalid moods in a conditional syllogism.
Chap 7
#1 Modus Ponens (Affirming antecedent), #2 Modus Tollens (Denying consequent), #3 Fallacy of Affirming the Consequent, #4 Fallacy of Denying the Antecedent (First two valid, 2nd two invalid)
Construct syllogism: Destructive Conditional Syllogism where God loves the world (P), everyone will be saved (Q)
Chap 7
If P, then Q (If God loves the world, then everyone will be saved.)
Not Q (Everyone will not be saved.)
Therefore, not P. (Therefore, God does not love the world.)
These are the forms of a Conjunctive Syllogism
Chap 9 - Page 62 - must know each form
Valid - Ponendo Tollens:
Invalid - Tollendo Ponens
Quantitative Rules
If the term is distributed in the conclusion, it must also be distributed in the premises.
The middle term has to be distributed at least once.
Not both P and Q
P
Therefore, not Q
Chap 9
Conjunctive Syllogism: Affirming the 1st Conjunct (Valid - Ponendo Pollens)
Construct syllogism: CESARE where peace (M), bitter man (P), saint (S)
No bitter man has peace.
All saints have peace.
Therefore, no saint is a bitter man.
Construct syllogism: Disjunctive Syllogism where faith (P) and works (Q); mood + validity
Chap 8
Either P or Q (You are saved either by faith or by works.)
P (We are saved by faith.)
Therefore, not Q (Therefore, we are not saved by works.)
How to test a Polysyllogism
Chap 10
All the simple syllogisms that make up the complex polysyllogism must be valid to be valid.
Dilemma
Rule #1: Major Premise must be true (Consequents (if) must follow antecedents (then)).
Rule #2: Minor Premise must have no third possibility.
Rule #3: Conclusion can be no other inferred from the premises.
If P, then Q; and if P, then R
Either not Q or not R
Therefore, not P
Chap 13
Simple Destructive Dilemma
Construct syllogism: CAMESTRES -> CELARENT where Man (M), Roman (P), god (S)
All Romans are men. No god is a man. Therefore, no god is a Roman. -->. No man is a god. All Romans are men. Therefore, no Roman is a god. (Chapt 3)
Construct syllogism: 1st Order [Destructive] Epicheirema w/Extrapolation where cats (M), exasperating (P), independent (R), worth having (S)
Chap 12
All cats are exasperating since they are independent. [All M is P, since (because) r]
No exasperating things are worth having. [All S is M]
Therefore, no cat is worth having. [Therefore, S is P]
EXTRAPOLATED:
Proof: All independent things are exasperating. All cats are independent. Therefore, all cats are exasperating.
How to test Sorties
Chap 10
Step #1: Put the sorites in standard form.
Step #2: Provide the missing conclusions.
Step #3: Test each resulting component syllogism for validity.
Sorites
Rule #1: Only the premises which contains the minor term may be particular.
Rule #2: Only the premises which contains the major term may be negative.
This is the form of a Polysyllogism.
Chap 10
All A is B
All C is A
Therefore, all C is B
All D is C
Therefore, all D is B
Construct syllogism: DARAPTI -> DARII where Saints (M), Holy (P), Wise (S)
All saints are holy. All saints are wise. Therefore, some wise men are holy. -> All saints are holy. Some wise men are saints. Therefore, some wise men are holy.
What kind of dilemma, what mood; and determine validity and soundness:
If God is all-powerful, then He can do logically impossible things, and if God is all-knowing, then it is reasonable to think that He can prevent evil and suffering.
Either God cannot do logically impossible things or it is not reasonable to think that He can prevent evil and suffering.
Either God is not all-powerful or God is not all-knowing.
Chap 13
Complex Destructive
Modus Tollens
Valid
Unsound - violates all 3 rules - counter: Page 166 - FINAL TEST
If the United States is spending money that it doesn't have, then economic growth will not happen. The US is not spending money that it doesn't have, so therefore, economic growth will happen.
Chap 7 (quiz)
Invalid - denying the Antecedent (If the US is spending money that it doesn't have...)
Translating Sentences
Rules A - I - page 26 in book